From 586e4a7d2b4d9a628e7379e39a153888a31dd7eb Mon Sep 17 00:00:00 2001 From: Paul Riseborough Date: Thu, 2 Apr 2015 07:54:15 +1100 Subject: [PATCH] AP_NavEKF: Add Matlab derivations and simulations behind small EKF --- .../AttErrVecMathExample/AlignHeading.m | 47 ++ .../Models/AttErrVecMathExample/AlignTilt.m | 20 + .../AttErrVecMathExample/FuseMagnetometer.m | 91 +++ .../AttErrVecMathExample/FuseVelocity.m | 72 +++ .../AttErrVecMathExample/GenerateEquations.m | 161 +++++ .../Models/AttErrVecMathExample/PlotData.m | 28 + .../AttErrVecMathExample/PredictCovariance.m | 61 ++ .../AttErrVecMathExample/PredictStates.m | 70 +++ .../Models/AttErrVecMathExample/RunRealData.m | 86 +++ .../AttErrVecMathExample/RunSyntheticData.m | 78 +++ .../Models/AttErrVecMathExample/calcF.m | 65 ++ .../Models/AttErrVecMathExample/calcH_MAG.m | 38 ++ .../Models/AttErrVecMathExample/calcQ.m | 34 ++ .../with initial alignment.fig | Bin 0 -> 2127711 bytes .../AP_NavEKF/Models/Common/ConvertToC.m | 220 +++++++ .../AP_NavEKF/Models/Common/ConvertToM.m | 46 ++ libraries/AP_NavEKF/Models/Common/EulToQuat.m | 23 + libraries/AP_NavEKF/Models/Common/NormQuat.m | 5 + .../AP_NavEKF/Models/Common/OptimiseAlgebra.m | 29 + libraries/AP_NavEKF/Models/Common/Quat2Tbn.m | 14 + .../AP_NavEKF/Models/Common/QuatDivide.m | 16 + libraries/AP_NavEKF/Models/Common/QuatMult.m | 5 + libraries/AP_NavEKF/Models/Common/QuatToEul.m | 9 + libraries/AP_NavEKF/Models/Common/RotToQuat.m | 10 + .../GimbalEstimatorExample/AlignHeading.m | 51 ++ .../Models/GimbalEstimatorExample/AlignTilt.m | 20 + .../Models/GimbalEstimatorExample/C_code.txt | 347 +++++++++++ .../GimbalEstimatorExample/FixAutoGenCCode.m | 94 +++ .../GimbalEstimatorExample/FuseMagnetometer.m | 91 +++ .../GimbalEstimatorExample/FuseVelocity.m | 72 +++ .../GenerateEquations.m | 241 ++++++++ .../Models/GimbalEstimatorExample/PlotData.m | 65 ++ .../PredictCovariance.m | 61 ++ .../PredictCovarianceOptimised.m | 404 +++++++++++++ .../GimbalEstimatorExample/PredictStates.m | 55 ++ .../GimbalEstimatorExample/RunSimulation.m | 203 +++++++ .../Models/GimbalEstimatorExample/calcEKF.m | 96 +++ .../Models/GimbalEstimatorExample/calcF.c | 0 .../Models/GimbalEstimatorExample/calcF.cpp | 0 .../Models/GimbalEstimatorExample/calcF.m | 68 +++ .../Models/GimbalEstimatorExample/calcH_MAG.c | 75 +++ .../GimbalEstimatorExample/calcH_MAG.cpp | 75 +++ .../Models/GimbalEstimatorExample/calcH_MAG.m | 80 +++ .../GimbalEstimatorExample/calcMagAng.m | 18 + .../Models/GimbalEstimatorExample/calcP.c | 556 ++++++++++++++++++ .../Models/GimbalEstimatorExample/calcP.cpp | 556 ++++++++++++++++++ .../Models/GimbalEstimatorExample/calcP.m | 420 +++++++++++++ .../Models/GimbalEstimatorExample/calcP.txt | 152 +++++ .../Models/GimbalEstimatorExample/calcQ.c | 38 ++ .../Models/GimbalEstimatorExample/calcQ.cpp | 38 ++ .../Models/GimbalEstimatorExample/calcQ.m | 34 ++ .../Models/GimbalEstimatorExample/calcSF.c | 51 ++ .../Models/GimbalEstimatorExample/calcSP.c | 40 ++ .../Models/GimbalEstimatorExample/calcTmn.c | 46 ++ .../Models/GimbalEstimatorExample/calcTmn.m | 45 ++ .../Models/GimbalEstimatorExample/calcTms.c | 1 + .../Models/GimbalEstimatorExample/calcTms.m | 14 + .../QuaternionMathExample/FuseMagnetometer.m | 56 ++ .../QuaternionMathExample/FuseVelocity.m | 51 ++ .../QuaternionMathExample/GenerateEquations.m | 113 ++++ .../Models/QuaternionMathExample/PlotData.m | 21 + .../QuaternionMathExample/PredictCovariance.m | 60 ++ .../QuaternionMathExample/PredictStates.m | 84 +++ .../QuaternionMathExample/RunRealData.m | 71 +++ .../Models/QuaternionMathExample/calcF.m | 36 ++ .../Models/QuaternionMathExample/calcG.m | 18 + .../Models/QuaternionMathExample/calcH_MAG.m | 52 ++ .../Models/QuaternionMathExample/calcQ.m | 45 ++ libraries/AP_NavEKF/Models/ReadMe.txt | 7 + .../AP_NavEKF/Models/testData/fltTest.mat | Bin 0 -> 1359364 bytes .../AP_NavEKF/Models/testData/gndTest.mat | Bin 0 -> 91540 bytes 71 files changed, 5949 insertions(+) create mode 100644 libraries/AP_NavEKF/Models/AttErrVecMathExample/AlignHeading.m create mode 100644 libraries/AP_NavEKF/Models/AttErrVecMathExample/AlignTilt.m create mode 100644 libraries/AP_NavEKF/Models/AttErrVecMathExample/FuseMagnetometer.m create mode 100644 libraries/AP_NavEKF/Models/AttErrVecMathExample/FuseVelocity.m create mode 100644 libraries/AP_NavEKF/Models/AttErrVecMathExample/GenerateEquations.m create mode 100644 libraries/AP_NavEKF/Models/AttErrVecMathExample/PlotData.m create mode 100644 libraries/AP_NavEKF/Models/AttErrVecMathExample/PredictCovariance.m create mode 100644 libraries/AP_NavEKF/Models/AttErrVecMathExample/PredictStates.m create mode 100644 libraries/AP_NavEKF/Models/AttErrVecMathExample/RunRealData.m create mode 100644 libraries/AP_NavEKF/Models/AttErrVecMathExample/RunSyntheticData.m create mode 100644 libraries/AP_NavEKF/Models/AttErrVecMathExample/calcF.m create mode 100644 libraries/AP_NavEKF/Models/AttErrVecMathExample/calcH_MAG.m create mode 100644 libraries/AP_NavEKF/Models/AttErrVecMathExample/calcQ.m create mode 100644 libraries/AP_NavEKF/Models/AttErrVecMathExample/with initial alignment.fig create mode 100644 libraries/AP_NavEKF/Models/Common/ConvertToC.m create mode 100644 libraries/AP_NavEKF/Models/Common/ConvertToM.m create mode 100644 libraries/AP_NavEKF/Models/Common/EulToQuat.m create mode 100644 libraries/AP_NavEKF/Models/Common/NormQuat.m create mode 100644 libraries/AP_NavEKF/Models/Common/OptimiseAlgebra.m create mode 100644 libraries/AP_NavEKF/Models/Common/Quat2Tbn.m create mode 100644 libraries/AP_NavEKF/Models/Common/QuatDivide.m create mode 100644 libraries/AP_NavEKF/Models/Common/QuatMult.m create mode 100644 libraries/AP_NavEKF/Models/Common/QuatToEul.m create mode 100644 libraries/AP_NavEKF/Models/Common/RotToQuat.m create mode 100644 libraries/AP_NavEKF/Models/GimbalEstimatorExample/AlignHeading.m create mode 100644 libraries/AP_NavEKF/Models/GimbalEstimatorExample/AlignTilt.m create mode 100644 libraries/AP_NavEKF/Models/GimbalEstimatorExample/C_code.txt create mode 100644 libraries/AP_NavEKF/Models/GimbalEstimatorExample/FixAutoGenCCode.m create mode 100644 libraries/AP_NavEKF/Models/GimbalEstimatorExample/FuseMagnetometer.m create mode 100644 libraries/AP_NavEKF/Models/GimbalEstimatorExample/FuseVelocity.m create mode 100644 libraries/AP_NavEKF/Models/GimbalEstimatorExample/GenerateEquations.m create mode 100644 libraries/AP_NavEKF/Models/GimbalEstimatorExample/PlotData.m create mode 100644 libraries/AP_NavEKF/Models/GimbalEstimatorExample/PredictCovariance.m create mode 100644 libraries/AP_NavEKF/Models/GimbalEstimatorExample/PredictCovarianceOptimised.m create mode 100644 libraries/AP_NavEKF/Models/GimbalEstimatorExample/PredictStates.m create mode 100644 libraries/AP_NavEKF/Models/GimbalEstimatorExample/RunSimulation.m create mode 100644 libraries/AP_NavEKF/Models/GimbalEstimatorExample/calcEKF.m create mode 100644 libraries/AP_NavEKF/Models/GimbalEstimatorExample/calcF.c create mode 100644 libraries/AP_NavEKF/Models/GimbalEstimatorExample/calcF.cpp create mode 100644 libraries/AP_NavEKF/Models/GimbalEstimatorExample/calcF.m create mode 100644 libraries/AP_NavEKF/Models/GimbalEstimatorExample/calcH_MAG.c create mode 100644 libraries/AP_NavEKF/Models/GimbalEstimatorExample/calcH_MAG.cpp create mode 100644 libraries/AP_NavEKF/Models/GimbalEstimatorExample/calcH_MAG.m create mode 100644 libraries/AP_NavEKF/Models/GimbalEstimatorExample/calcMagAng.m create mode 100644 libraries/AP_NavEKF/Models/GimbalEstimatorExample/calcP.c create mode 100644 libraries/AP_NavEKF/Models/GimbalEstimatorExample/calcP.cpp create mode 100644 libraries/AP_NavEKF/Models/GimbalEstimatorExample/calcP.m create mode 100644 libraries/AP_NavEKF/Models/GimbalEstimatorExample/calcP.txt create mode 100644 libraries/AP_NavEKF/Models/GimbalEstimatorExample/calcQ.c create mode 100644 libraries/AP_NavEKF/Models/GimbalEstimatorExample/calcQ.cpp create mode 100644 libraries/AP_NavEKF/Models/GimbalEstimatorExample/calcQ.m create mode 100644 libraries/AP_NavEKF/Models/GimbalEstimatorExample/calcSF.c create mode 100644 libraries/AP_NavEKF/Models/GimbalEstimatorExample/calcSP.c create mode 100644 libraries/AP_NavEKF/Models/GimbalEstimatorExample/calcTmn.c create mode 100644 libraries/AP_NavEKF/Models/GimbalEstimatorExample/calcTmn.m create mode 100644 libraries/AP_NavEKF/Models/GimbalEstimatorExample/calcTms.c create mode 100644 libraries/AP_NavEKF/Models/GimbalEstimatorExample/calcTms.m create mode 100644 libraries/AP_NavEKF/Models/QuaternionMathExample/FuseMagnetometer.m create mode 100644 libraries/AP_NavEKF/Models/QuaternionMathExample/FuseVelocity.m create mode 100644 libraries/AP_NavEKF/Models/QuaternionMathExample/GenerateEquations.m create mode 100644 libraries/AP_NavEKF/Models/QuaternionMathExample/PlotData.m create mode 100644 libraries/AP_NavEKF/Models/QuaternionMathExample/PredictCovariance.m create mode 100644 libraries/AP_NavEKF/Models/QuaternionMathExample/PredictStates.m create mode 100644 libraries/AP_NavEKF/Models/QuaternionMathExample/RunRealData.m create mode 100644 libraries/AP_NavEKF/Models/QuaternionMathExample/calcF.m create mode 100644 libraries/AP_NavEKF/Models/QuaternionMathExample/calcG.m create mode 100644 libraries/AP_NavEKF/Models/QuaternionMathExample/calcH_MAG.m create mode 100644 libraries/AP_NavEKF/Models/QuaternionMathExample/calcQ.m create mode 100644 libraries/AP_NavEKF/Models/ReadMe.txt create mode 100644 libraries/AP_NavEKF/Models/testData/fltTest.mat create mode 100644 libraries/AP_NavEKF/Models/testData/gndTest.mat diff --git a/libraries/AP_NavEKF/Models/AttErrVecMathExample/AlignHeading.m b/libraries/AP_NavEKF/Models/AttErrVecMathExample/AlignHeading.m new file mode 100644 index 0000000000..00f636cee6 --- /dev/null +++ b/libraries/AP_NavEKF/Models/AttErrVecMathExample/AlignHeading.m @@ -0,0 +1,47 @@ +function quat = AlignHeading( ... + quat, ... % quaternion state vector + magMea, ... % body frame magnetic flux measurements + declination) % Estimated magnetic field delination at current location + +% Calculate the predicted magnetic declination +Tbn = Quat2Tbn(quat); +magMeasNED = Tbn*magMea; +predDec = atan2(magMeasNED(2),magMeasNED(1)); + +% Calculate the measurement innovation +innovation = predDec - declination; + +if (innovation > pi) + innovation = innovation - 2*pi; +elseif (innovation < -pi) + innovation = innovation + 2*pi; +end + +% form the NED rotation vector +deltaRotNED = -[0;0;innovation]; + +% rotate into body axes +% Calculate the body to nav cosine matrix +Tbn = Quat2Tbn(quat); +deltaRotBody = transpose(Tbn)*deltaRotNED; + +% Convert the error rotation vector to its equivalent quaternion +% error = truth - estimate +rotationMag = abs(innovation); +if rotationMag<1e-6 + deltaQuat = single([1;0;0;0]); +else + deltaQuat = [cos(0.5*rotationMag); [deltaRotBody(1);deltaRotBody(2);deltaRotBody(3)]/rotationMag*sin(0.5*rotationMag)]; +end + +% Update the quaternion states by rotating from the previous attitude through +% the delta angle rotation quaternion +quat = [quat(1)*deltaQuat(1)-transpose(quat(2:4))*deltaQuat(2:4); quat(1)*deltaQuat(2:4) + deltaQuat(1)*quat(2:4) + cross(quat(2:4),deltaQuat(2:4))]; + +% normalise the updated quaternion states +quatMag = sqrt(quat(1)^2 + quat(2)^2 + quat(3)^2 + quat(4)^2); +if (quatMag > 1e-12) + quat = quat / quatMag; +end + +end \ No newline at end of file diff --git a/libraries/AP_NavEKF/Models/AttErrVecMathExample/AlignTilt.m b/libraries/AP_NavEKF/Models/AttErrVecMathExample/AlignTilt.m new file mode 100644 index 0000000000..fed5afc060 --- /dev/null +++ b/libraries/AP_NavEKF/Models/AttErrVecMathExample/AlignTilt.m @@ -0,0 +1,20 @@ +function quat = AlignTilt( ... + quat, ... % quaternion state vector + initAccel) % initial accelerometer vector +% check length +lengthAccel = sqrt(dot([initAccel(1);initAccel(2);initAccel(3)],[initAccel(1);initAccel(2);initAccel(3)])); +% if length is > 0.7g and < 1.4g initialise tilt using gravity vector +if (lengthAccel > 5 && lengthAccel < 14) + % calculate length of the tilt vector + tiltMagnitude = atan2(sqrt(dot([initAccel(1);initAccel(2)],[initAccel(1);initAccel(2)])),-initAccel(3)); + % take the unit cross product of the accel vector and the -Z vector to + % give the tilt unit vector + if (tiltMagnitude > 1e-3) + tiltUnitVec = cross([initAccel(1);initAccel(2);initAccel(3)],[0;0;-1]); + tiltUnitVec = tiltUnitVec/sqrt(dot(tiltUnitVec,tiltUnitVec)); + tiltVec = tiltMagnitude*tiltUnitVec; + quat = [cos(0.5*tiltMagnitude); tiltVec/tiltMagnitude*sin(0.5*tiltMagnitude)]; + end +end + +end \ No newline at end of file diff --git a/libraries/AP_NavEKF/Models/AttErrVecMathExample/FuseMagnetometer.m b/libraries/AP_NavEKF/Models/AttErrVecMathExample/FuseMagnetometer.m new file mode 100644 index 0000000000..90076d6826 --- /dev/null +++ b/libraries/AP_NavEKF/Models/AttErrVecMathExample/FuseMagnetometer.m @@ -0,0 +1,91 @@ +function [... + nextQuat, ... % quaternion state vector after fusion of measurements + nextStates, ... % state vector after fusion of measurements + nextP, ... % state covariance matrix after fusion of corrections + innovation, ... % Declination innovation - rad + varInnov] ... % + = FuseMagnetometer( ... + quat, ... % predicted quaternion states + states, ... % predicted states + P, ... % predicted covariance + magData, ... % body frame magnetic flux measurements + measDec, ... % magnetic field declination - azimuth angle measured from true north (rad) + Tbn) % Estimated coordinate transformation matrix from body to NED frame + +q0 = quat(1); +q1 = quat(2); +q2 = quat(3); +q3 = quat(4); + +magX = magData(1); +magY = magData(2); +magZ = magData(3); + +R_MAG = 0.1745^2; + +H = calcH_MAG(magX,magY,magZ,q0,q1,q2,q3); +varInnov = (H*P*transpose(H) + R_MAG); +Kfusion = (P*transpose(H))/varInnov; + +% Calculate the predicted magnetic declination +magMeasNED = Tbn*[magX;magY;magZ]; +predDec = atan2(magMeasNED(2),magMeasNED(1)); + +% Calculate the measurement innovation +innovation = predDec - measDec; + +if (innovation > pi) + innovation = innovation - 2*pi; +elseif (innovation < -pi) + innovation = innovation + 2*pi; +end +if (innovation > 0.5) + innovation = 0.5; +elseif (innovation < -0.5) + innovation = -0.5; +end + +% correct the state vector +states(1:3) = 0; +states = states - Kfusion * innovation; + +% the first 3 states represent the angular misalignment vector. This is +% is used to correct the estimate quaternion +% Convert the error rotation vector to its equivalent quaternion +% error = truth - estimate +rotationMag = sqrt(states(1)^2 + states(2)^2 + states(3)^2); +if rotationMag<1e-6 + deltaQuat = single([1;0;0;0]); +else + deltaQuat = [cos(0.5*rotationMag); [states(1);states(2);states(3)]/rotationMag*sin(0.5*rotationMag)]; +end + +% Update the quaternion states by rotating from the previous attitude through +% the delta angle rotation quaternion +nextQuat = [quat(1)*deltaQuat(1)-transpose(quat(2:4))*deltaQuat(2:4); quat(1)*deltaQuat(2:4) + deltaQuat(1)*quat(2:4) + cross(quat(2:4),deltaQuat(2:4))]; + +% normalise the updated quaternion states +quatMag = sqrt(nextQuat(1)^2 + nextQuat(2)^2 + nextQuat(3)^2 + nextQuat(4)^2); +if (quatMag > 1e-6) + nextQuat = nextQuat / quatMag; +end + +% correct the covariance P = P - K*H*P +P = P - Kfusion*H*P; + +% Force symmetry on the covariance matrix to prevent ill-conditioning +% of the matrix which would cause the filter to blow-up +P = 0.5*(P + transpose(P)); + +% ensure diagonals are positive +for i=1:9 + if P(i,i) < 0 + P(i,i) = 0; + end +end + +% Set default output for states and covariance +nextP = P; +nextStates = states; + +end \ No newline at end of file diff --git a/libraries/AP_NavEKF/Models/AttErrVecMathExample/FuseVelocity.m b/libraries/AP_NavEKF/Models/AttErrVecMathExample/FuseVelocity.m new file mode 100644 index 0000000000..8f051138f6 --- /dev/null +++ b/libraries/AP_NavEKF/Models/AttErrVecMathExample/FuseVelocity.m @@ -0,0 +1,72 @@ +function [... + quat, ... % quaternion state vector after fusion of measurements + states, ... % state vector after fusion of measurements + angErr, ... % angle error + P, ... % state covariance matrix after fusion of corrections + innovation,... % NED velocity innovations (m/s) + varInnov] ... % NED velocity innovation variance ((m/s)^2) + = FuseVelocity( ... + quat, ... % predicted quaternion states from the INS + states, ... % predicted states from the INS + P, ... % predicted covariance + measVel) % NED velocity measurements (m/s) + +R_OBS = 0.5^2; +innovation = zeros(1,3); +varInnov = zeros(1,3); +% Fuse measurements sequentially +angErrVec = [0;0;0]; +for obsIndex = 1:3 + stateIndex = 3 + obsIndex; + % Calculate the velocity measurement innovation + innovation(obsIndex) = states(stateIndex) - measVel(obsIndex); + + % Calculate the Kalman Gain + H = zeros(1,9); + H(1,stateIndex) = 1; + varInnov(obsIndex) = (H*P*transpose(H) + R_OBS); + K = (P*transpose(H))/varInnov(obsIndex); + + % Calculate state corrections + xk = K * innovation(obsIndex); + + % Apply the state corrections + states(1:3) = 0; + states = states - xk; + + % Store tilt error estimate for external monitoring + angErrVec = angErrVec + states(1:3); + + % the first 3 states represent the angular misalignment vector. This is + % is used to correct the estimated quaternion + % Convert the error rotation vector to its equivalent quaternion + % truth = estimate + error + rotationMag = sqrt(states(1)^2 + states(2)^2 + states(3)^2); + if rotationMag > 1e-12 + deltaQuat = [cos(0.5*rotationMag); [states(1);states(2);states(3)]/rotationMag*sin(0.5*rotationMag)]; + % Update the quaternion states by rotating from the previous attitude through + % the error quaternion + quat = QuatMult(quat,deltaQuat); + % re-normalise the quaternion + quatMag = sqrt(quat(1)^2 + quat(2)^2 + quat(3)^2 + quat(4)^2); + quat = quat / quatMag; + end + + % Update the covariance + P = P - K*H*P; + + % Force symmetry on the covariance matrix to prevent ill-conditioning + P = 0.5*(P + transpose(P)); + + % ensure diagonals are positive + for i=1:9 + if P(i,i) < 0 + P(i,i) = 0; + end + end + +end + +angErr = sqrt(dot(angErrVec,angErrVec)); + +end \ No newline at end of file diff --git a/libraries/AP_NavEKF/Models/AttErrVecMathExample/GenerateEquations.m b/libraries/AP_NavEKF/Models/AttErrVecMathExample/GenerateEquations.m new file mode 100644 index 0000000000..e07c5d7eb3 --- /dev/null +++ b/libraries/AP_NavEKF/Models/AttErrVecMathExample/GenerateEquations.m @@ -0,0 +1,161 @@ +% IMPORTANT - This script requires the Matlab symbolic toolbox + +% Author: Paul Riseborough +% Last Modified: 16 Feb 2015 + +% Derivation of a navigation EKF using a local NED earth Tangent Frame for +% the initial alignment and gyro bias estimation from a moving platform +% Based on use of a rotation vector for attitude estimation as described +% here: +% +% Mark E. Pittelkau. "Rotation Vector in Attitude Estimation", +% Journal of Guidance, Control, and Dynamics, Vol. 26, No. 6 (2003), +% pp. 855-860. +% +% The benefits for use of rotation error vector over use of a four parameter +% quaternion representation of the estiamted orientation are: +% a) Reduced computational load +% b) Improved stability +% c) The ability to recover faster from large orientation errors. This +% makes this filter particularly suitable where the initial alignment is +% uncertain + +% State vector: +% error rotation vector +% Velocity - North, East, Down (m/s) +% Delta Angle bias - X,Y,Z (rad) + +% Observations: +% NED velocity - N,E,D (m/s) +% body fixed magnetic field vector - X,Y,Z + +% Time varying parameters: +% XYZ delta angle measurements in body axes - rad +% XYZ delta velocity measurements in body axes - m/sec +% magnetic declination +clear all; + +%% define symbolic variables and constants +syms dax day daz real % IMU delta angle measurements in body axes - rad +syms dvx dvy dvz real % IMU delta velocity measurements in body axes - m/sec +syms q0 q1 q2 q3 real % quaternions defining attitude of body axes relative to local NED +syms vn ve vd real % NED velocity - m/sec +syms dax_b day_b daz_b real % delta angle bias - rad +syms dvx_b dvy_b dvz_b real % delta velocity bias - m/sec +syms dt real % IMU time step - sec +syms gravity real % gravity - m/sec^2 +syms daxNoise dayNoise dazNoise dvxNoise dvyNoise dvzNoise real; % IMU delta angle and delta velocity measurement noise +syms vwn vwe real; % NE wind velocity - m/sec +syms magX magY magZ real; % XYZ body fixed magnetic field measurements - milligauss +syms magN magE magD real; % NED earth fixed magnetic field components - milligauss +syms R_VN R_VE R_VD real % variances for NED velocity measurements - (m/sec)^2 +syms R_MAG real % variance for magnetic flux measurements - milligauss^2 +syms rotErr1 rotErr2 rotErr3 real; % error rotation vector + +%% define the process equations + +% define the measured Delta angle and delta velocity vectors +dAngMeas = [dax; day; daz]; +dVelMeas = [dvx; dvy; dvz]; + +% define the delta angle bias errors +dAngBias = [dax_b; day_b; daz_b]; + +% define the quaternion rotation vector for the state estimate +estQuat = [q0;q1;q2;q3]; + +% define the attitude error rotation vector, where error = truth - estimate +errRotVec = [rotErr1;rotErr2;rotErr3]; + +% define the attitude error quaternion using a first order linearisation +errQuat = [1;0.5*errRotVec]; + +% Define the truth quaternion as the estimate + error +truthQuat = QuatMult(estQuat, errQuat); + +% derive the truth body to nav direction cosine matrix +Tbn = Quat2Tbn(truthQuat); + +% define the truth delta angle +% ignore coning acompensation as these effects are negligible in terms of +% covariance growth for our application and grade of sensor +dAngTruth = dAngMeas - dAngBias - [daxNoise;dayNoise;dazNoise]; + +% Define the truth delta velocity +dVelTruth = dVelMeas - [dvxNoise;dvyNoise;dvzNoise]; + +% define the attitude update equations +% use a first order expansion of rotation to calculate the quaternion increment +% acceptable for propagation of covariances +deltaQuat = [1; + 0.5*dAngTruth(1); + 0.5*dAngTruth(2); + 0.5*dAngTruth(3); + ]; +truthQuatNew = QuatMult(truthQuat,deltaQuat); +% calculate the updated attitude error quaternion with respect to the previous estimate +errQuatNew = QuatDivide(truthQuatNew,estQuat); +% change to a rotaton vector - this is the error rotation vector updated state +errRotNew = 2 * [errQuatNew(2);errQuatNew(3);errQuatNew(4)]; + +% define the velocity update equations +% ignore coriolis terms for linearisation purposes +vNew = [vn;ve;vd] + [0;0;gravity]*dt + Tbn*dVelTruth; + +% define the IMU bias error update equations +dabNew = [dax_b; day_b; daz_b]; + +% Define the state vector & number of states +stateVector = [errRotVec;vn;ve;vd;dAngBias]; +nStates=numel(stateVector); + +%% derive the covariance prediction equation +% This reduces the number of floating point operations by a factor of 6 or +% more compared to using the standard matrix operations in code + +% Define the control (disturbance) vector. Error growth in the inertial +% solution is assumed to be driven by 'noise' in the delta angles and +% velocities, after bias effects have been removed. This is OK becasue we +% have sensor bias accounted for in the state equations. +distVector = [daxNoise;dayNoise;dazNoise;dvxNoise;dvyNoise;dvzNoise]; + +% derive the control(disturbance) influence matrix +G = jacobian([errRotNew;vNew;dabNew], distVector); +G = subs(G, {'rotErr1', 'rotErr2', 'rotErr3'}, {0,0,0}); + +% derive the state error matrix +distMatrix = diag(distVector); +Q = G*distMatrix*transpose(G); +f = matlabFunction(Q,'file','calcQ.m'); + +% derive the state transition matrix +vNew = subs(vNew,{'daxNoise','dayNoise','dazNoise','dvxNoise','dvyNoise','dvzNoise'}, {0,0,0,0,0,0}); +errRotNew = subs(errRotNew,{'daxNoise','dayNoise','dazNoise','dvxNoise','dvyNoise','dvzNoise'}, {0,0,0,0,0,0}); +F = jacobian([errRotNew;vNew;dabNew], stateVector); +F = subs(F, {'rotErr1', 'rotErr2', 'rotErr3'}, {0,0,0}); +f = matlabFunction(F,'file','calcF.m'); + +% define a symbolic covariance matrix using strings to represent +% '_l_' to represent '( ' +% '_c_' to represent , +% '_r_' to represent ')' +% these can be substituted later to create executable code +% for rowIndex = 1:nStates +% for colIndex = 1:nStates +% eval(['syms OP_l_',num2str(rowIndex),'_c_',num2str(colIndex), '_r_ real']); +% eval(['P(',num2str(rowIndex),',',num2str(colIndex), ') = OP_l_',num2str(rowIndex),'_c_',num2str(colIndex),'_r_;']); +% end +% end + +% Derive the predicted covariance matrix using the standard equation +% nextP = F*P*transpose(F) + Q; +% f = matlabFunction(nextP,'file','calcP.m'); +%% derive equations for fusion of magnetic deviation measurement +% rotate body measured field into earth axes +magMeasNED = Tbn*[magX;magY;magZ]; +% the predicted measurement is the angle wrt true north of the horizontal +% component of the measured field +angMeas = tan(magMeasNED(2)/magMeasNED(1)); +H_MAG = jacobian(angMeas,stateVector); % measurement Jacobian +H_MAG = subs(H_MAG, {'rotErr1', 'rotErr2', 'rotErr3'}, {0,0,0}); +f = matlabFunction(H_MAG,'file','calcH_MAG.m'); diff --git a/libraries/AP_NavEKF/Models/AttErrVecMathExample/PlotData.m b/libraries/AP_NavEKF/Models/AttErrVecMathExample/PlotData.m new file mode 100644 index 0000000000..4709b39502 --- /dev/null +++ b/libraries/AP_NavEKF/Models/AttErrVecMathExample/PlotData.m @@ -0,0 +1,28 @@ +%% calculate and plot tilt correction magnitude +figure; +plot(angErrLog(1,:)*0.001,angErrLog(2,:)); +grid on; +ylabel('Tilt correction magnitude (deg)'); +xlabel('time (sec)'); + +%% plot gyro bias estimates +figure; +plot(statesLog(1,:)*0.001,statesLog(8:10,:)/dt*180/pi); +grid on; +ylabel('Gyro Bias Estimate (deg/sec)'); +xlabel('time (sec)'); + +%% plot Euler angle estimates +figure; +eulLog(4,:) = eulLog(4,:) + pi; +plot(eulLog(1,:)*0.001,eulLog(2:4,:)*180/pi); +grid on; +ylabel('Euler Angle Estimates (deg)'); +xlabel('time (sec)'); + +%% plot velocity innovations +figure; +plot(statesLog(1,:)*0.001,statesLog(5:7,:)); +grid on; +ylabel('EKF velocity Innovations (m/s)'); +xlabel('time (sec)'); \ No newline at end of file diff --git a/libraries/AP_NavEKF/Models/AttErrVecMathExample/PredictCovariance.m b/libraries/AP_NavEKF/Models/AttErrVecMathExample/PredictCovariance.m new file mode 100644 index 0000000000..8cae416a65 --- /dev/null +++ b/libraries/AP_NavEKF/Models/AttErrVecMathExample/PredictCovariance.m @@ -0,0 +1,61 @@ +function P = PredictCovariance(deltaAngle, ... + deltaVelocity, ... + quat, ... + states,... + P, ... % Previous state covariance matrix + dt) ... % IMU and prediction time step + +% Set filter state process noise other than IMU errors, which are already +% built into the derived covariance predition equations. +% This process noise determines the rate of estimation of IMU bias errors +dAngBiasSigma = dt*5E-6; +processNoise = [0*ones(1,6), dAngBiasSigma*[1 1 1]]; + +% Specify the estimated errors on the IMU delta angles and delta velocities +% Allow for 0.5 deg/sec of gyro error +daxNoise = (dt*0.5*pi/180)^2; +dayNoise = (dt*0.5*pi/180)^2; +dazNoise = (dt*0.5*pi/180)^2; +% Allow for 0.5 m/s/s of accelerometer error +dvxNoise = (dt*0.5)^2; +dvyNoise = (dt*0.5)^2; +dvzNoise = (dt*0.5)^2; + +dvx = deltaVelocity(1); +dvy = deltaVelocity(2); +dvz = deltaVelocity(3); +dax = deltaAngle(1); +day = deltaAngle(2); +daz = deltaAngle(3); + +q0 = quat(1); +q1 = quat(2); +q2 = quat(3); +q3 = quat(4); + +dax_b = states(7); +day_b = states(8); +daz_b = states(9); + +% Predicted covariance +F = calcF(dax,dax_b,day,day_b,daz,daz_b,dvx,dvy,dvz,q0,q1,q2,q3); +Q = calcQ(daxNoise,dayNoise,dazNoise,dvxNoise,dvyNoise,dvzNoise,q0,q1,q2,q3); +P = F*P*transpose(F) + Q; + +% Add the general process noise +for i = 1:9 + P(i,i) = P(i,i) + processNoise(i)^2; +end + +% Force symmetry on the covariance matrix to prevent ill-conditioning +% of the matrix which would cause the filter to blow-up +P = 0.5*(P + transpose(P)); + +% ensure diagonals are positive +for i=1:9 + if P(i,i) < 0 + P(i,i) = 0; + end +end + +end \ No newline at end of file diff --git a/libraries/AP_NavEKF/Models/AttErrVecMathExample/PredictStates.m b/libraries/AP_NavEKF/Models/AttErrVecMathExample/PredictStates.m new file mode 100644 index 0000000000..190b9d5a7a --- /dev/null +++ b/libraries/AP_NavEKF/Models/AttErrVecMathExample/PredictStates.m @@ -0,0 +1,70 @@ +function [quat, states, Tbn, correctedDelAng, correctedDelVel] = PredictStates( ... + quat, ... % previous quaternion states 4x1 + states, ... % previous states (3x1 rotation error, 3x1 velocity, 3x1 gyro bias) + angRate, ... % IMU rate gyro measurements, 3x1 (rad/sec) + accel, ... % IMU accelerometer measurements 3x1 (m/s/s) + dt) % time since last IMU measurement (sec) + +% Define parameters used for previous angular rates and acceleration shwich +% are used for trapezoidal integration +persistent prevAngRate; +if isempty(prevAngRate) + prevAngRate = angRate; +end +persistent prevAccel; +if isempty(prevAccel) + prevAccel = accel; +end +% define persistent variables for previous delta angle and velocity which +% are required for sculling and coning error corrections +persistent prevDelAng; +if isempty(prevDelAng) + prevDelAng = prevAngRate*dt; +end +persistent prevDelVel; +if isempty(prevDelVel) + prevDelVel = prevAccel*dt; +end + +% Convert IMU data to delta angles and velocities using trapezoidal +% integration +dAng = 0.5*(angRate + prevAngRate)*dt; +dVel = 0.5*(accel + prevAccel )*dt; +prevAngRate = angRate; +prevAccel = accel; + +% Remove sensor bias errors +dAng = dAng - states(7:9); + +% Apply rotational and skulling corrections +correctedDelVel= dVel + ... + 0.5*cross(prevDelAng + dAng , prevDelVel + dVel) + 1/6*cross(prevDelAng + dAng , cross(prevDelAng + dAng , prevDelVel + dVel)) + ... % rotational correction + 1/12*(cross(prevDelAng , dVel) + cross(prevDelVel , dAng)); % sculling correction + +% Apply corrections for coning errors +correctedDelAng = dAng - 1/12*cross(prevDelAng , dAng); + +% Save current measurements +prevDelAng = dAng; +prevDelVel = dVel; + +% Convert the rotation vector to its equivalent quaternion +deltaQuat = RotToQuat(correctedDelAng); + +% Update the quaternions by rotating from the previous attitude through +% the delta angle rotation quaternion +quat = QuatMult(quat,deltaQuat); + +% Normalise the quaternions +quat = NormQuat(quat); + +% Calculate the body to nav cosine matrix +Tbn = Quat2Tbn(quat); + +% transform body delta velocities to delta velocities in the nav frame +delVelNav = Tbn * correctedDelVel + [0;0;9.807]*dt; + +% Sum delta velocities to get velocity +states(4:6) = states(4:6) + delVelNav(1:3); + +end \ No newline at end of file diff --git a/libraries/AP_NavEKF/Models/AttErrVecMathExample/RunRealData.m b/libraries/AP_NavEKF/Models/AttErrVecMathExample/RunRealData.m new file mode 100644 index 0000000000..6fdf9a069b --- /dev/null +++ b/libraries/AP_NavEKF/Models/AttErrVecMathExample/RunRealData.m @@ -0,0 +1,86 @@ +%% Set initial conditions +clear all; +load('fltTest.mat'); +startDelayTime = 100; % number of seconds to delay filter start (used to simulate in-flight restart) +dt = 1/50; +indexLimit = length(IMU); +magIndexlimit = length(MAG); +statesLog = zeros(10,indexLimit); +eulLog = zeros(4,indexLimit); +velInnovLog = zeros(4,indexLimit); +angErrLog = zeros(2,indexLimit); +decInnovLog = zeros(2,magIndexlimit); +velInnovVarLog = velInnovLog; +decInnovVarLog = decInnovLog; +% initialise the state vector and quaternion +states = zeros(9,1); +quat = [1;0;0;0]; +Tbn = Quat2Tbn(quat); +% average last 10 accel readings to reduce effect of noise +initAccel(1) = mean(IMU(1:10,6)); +initAccel(2) = mean(IMU(1:10,7)); +initAccel(3) = mean(IMU(1:10,8)); +% Use averaged accel readings to align tilt +quat = AlignTilt(quat,initAccel); +% Set the expected declination +measDec = 0.18; +% define the state covariances +Sigma_velNED = 0.5; % 1 sigma uncertainty in horizontal velocity components +Sigma_dAngBias = 5*pi/180*dt; % 1 Sigma uncertainty in delta angle bias +Sigma_angErr = 1; % 1 Sigma uncertainty in angular misalignment (rad) +covariance = single(diag([Sigma_angErr*[1;1;1];Sigma_velNED*[1;1;1];Sigma_dAngBias*[1;1;1]].^2)); +%% Main Loop +magIndex = 1; +time = 0; +angErr = 0; +headingAligned = 0; +% delay start by a minimum of 10 IMU samples to allow for initial tilt +% alignment delay +startIndex = max(11,ceil(startDelayTime/dt)); +for index = startIndex:indexLimit + time=time+dt + startIndex*dt; + % read IMU measurements + angRate = IMU(index,3:5)'; + % switch in a bias offset to test the filter + if (time > +inf) + angRate = angRate + [1;-1;1]*pi/180; + end + accel = IMU(index,6:8)'; + % predict states + [quat, states, Tbn, delAng, delVel] = PredictStates(quat,states,angRate,accel,dt); + statesLog(1,index) = time; + statesLog(2:10,index) = states; + eulLog(1,index) = time; + eulLog(2:4,index) = QuatToEul(quat); + % predict covariance matrix + covariance = PredictCovariance(delAng,delVel,quat,states,covariance,dt); + % fuse velocity measurements - use synthetic measurements + measVel = [0;0;0]; + [quat,states,angErr,covariance,velInnov,velInnovVar] = FuseVelocity(quat,states,covariance,measVel); + velInnovLog(1,index) = time; + velInnovLog(2:4,index) = velInnov; + velInnovVarLog(1,index) = time; + velInnovVarLog(2:4,index) = velInnovVar; + angErrLog(1,index) = time; + angErrLog(2,index) = angErr; + % read magnetometer measurements + while ((MAG(magIndex,1) < IMU(index,1)) && (magIndex < magIndexlimit)) + magIndex = magIndex + 1; + magBody = 0.001*MAG(magIndex,3:5)'; + if (time >= 1.0 && headingAligned==0 && angErr < 1e-3) + quat = AlignHeading(quat,magBody,measDec); + headingAligned = 1; + end + % fuse magnetometer measurements if new data available and when tilt has settled + if (headingAligned == 1) + [quat,states,covariance,decInnov,decInnovVar] = FuseMagnetometer(quat,states,covariance,magBody,measDec,Tbn); + decInnovLog(1,magIndex) = time; + decInnovLog(2,magIndex) = decInnov; + decInnovVarLog(1,magIndex) = time; + decInnovVarLog(2,magIndex) = decInnovVar; + end + end +end + +%% Generate plots +PlotData; \ No newline at end of file diff --git a/libraries/AP_NavEKF/Models/AttErrVecMathExample/RunSyntheticData.m b/libraries/AP_NavEKF/Models/AttErrVecMathExample/RunSyntheticData.m new file mode 100644 index 0000000000..9819cc8e5f --- /dev/null +++ b/libraries/AP_NavEKF/Models/AttErrVecMathExample/RunSyntheticData.m @@ -0,0 +1,78 @@ +%% Set initial conditions +clear all; +dt = 1/100; +duration = 10; +indexLimit = round(duration/dt); +statesLog = zeros(10,indexLimit); +eulLog = zeros(4,indexLimit); +velInnovLog = zeros(4,indexLimit); +decInnovLog = zeros(2,indexLimit); +velInnovVarLog = velInnovLog; +decInnovVarLog = decInnovLog; +angErrLog = zeros(2,indexLimit); +% Use a random initial orientation +quatTruth = [rand;randn;randn;randn]; +quatLength = sqrt(quatTruth(1)^2 + quatTruth(2)^2 + quatTruth(3)^2 + quatTruth(4)^2); +quatTruth = quatTruth / quatLength; +TbnTruth = Quat2Tbn(quatTruth); +% initialise the filter to level +quat = [1;0;0;0]; +states = zeros(9,1); +Tbn = Quat2Tbn(quat); +% define the earths truth magnetic field +magEarthTruth = [0.3;0.1;-0.5]; +% define the assumed declination using th etruth field plus location +% variation +measDec = atan2(magEarthTruth(2),magEarthTruth(1)) + 2*pi/180*randn; +% define the magnetometer bias errors +magMeasBias = 0.02*[randn;randn;randn]; +% define the state covariances with the exception of the quaternion covariances +Sigma_velNED = 0.5; % 1 sigma uncertainty in horizontal velocity components +Sigma_dAngBias = 1*pi/180*dt; % 1 Sigma uncertainty in delta angle bias +Sigma_angErr = 1; % 1 Sigma uncertainty in angular misalignment (rad) +covariance = single(diag([Sigma_angErr*[1;1;1];Sigma_velNED*[1;1;1];Sigma_dAngBias*[1;1;1]].^2)); +%% Main Loop +headingAligned=0; +time = 0; +for index = 1:indexLimit + time=time+dt; + % synthesise IMU measurements + angRate = 0*[randn;randn;randn]; + accel = 0*[randn;randn;randn] + transpose(TbnTruth)*[0;0;-9.81]; + % predict states + [quat, states, Tbn, delAng, delVel] = PredictStates(quat,states,angRate,accel,dt); + statesLog(1,index) = time; + statesLog(2:10,index) = states; + eulLog(1,index) = time; + eulLog(2:4,index) = QuatToEul(quat); + % predict covariance matrix + covariance = PredictCovariance(delAng,delVel,quat,states,covariance,dt); + % synthesise velocity measurements + measVel = [0;0;0]; + % fuse velocity measurements + [quat,states,angErr,covariance,velInnov,velInnovVar] = FuseVelocity(quat,states,covariance,measVel); + velInnovLog(1,index) = time; + velInnovLog(2:4,index) = velInnov; + velInnovVarLog(1,index) = time; + velInnovVarLog(2:4,index) = velInnovVar; + angErrLog(1,index) = time; + angErrLog(2,index) = angErr; + % synthesise magnetometer measurements adding sensor bias + magBody = transpose(TbnTruth)*magEarthTruth + magMeasBias; + % fuse magnetometer measurements + if (index > 500 && headingAligned==0 && angErr < 1e-4) + quat = AlignHeading(quat,magBody,measDec); + headingAligned = 1; + end + if (headingAligned == 1) + [quat,states,covariance,decInnov,decInnovVar] = FuseMagnetometer(quat,states,covariance,magBody,measDec,Tbn); + decInnovLog(1,index) = time; + decInnovLog(2,index) = decInnov; + decInnovVarLog(1,index) = time; + decInnovVarLog(2,index) = decInnovVar; + end + +end + +%% Generate Plots +PlotData; \ No newline at end of file diff --git a/libraries/AP_NavEKF/Models/AttErrVecMathExample/calcF.m b/libraries/AP_NavEKF/Models/AttErrVecMathExample/calcF.m new file mode 100644 index 0000000000..6b4c6a3c1d --- /dev/null +++ b/libraries/AP_NavEKF/Models/AttErrVecMathExample/calcF.m @@ -0,0 +1,65 @@ +function F = calcF(dax,dax_b,day,day_b,daz,daz_b,dvx,dvy,dvz,q0,q1,q2,q3) +%CALCF +% F = CALCF(DAX,DAX_B,DAY,DAY_B,DAZ,DAZ_B,DVX,DVY,DVZ,Q0,Q1,Q2,Q3) + +% This function was generated by the Symbolic Math Toolbox version 5.8. +% 27-Dec-2014 13:59:07 + +t2 = dax.*(1.0./2.0); +t3 = dax_b.*(1.0./2.0); +t4 = t2-t3; +t5 = day.*(1.0./2.0); +t6 = day_b.*(1.0./2.0); +t7 = t5-t6; +t8 = daz.*(1.0./2.0); +t9 = daz_b.*(1.0./2.0); +t10 = t8-t9; +t11 = q2.*t4.*(1.0./2.0); +t12 = q1.*t7.*(1.0./2.0); +t13 = q0.*t10.*(1.0./2.0); +t14 = q2.*(1.0./2.0); +t15 = q3.*t4.*(1.0./2.0); +t16 = q1.*t10.*(1.0./2.0); +t17 = q1.*(1.0./2.0); +t18 = q0.*t4.*(1.0./2.0); +t19 = q3.*t7.*(1.0./2.0); +t20 = q0.*(1.0./2.0); +t21 = q2.*t7.*(1.0./2.0); +t22 = q3.*t10.*(1.0./2.0); +t23 = q0.*t7.*(1.0./2.0); +t24 = q3.*(1.0./2.0); +t25 = q1.*t4.*(1.0./2.0); +t26 = q2.*t10.*(1.0./2.0); +t27 = t20-t21+t22+t25; +t28 = -t17+t18+t19+t26; +t29 = t14-t15+t16+t23; +t30 = t11+t12-t13+t24; +t31 = t17-t18+t19+t26; +t32 = t20+t21-t22+t25; +t33 = t11-t12+t13+t24; +t34 = -t14+t15+t16+t23; +t35 = q0.^2; +t36 = q1.^2; +t37 = q2.^2; +t38 = q3.^2; +t39 = -t35-t36-t37-t38; +t40 = t14+t15+t16-t23; +t41 = t11+t12+t13-t24; +t42 = t20+t21+t22-t25; +t43 = t17+t18+t19-t26; +t44 = q0.*q2.*2.0; +t45 = q1.*q3.*2.0; +t46 = t44+t45; +t47 = t35+t36-t37-t38; +t48 = q0.*q3.*2.0; +t52 = q1.*q2.*2.0; +t49 = t48-t52; +t50 = q0.*q1.*2.0; +t55 = q2.*q3.*2.0; +t51 = t50-t55; +t53 = t35-t36+t37-t38; +t54 = t48+t52; +t56 = t35-t36-t37+t38; +t57 = t50+t55; +t58 = t44-t45; +F = reshape([q3.*(q3.*(-1.0./2.0)+t11+t12+t13).*-2.0+q2.*(t14+t15+t16-q0.*t7.*(1.0./2.0)).*2.0+q1.*(t17+t18+t19-q2.*t10.*(1.0./2.0)).*2.0+q0.*(t20+t21+t22-q1.*t4.*(1.0./2.0)).*2.0,q0.*t41.*-2.0-q1.*t40.*2.0+q2.*t43.*2.0-q3.*t42.*2.0,q0.*t40.*-2.0+q1.*t41.*2.0+q2.*t42.*2.0+q3.*t43.*2.0,dvy.*t46+dvz.*t49,-dvy.*t51-dvz.*t53,dvy.*t56-dvz.*t57,0.0,0.0,0.0,q0.*t30.*-2.0+q1.*t29.*2.0+q2.*t28.*2.0+q3.*t27.*2.0,q0.*t27.*2.0-q1.*t28.*2.0+q2.*t29.*2.0+q3.*t30.*2.0,q0.*t28.*-2.0-q1.*t27.*2.0-q2.*t30.*2.0+q3.*t29.*2.0,-dvx.*t46+dvz.*t47,dvx.*t51+dvz.*t54,-dvx.*t56-dvz.*t58,0.0,0.0,0.0,q0.*t34.*-2.0+q1.*t33.*2.0-q2.*t32.*2.0-q3.*t31.*2.0,q0.*t31.*-2.0+q1.*t32.*2.0+q2.*t33.*2.0+q3.*t34.*2.0,q0.*t32.*2.0+q1.*t31.*2.0-q2.*t34.*2.0+q3.*t33.*2.0,-dvx.*t49-dvy.*t47,dvx.*t53-dvy.*t54,dvx.*t57+dvy.*t58,0.0,0.0,0.0,0.0,0.0,0.0,1.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,1.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,1.0,0.0,0.0,0.0,t39,0.0,0.0,0.0,0.0,0.0,1.0,0.0,0.0,0.0,t39,0.0,0.0,0.0,0.0,0.0,1.0,0.0,0.0,0.0,t39,0.0,0.0,0.0,0.0,0.0,1.0],[9, 9]); diff --git a/libraries/AP_NavEKF/Models/AttErrVecMathExample/calcH_MAG.m b/libraries/AP_NavEKF/Models/AttErrVecMathExample/calcH_MAG.m new file mode 100644 index 0000000000..585d5d0bc2 --- /dev/null +++ b/libraries/AP_NavEKF/Models/AttErrVecMathExample/calcH_MAG.m @@ -0,0 +1,38 @@ +function H_MAG = calcH_MAG(magX,magY,magZ,q0,q1,q2,q3) +%CALCH_MAG +% H_MAG = CALCH_MAG(MAGX,MAGY,MAGZ,Q0,Q1,Q2,Q3) + +% This function was generated by the Symbolic Math Toolbox version 5.8. +% 27-Dec-2014 13:59:09 + +t2 = q0.^2; +t3 = q1.^2; +t4 = q2.^2; +t5 = q3.^2; +t6 = q0.*q2.*2.0; +t7 = q1.*q3.*2.0; +t8 = t6+t7; +t9 = q0.*q3.*2.0; +t13 = q1.*q2.*2.0; +t10 = t9-t13; +t11 = t2+t3-t4-t5; +t12 = magX.*t11; +t14 = magZ.*t8; +t19 = magY.*t10; +t15 = t12+t14-t19; +t16 = t2-t3+t4-t5; +t17 = q0.*q1.*2.0; +t24 = q2.*q3.*2.0; +t18 = t17-t24; +t20 = 1.0./t15; +t21 = magY.*t16; +t22 = t9+t13; +t23 = magX.*t22; +t28 = magZ.*t18; +t25 = t21+t23-t28; +t29 = t20.*t25; +t26 = tan(t29); +t27 = 1.0./t15.^2; +t30 = t26.^2; +t31 = t30+1.0; +H_MAG = [-t31.*(t20.*(magZ.*t16+magY.*t18)+t25.*t27.*(magY.*t8+magZ.*t10)),t31.*(t20.*(magX.*t18+magZ.*t22)+t25.*t27.*(magX.*t8-magZ.*t11)),t31.*(t20.*(magX.*t16-magY.*t22)+t25.*t27.*(magX.*t10+magY.*t11)),0.0,0.0,0.0,0.0,0.0,0.0]; diff --git a/libraries/AP_NavEKF/Models/AttErrVecMathExample/calcQ.m b/libraries/AP_NavEKF/Models/AttErrVecMathExample/calcQ.m new file mode 100644 index 0000000000..e9c0dc3471 --- /dev/null +++ b/libraries/AP_NavEKF/Models/AttErrVecMathExample/calcQ.m @@ -0,0 +1,34 @@ +function Q = calcQ(daxNoise,dayNoise,dazNoise,dvxNoise,dvyNoise,dvzNoise,q0,q1,q2,q3) +%CALCQ +% Q = CALCQ(DAXNOISE,DAYNOISE,DAZNOISE,DVXNOISE,DVYNOISE,DVZNOISE,Q0,Q1,Q2,Q3) + +% This function was generated by the Symbolic Math Toolbox version 5.8. +% 27-Dec-2014 13:59:04 + +t3 = q0.^2; +t4 = q1.^2; +t5 = q2.^2; +t6 = q3.^2; +t2 = t3+t4+t5+t6; +t7 = t2.^2; +t11 = q0.*q3.*2.0; +t12 = q1.*q2.*2.0; +t8 = t11-t12; +t13 = q0.*q2.*2.0; +t14 = q1.*q3.*2.0; +t9 = t13+t14; +t10 = t3+t4-t5-t6; +t15 = q0.*q1.*2.0; +t16 = t11+t12; +t17 = dvxNoise.*t10.*t16; +t18 = t3-t4+t5-t6; +t19 = q2.*q3.*2.0; +t20 = t15-t19; +t21 = t15+t19; +t22 = t3-t4-t5+t6; +t23 = t13-t14; +t24 = dvzNoise.*t9.*t22; +t25 = t24-dvxNoise.*t10.*t23-dvyNoise.*t8.*t21; +t26 = dvyNoise.*t18.*t21; +t27 = t26-dvxNoise.*t16.*t23-dvzNoise.*t20.*t22; +Q = reshape([daxNoise.*t7,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,dayNoise.*t7,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,dazNoise.*t7,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,dvxNoise.*t10.^2+dvyNoise.*t8.^2+dvzNoise.*t9.^2,t17-dvyNoise.*t8.*t18-dvzNoise.*t9.*t20,t25,0.0,0.0,0.0,0.0,0.0,0.0,t17-dvzNoise.*t9.*(t15-q2.*q3.*2.0)-dvyNoise.*t8.*t18,dvxNoise.*t16.^2+dvyNoise.*t18.^2+dvzNoise.*t20.^2,t27,0.0,0.0,0.0,0.0,0.0,0.0,t25,t27,dvxNoise.*t23.^2+dvyNoise.*t21.^2+dvzNoise.*t22.^2,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0],[9, 9]); diff --git 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startIndex(pwrIndex) = index; + % strPat = strcat(strIn{1}(startIndex(pwrIndex):endIndex(pwrIndex)),'^2'); + strRep = strcat('sq',strIn{1}(startIndex(pwrIndex):endIndex(pwrIndex))); + % cellStrPat(pwrIndex) = cellstr(strPat); + cellStrRep(pwrIndex) = cellstr(strRep); + end + for pwrIndex = 1:length(idxsq{1}) + strRep = char(cellStrRep(pwrIndex)); + strIn{1}(startIndex(pwrIndex):endIndex(pwrIndex)+2) = strRep; + end + SymbolicOutput(lineIndex) = strIn; + end +end + +% replace where adjacent to ] parenthesis +for lineIndex = 1:length(SymbolicOutput) + strIn = char(SymbolicOutput(lineIndex)); + [match,idxsq1,idxsq2] = regexp(strIn,'\w*\[\w*\]\^2','match','start','end'); + [idxsq3] = regexp(strIn,'\[\w*\]\^2','start'); + if ~isempty(match) + for pwrIndex = 1:length(match) + strVar = strIn(idxsq1(pwrIndex):idxsq3(pwrIndex)-1); + strIndex = strIn(idxsq3(pwrIndex)+1:idxsq2(pwrIndex)-3); + strPat = strcat(strVar,'\[',strIndex,'\]\^2'); + strRep = strcat('sq(',strVar,'[',strIndex,']',')'); + strIn = regexprep(strIn,strPat,strRep); + end + SymbolicOutput(lineIndex) = cellstr(strIn); + end +end + +% replace where adjacent to alpanumeric characters +for lineIndex = 1:length(SymbolicOutput) + strIn = char(SymbolicOutput(lineIndex)); + [match,idxsq1,idxsq2] = regexp(strIn,'\w*\^2','match','start','end'); + [idxsq3] = regexp(strIn,'\^2','start'); + if ~isempty(match) + for pwrIndex = 1:length(match) + strVar = strIn(idxsq1(pwrIndex)+2*(pwrIndex-1):idxsq2(pwrIndex)-2+2*(pwrIndex-1)); + strPat = strcat(strVar,'\^2'); + strRep = strcat('sq(',strVar,')'); + strIn = regexprep(strIn,strPat,strRep); + end + SymbolicOutput(lineIndex) = cellstr(strIn); + end +end + +%% Replace ^(1/2) + +% replace where adjacent to ) parenthesis +for lineIndex = 1:length(SymbolicOutput) + idxsq = regexp(SymbolicOutput(lineIndex),'\)\^\(1\/2\)'); + if ~isempty(idxsq{1}) + strIn = SymbolicOutput(lineIndex); + idxlp = regexp(strIn,'\('); + idxrp = regexp(strIn,'\)'); + for pwrIndex = 1:length(idxsq{1}) + counter = 1; + index = idxsq{1}(pwrIndex); + endIndex(pwrIndex) = index; + while (counter > 0 && index > 0) + index = index - 1; + counter = counter + ~isempty(find(idxrp{1} == index, 1)); + counter = counter - ~isempty(find(idxlp{1} == index, 1)); + end + startIndex(pwrIndex) = index; + % strPat = strcat(strIn{1}(startIndex(pwrIndex):endIndex(pwrIndex)),'^2'); + strRep = strcat('(sqrt',strIn{1}(startIndex(pwrIndex):endIndex(pwrIndex)),')'); + % cellStrPat(pwrIndex) = cellstr(strPat); + cellStrRep(pwrIndex) = cellstr(strRep); + end + for pwrIndex = 1:length(idxsq{1}) + strRep = char(cellStrRep(pwrIndex)); + strIn{1}(startIndex(pwrIndex):endIndex(pwrIndex)+6) = strRep; + end + SymbolicOutput(lineIndex) = strIn; + end +end + +%% Replace Divisions +% Compiler looks after this type of optimisation for us +% for lineIndex = 1:length(SymbolicOutput) +% strIn = char(SymbolicOutput(lineIndex)); +% strIn = regexprep(strIn,'\/2','\*0\.5'); +% strIn = regexprep(strIn,'\/4','\*0\.25'); +% SymbolicOutput(lineIndex) = cellstr(strIn); +% end + +%% Convert declarations +for lineIndex = 1:length(SymbolicOutput) + str = char(SymbolicOutput(lineIndex)); + if ~isempty(regexp(str,'zeros', 'once')) + index1 = regexp(str,' = zeros[','once')-1; + index2 = regexp(str,' = zeros[','end','once')+1; + index3 = regexp(str,'\]\[','once')-1; + index4 = index3 + 3; + index5 = max(regexp(str,'\]'))-1; + str1 = {'float '}; + str2 = str(1:index1); + str3 = '['; + str4 = str(index2:index3); + str4 = num2str(str2num(str4)+1); + str5 = ']['; + str6 = str(index4:index5); + str6 = num2str(str2num(str6)+1); + str7 = '];'; + SymbolicOutput(lineIndex) = strcat(str1,str2,str3,str4,str5,str6,str7); + end +end + +%% Change covariance matrix variable name to P +for lineIndex = 1:length(SymbolicOutput) + strIn = char(SymbolicOutput(lineIndex)); + strIn = regexprep(strIn,'OP\[','P['); + SymbolicOutput(lineIndex) = cellstr(strIn); +end + +%% Write to file +fileName = strcat(fileName,'.cpp'); +fid = fopen(fileName,'wt'); +for lineIndex = 1:length(SymbolicOutput) + fprintf(fid,char(SymbolicOutput(lineIndex))); + fprintf(fid,'\n'); +end +fclose(fid); +clear all; \ No newline at end of file diff --git a/libraries/AP_NavEKF/Models/Common/ConvertToM.m b/libraries/AP_NavEKF/Models/Common/ConvertToM.m new file mode 100644 index 0000000000..1e5f7f4388 --- /dev/null +++ b/libraries/AP_NavEKF/Models/Common/ConvertToM.m @@ -0,0 +1,46 @@ +function ConvertToM(nStates) +%% Initialize variables +fileName = strcat('SymbolicOutput',int2str(nStates),'.txt'); +delimiter = ''; + +%% Format string for each line of text: +% column1: text (%s) +% For more information, see the TEXTSCAN documentation. +formatSpec = '%s%[^\n\r]'; + +%% Open the text file. +fileID = fopen(fileName,'r'); + +%% Read columns of data according to format string. +% This call is based on the structure of the file used to generate this +% code. If an error occurs for a different file, try regenerating the code +% from the Import Tool. +dataArray = textscan(fileID, formatSpec, 'Delimiter', delimiter, 'ReturnOnError', false,'Bufsize',65535); + +%% Close the text file. +fclose(fileID); + +%% Create output variable +SymbolicOutput = [dataArray{1:end-1}]; + +%% Clear temporary variables +clearvars filename delimiter formatSpec fileID dataArray ans; + +%% replace brackets and commas +for lineIndex = 1:length(SymbolicOutput) + SymbolicOutput(lineIndex) = regexprep(SymbolicOutput(lineIndex), '_l_', '('); + SymbolicOutput(lineIndex) = regexprep(SymbolicOutput(lineIndex), '_c_', ','); + SymbolicOutput(lineIndex) = regexprep(SymbolicOutput(lineIndex), '_r_', ')'); +end + +%% Write to file +fileName = strcat('M_code',int2str(nStates),'.txt'); +fid = fopen(fileName,'wt'); +for lineIndex = 1:length(SymbolicOutput) + fprintf(fid,char(SymbolicOutput(lineIndex))); + fprintf(fid,'\n'); +end +fclose(fid); +clear all; + +end \ No newline at end of file diff --git a/libraries/AP_NavEKF/Models/Common/EulToQuat.m b/libraries/AP_NavEKF/Models/Common/EulToQuat.m new file mode 100644 index 0000000000..9b57a20b5d --- /dev/null +++ b/libraries/AP_NavEKF/Models/Common/EulToQuat.m @@ -0,0 +1,23 @@ +function quaterion = EulToQuat(Euler) + +% Convert from a 321 Euler rotation sequence specified in radians to a +% Quaternion + +quaterion = zeros(4,1); + +Euler = Euler * 0.5; +cosPhi = cos(Euler(1)); +sinPhi = sin(Euler(1)); +cosTheta = cos(Euler(2)); +sinTheta = sin(Euler(2)); +cosPsi = cos(Euler(3)); +sinPsi = sin(Euler(3)); + +quaterion(1,1) = (cosPhi*cosTheta*cosPsi + sinPhi*sinTheta*sinPsi); +quaterion(2,1) = (sinPhi*cosTheta*cosPsi - cosPhi*sinTheta*sinPsi); +quaterion(3,1) = (cosPhi*sinTheta*cosPsi + sinPhi*cosTheta*sinPsi); +quaterion(4,1) = (cosPhi*cosTheta*sinPsi - sinPhi*sinTheta*cosPsi); + +return; + + diff --git a/libraries/AP_NavEKF/Models/Common/NormQuat.m b/libraries/AP_NavEKF/Models/Common/NormQuat.m new file mode 100644 index 0000000000..7d1913efda --- /dev/null +++ b/libraries/AP_NavEKF/Models/Common/NormQuat.m @@ -0,0 +1,5 @@ +% normalise the quaternion +function quaternion = normQuat(quaternion) + +quatMag = sqrt(quaternion(1)^2 + quaternion(2)^2 + quaternion(3)^2 + quaternion(4)^2); +quaternion(1:4) = quaternion / quatMag; diff --git a/libraries/AP_NavEKF/Models/Common/OptimiseAlgebra.m b/libraries/AP_NavEKF/Models/Common/OptimiseAlgebra.m new file mode 100644 index 0000000000..16d4c353ca --- /dev/null +++ b/libraries/AP_NavEKF/Models/Common/OptimiseAlgebra.m @@ -0,0 +1,29 @@ +function [SymExpOut,SubExpArray] = OptimiseAlgebra(SymExpIn,SubExpName) + +% Loop through symbolic expression, identifying repeated expressions and +% bringing them out as shared expression or sub expressions +% do this until no further repeated expressions found +% This can significantly reduce computations + +syms SubExpIn SubExpArray ; + +SubExpArray(1,1) = 'invalid'; +index = 0; +f_complete = 0; +while f_complete==0 + index = index + 1; + SubExpIn = [SubExpName,'(',num2str(index),')']; + SubExpInStore{index} = SubExpIn; + [SymExpOut,SubExpOut]=subexpr(SymExpIn,SubExpIn); + for k = 1:index + if SubExpOut == SubExpInStore{k} + f_complete = 1; + end + end + if f_complete || index > 100 + SymExpOut = SymExpIn; + else + SubExpArray(index,1) = SubExpOut; + SymExpIn = SymExpOut; + end +end \ No newline at end of file diff --git a/libraries/AP_NavEKF/Models/Common/Quat2Tbn.m b/libraries/AP_NavEKF/Models/Common/Quat2Tbn.m new file mode 100644 index 0000000000..663d19cde8 --- /dev/null +++ b/libraries/AP_NavEKF/Models/Common/Quat2Tbn.m @@ -0,0 +1,14 @@ +function Tbn = Quat2Tbn(quat) + +% Convert from quaternions defining the flight vehicles rotation to +% the direction cosine matrix defining the rotation from body to navigation +% coordinates + +q0 = quat(1); +q1 = quat(2); +q2 = quat(3); +q3 = quat(4); + +Tbn = [q0^2 + q1^2 - q2^2 - q3^2, 2*(q1*q2 - q0*q3), 2*(q1*q3 + q0*q2); ... + 2*(q1*q2 + q0*q3), q0^2 - q1^2 + q2^2 - q3^2, 2*(q2*q3 - q0*q1); ... + 2*(q1*q3-q0*q2), 2*(q2*q3 + q0*q1), q0^2 - q1^2 - q2^2 + q3^2]; \ No newline at end of file diff --git a/libraries/AP_NavEKF/Models/Common/QuatDivide.m b/libraries/AP_NavEKF/Models/Common/QuatDivide.m new file mode 100644 index 0000000000..20e789dcfb --- /dev/null +++ b/libraries/AP_NavEKF/Models/Common/QuatDivide.m @@ -0,0 +1,16 @@ +function q_out = QuatDivide(qin1,qin2) + +q0 = qin1(1); +q1 = qin1(2); +q2 = qin1(3); +q3 = qin1(4); + +r0 = qin2(1); +r1 = qin2(2); +r2 = qin2(3); +r3 = qin2(4); + +q_out(1,1) = (qin2(1)*qin1(1) + qin2(2)*qin1(2) + qin2(3)*qin1(3) + qin2(4)*qin1(4)); +q_out(2,1) = (r0*q1 - r1*q0 - r2*q3 + r3*q2); +q_out(3,1) = (r0*q2 + r1*q3 - r2*q0 - r3*q1); +q_out(4,1) = (r0*q3 - r1*q2 + r2*q1 - r3*q0); diff --git a/libraries/AP_NavEKF/Models/Common/QuatMult.m b/libraries/AP_NavEKF/Models/Common/QuatMult.m new file mode 100644 index 0000000000..357c545d22 --- /dev/null +++ b/libraries/AP_NavEKF/Models/Common/QuatMult.m @@ -0,0 +1,5 @@ +function quatOut = QuatMult(quatA,quatB) +% Calculate the following quaternion product quatA * quatB using the +% standard identity + +quatOut = [quatA(1)*quatB(1)-quatA(2:4)'*quatB(2:4); quatA(1)*quatB(2:4) + quatB(1)*quatA(2:4) + cross(quatA(2:4),quatB(2:4))]; \ No newline at end of file diff --git a/libraries/AP_NavEKF/Models/Common/QuatToEul.m b/libraries/AP_NavEKF/Models/Common/QuatToEul.m new file mode 100644 index 0000000000..09b1505b6f --- /dev/null +++ b/libraries/AP_NavEKF/Models/Common/QuatToEul.m @@ -0,0 +1,9 @@ +% Convert from a quaternion to a 321 Euler rotation sequence in radians + +function Euler = QuatToEul(quat) + +Euler = zeros(3,1); + +Euler(1) = atan2(2*(quat(3)*quat(4)+quat(1)*quat(2)), quat(1)*quat(1) - quat(2)*quat(2) - quat(3)*quat(3) + quat(4)*quat(4)); +Euler(2) = -asin(2*(quat(2)*quat(4)-quat(1)*quat(3))); +Euler(3) = atan2(2*(quat(2)*quat(3)+quat(1)*quat(4)), quat(1)*quat(1) + quat(2)*quat(2) - quat(3)*quat(3) - quat(4)*quat(4)); \ No newline at end of file diff --git a/libraries/AP_NavEKF/Models/Common/RotToQuat.m b/libraries/AP_NavEKF/Models/Common/RotToQuat.m new file mode 100644 index 0000000000..3c9777acd5 --- /dev/null +++ b/libraries/AP_NavEKF/Models/Common/RotToQuat.m @@ -0,0 +1,10 @@ +% convert froma rotation vector in radians to a quaternion +function quaternion = RotToQuat(rotVec) + +vecLength = sqrt(rotVec(1)^2 + rotVec(2)^2 + rotVec(3)^2); + +if vecLength < 1e-6 + quaternion = [1;0;0;0]; +else + quaternion = [cos(0.5*vecLength); rotVec/vecLength*sin(0.5*vecLength)]; +end \ No newline at end of file diff --git a/libraries/AP_NavEKF/Models/GimbalEstimatorExample/AlignHeading.m b/libraries/AP_NavEKF/Models/GimbalEstimatorExample/AlignHeading.m new file mode 100644 index 0000000000..6982596f1a --- /dev/null +++ b/libraries/AP_NavEKF/Models/GimbalEstimatorExample/AlignHeading.m @@ -0,0 +1,51 @@ +function quat = AlignHeading( ... + gPhi, ... % gimbal roll angle + gPsi, ... % gimbal yaw angle + gTheta, ... % gimbal pitch angle + Tsn, ... % sensor to NED rotation matrix + magMea, ... % body frame magnetic flux measurements + quat, ... % quaternion defining rotation from sensor to NED axes + declination) % Estimated magnetic field delination at current location + +% calculate rotation from magnetometer to NED axes +Tmn = calcTmn(gPhi,gPsi,gTheta,quat(1),quat(2),quat(3),quat(4)); + +% Calculate the predicted magnetic declination +magMeasNED = Tmn*magMea; +predDec = atan2(magMeasNED(2),magMeasNED(1)); + +% Calculate the measurement innovation +innovation = predDec - declination; + +if (innovation > pi) + innovation = innovation - 2*pi; +elseif (innovation < -pi) + innovation = innovation + 2*pi; +end + +% form the NED rotation vector +deltaRotNED = -[0;0;innovation]; + +% rotate into sensor axes +deltaRotBody = transpose(Tsn)*deltaRotNED; + +% Convert the error rotation vector to its equivalent quaternion +% error = truth - estimate +rotationMag = abs(innovation); +if rotationMag<1e-6 + deltaQuat = single([1;0;0;0]); +else + deltaQuat = [cos(0.5*rotationMag); [deltaRotBody(1);deltaRotBody(2);deltaRotBody(3)]/rotationMag*sin(0.5*rotationMag)]; +end + +% Update the quaternion states by rotating from the previous attitude through +% the delta angle rotation quaternion +quat = [quat(1)*deltaQuat(1)-transpose(quat(2:4))*deltaQuat(2:4); quat(1)*deltaQuat(2:4) + deltaQuat(1)*quat(2:4) + cross(quat(2:4),deltaQuat(2:4))]; + +% normalise the updated quaternion states +quatMag = sqrt(quat(1)^2 + quat(2)^2 + quat(3)^2 + quat(4)^2); +if (quatMag > 1e-12) + quat = quat / quatMag; +end + +end \ No newline at end of file diff --git a/libraries/AP_NavEKF/Models/GimbalEstimatorExample/AlignTilt.m b/libraries/AP_NavEKF/Models/GimbalEstimatorExample/AlignTilt.m new file mode 100644 index 0000000000..fed5afc060 --- /dev/null +++ b/libraries/AP_NavEKF/Models/GimbalEstimatorExample/AlignTilt.m @@ -0,0 +1,20 @@ +function quat = AlignTilt( ... + quat, ... % quaternion state vector + initAccel) % initial accelerometer vector +% check length +lengthAccel = sqrt(dot([initAccel(1);initAccel(2);initAccel(3)],[initAccel(1);initAccel(2);initAccel(3)])); +% if length is > 0.7g and < 1.4g initialise tilt using gravity vector +if (lengthAccel > 5 && lengthAccel < 14) + % calculate length of the tilt vector + tiltMagnitude = atan2(sqrt(dot([initAccel(1);initAccel(2)],[initAccel(1);initAccel(2)])),-initAccel(3)); + % take the unit cross product of the accel vector and the -Z vector to + % give the tilt unit vector + if (tiltMagnitude > 1e-3) + tiltUnitVec = cross([initAccel(1);initAccel(2);initAccel(3)],[0;0;-1]); + tiltUnitVec = tiltUnitVec/sqrt(dot(tiltUnitVec,tiltUnitVec)); + tiltVec = tiltMagnitude*tiltUnitVec; + quat = [cos(0.5*tiltMagnitude); tiltVec/tiltMagnitude*sin(0.5*tiltMagnitude)]; + end +end + +end \ No newline at end of file diff --git a/libraries/AP_NavEKF/Models/GimbalEstimatorExample/C_code.txt b/libraries/AP_NavEKF/Models/GimbalEstimatorExample/C_code.txt new file mode 100644 index 0000000000..79a2051b21 --- /dev/null +++ b/libraries/AP_NavEKF/Models/GimbalEstimatorExample/C_code.txt @@ -0,0 +1,347 @@ +t2 = dax*(1.0/2.0); +t3 = dax_b*(1.0/2.0); +t4 = t2-t3; +t5 = day*(1.0/2.0); +t6 = day_b*(1.0/2.0); +t7 = t5-t6; +t8 = daz*(1.0/2.0); +t9 = daz_b*(1.0/2.0); +t10 = t8-t9; +t11 = q2*t4*(1.0/2.0); +t12 = q1*t7*(1.0/2.0); +t13 = q0*t10*(1.0/2.0); +t14 = q2*(1.0/2.0); +t15 = q3*t4*(1.0/2.0); +t16 = q1*t10*(1.0/2.0); +t17 = q1*(1.0/2.0); +t18 = q0*t4*(1.0/2.0); +t19 = q3*t7*(1.0/2.0); +t20 = q0*(1.0/2.0); +t21 = q2*t7*(1.0/2.0); +t22 = q3*t10*(1.0/2.0); +t23 = q0*t7*(1.0/2.0); +t24 = q3*(1.0/2.0); +t25 = q1*t4*(1.0/2.0); +t26 = q2*t10*(1.0/2.0); +t27 = t11+t12+t13-t24; +t28 = t14+t15+t16-t23; +t29 = q2*t28*2.0; +t30 = t17+t18+t19-t26; +t31 = q1*t30*2.0; +t32 = t20+t21+t22-t25; +t33 = q0*t32*2.0; +t40 = q3*t27*2.0; +t34 = t29+t31+t33-t40; +t35 = q0*q0; +t36 = q1*q1; +t37 = q2*q2; +t38 = q3*q3; +t39 = t35+t36+t37+t38; +t41 = t11+t12-t13+t24; +t42 = t14-t15+t16+t23; +t43 = q1*t42*2.0; +t44 = -t17+t18+t19+t26; +t45 = q2*t44*2.0; +t46 = t20-t21+t22+t25; +t47 = q3*t46*2.0; +t57 = q0*t41*2.0; +t48 = t43+t45+t47-t57; +t49 = -t14+t15+t16+t23; +t50 = q0*t49*2.0; +t51 = t11-t12+t13+t24; +t52 = t20+t21-t22+t25; +t53 = q2*t52*2.0; +t54 = t17-t18+t19+t26; +t55 = q3*t54*2.0; +t58 = q1*t51*2.0; +t56 = t50+t53+t55-t58; +t59 = OP[0][0]*t34; +t60 = OP[1][0]*t48; +t66 = OP[6][0]*t39; +t67 = OP[2][0]*t56; +t61 = t59+t60-t66-t67; +t62 = OP[0][1]*t34; +t63 = OP[1][1]*t48; +t64 = OP[0][2]*t34; +t65 = OP[1][2]*t48; +t71 = OP[6][1]*t39; +t72 = OP[2][1]*t56; +t68 = t62+t63-t71-t72; +t79 = OP[6][2]*t39; +t80 = OP[2][2]*t56; +t69 = t64+t65-t79-t80; +t70 = t35+t36-t37-t38; +t73 = q0*q2*2.0; +t74 = q1*q3*2.0; +t75 = t73+t74; +t76 = q0*q3*2.0; +t78 = q1*q2*2.0; +t77 = t76-t78; +t81 = t35-t36+t37-t38; +t82 = q0*q1*2.0; +t86 = q2*q3*2.0; +t83 = t82-t86; +t84 = t76+t78; +t85 = t35-t36-t37+t38; +t87 = t82+t86; +t88 = t73-t74; +t89 = OP[0][6]*t34; +t90 = OP[1][6]*t48; +t265 = OP[6][6]*t39; +t91 = t89+t90-t265-OP[2][6]*t56; +t92 = OP[0][7]*t34; +t93 = OP[1][7]*t48; +t266 = OP[6][7]*t39; +t94 = t92+t93-t266-OP[2][7]*t56; +t95 = OP[0][8]*t34; +t96 = OP[1][8]*t48; +t267 = OP[6][8]*t39; +t97 = t95+t96-t267-OP[2][8]*t56; +t98 = q0*t27*2.0; +t99 = q1*t28*2.0; +t100 = q3*t32*2.0; +t110 = q2*t30*2.0; +t101 = t98+t99+t100-t110; +t102 = q0*t46*2.0; +t103 = q2*t42*2.0; +t104 = q3*t41*2.0; +t111 = q1*t44*2.0; +t105 = t102+t103+t104-t111; +t106 = q1*t52*2.0; +t107 = q2*t51*2.0; +t108 = q3*t49*2.0; +t112 = q0*t54*2.0; +t109 = t106+t107+t108-t112; +t113 = OP[7][0]*t39; +t114 = OP[0][0]*t101; +t123 = OP[1][0]*t105; +t124 = OP[2][0]*t109; +t115 = t113+t114-t123-t124; +t116 = OP[7][1]*t39; +t117 = OP[0][1]*t101; +t129 = OP[1][1]*t105; +t130 = OP[2][1]*t109; +t118 = t116+t117-t129-t130; +t119 = OP[7][2]*t39; +t120 = OP[0][2]*t101; +t135 = OP[1][2]*t105; +t136 = OP[2][2]*t109; +t121 = t119+t120-t135-t136; +t122 = t39*t39; +t125 = q1*t27*2.0; +t126 = q2*t32*2.0; +t127 = q3*t30*2.0; +t170 = q0*t28*2.0; +t128 = t125+t126+t127-t170; +t131 = q0*t44*2.0; +t132 = q1*t46*2.0; +t133 = q2*t41*2.0; +t171 = q3*t42*2.0; +t134 = t131+t132+t133-t171; +t137 = q0*t52*2.0; +t138 = q1*t54*2.0; +t139 = q3*t51*2.0; +t172 = q2*t49*2.0; +t140 = t137+t138+t139-t172; +t141 = dvy*t70; +t142 = dvx*t77; +t143 = t141+t142; +t144 = dvx*t75; +t145 = dvy*t75; +t146 = dvz*t77; +t147 = t145+t146; +t148 = dvx*t81; +t188 = dvy*t84; +t149 = t148-t188; +t150 = dvz*t81; +t151 = dvy*t83; +t152 = t150+t151; +t153 = dvx*t83; +t154 = dvz*t84; +t155 = t153+t154; +t156 = dvx*t85; +t157 = dvz*t88; +t158 = t156+t157; +t159 = dvy*t85; +t189 = dvz*t87; +t160 = t159-t189; +t161 = dvx*t87; +t162 = dvy*t88; +t163 = t161+t162; +t164 = OP[7][6]*t39; +t165 = OP[0][6]*t101; +t166 = OP[7][7]*t39; +t167 = OP[0][7]*t101; +t168 = OP[7][8]*t39; +t169 = OP[0][8]*t101; +t173 = OP[8][0]*t39; +t174 = OP[1][0]*t134; +t182 = OP[0][0]*t128; +t183 = OP[2][0]*t140; +t175 = t173+t174-t182-t183; +t176 = OP[8][1]*t39; +t177 = OP[1][1]*t134; +t184 = OP[0][1]*t128; +t185 = OP[2][1]*t140; +t178 = t176+t177-t184-t185; +t179 = OP[8][2]*t39; +t180 = OP[1][2]*t134; +t186 = OP[0][2]*t128; +t187 = OP[2][2]*t140; +t181 = t179+t180-t186-t187; +t190 = OP[8][6]*t39; +t191 = OP[1][6]*t134; +t192 = OP[8][7]*t39; +t193 = OP[1][7]*t134; +t194 = OP[8][8]*t39; +t195 = OP[1][8]*t134; +t197 = dvz*t70; +t196 = t144-t197; +t198 = OP[0][0]*t147; +t204 = OP[2][0]*t143; +t205 = OP[1][0]*t196; +t199 = OP[3][0]+t198-t204-t205; +t200 = OP[0][1]*t147; +t206 = OP[2][1]*t143; +t207 = OP[1][1]*t196; +t201 = OP[3][1]+t200-t206-t207; +t202 = OP[0][2]*t147; +t208 = OP[2][2]*t143; +t209 = OP[1][2]*t196; +t203 = OP[3][2]+t202-t208-t209; +t210 = -t144+t197; +t211 = OP[1][0]*t210; +t212 = OP[3][0]+t198-t204+t211; +t213 = OP[1][1]*t210; +t214 = OP[3][1]+t200-t206+t213; +t215 = OP[1][2]*t210; +t216 = OP[3][2]+t202-t208+t215; +t217 = OP[0][6]*t147; +t218 = OP[0][7]*t147; +t219 = OP[0][8]*t147; +t220 = OP[1][0]*t155; +t221 = OP[2][0]*t149; +t229 = OP[0][0]*t152; +t222 = OP[4][0]+t220+t221-t229; +t223 = OP[1][1]*t155; +t224 = OP[2][1]*t149; +t230 = OP[0][1]*t152; +t225 = OP[4][1]+t223+t224-t230; +t226 = OP[1][2]*t155; +t227 = OP[2][2]*t149; +t231 = OP[0][2]*t152; +t228 = OP[4][2]+t226+t227-t231; +t232 = dvxNoise*t70*t84; +t233 = OP[1][6]*t155; +t234 = OP[2][6]*t149; +t235 = OP[4][6]+t233+t234-OP[0][6]*t152; +t236 = OP[1][7]*t155; +t237 = OP[2][7]*t149; +t238 = OP[4][7]+t236+t237-OP[0][7]*t152; +t239 = OP[1][8]*t155; +t240 = OP[2][8]*t149; +t241 = OP[4][8]+t239+t240-OP[0][8]*t152; +t242 = OP[2][0]*t163; +t243 = OP[0][0]*t160; +t251 = OP[1][0]*t158; +t244 = OP[5][0]+t242+t243-t251; +t245 = OP[2][1]*t163; +t246 = OP[0][1]*t160; +t252 = OP[1][1]*t158; +t247 = OP[5][1]+t245+t246-t252; +t248 = OP[2][2]*t163; +t249 = OP[0][2]*t160; +t253 = OP[1][2]*t158; +t250 = OP[5][2]+t248+t249-t253; +t254 = dvzNoise*t75*t85; +t255 = dvyNoise*t81*t87; +t256 = OP[2][6]*t163; +t257 = OP[0][6]*t160; +t258 = OP[5][6]+t256+t257-OP[1][6]*t158; +t259 = OP[2][7]*t163; +t260 = OP[0][7]*t160; +t261 = OP[5][7]+t259+t260-OP[1][7]*t158; +t262 = OP[2][8]*t163; +t263 = OP[0][8]*t160; +t264 = OP[5][8]+t262+t263-OP[1][8]*t158; +A0[0][0] = daxNoise*t122+t34*t61+t48*t68-t56*t69-t39*t91; +A0[0][0] = -t39*t94-t61*t101+t68*t105+t69*t109; +A0[0][1] = -t39*t97-t68*t134+t69*t140+t128*(t59+t60-t66-t67); +A0[0][2] = OP[0][3]*t34+OP[1][3]*t48-OP[2][3]*t56-OP[6][3]*t39-t69*t143+t147*(t59+t60-t66-t67)-t196*(t62+t63-t71-t72); +A0[0][3] = OP[0][4]*t34+OP[1][4]*t48-OP[2][4]*t56-OP[6][4]*t39-t61*t152+t69*t149+t155*(t62+t63-t71-t72); +A0[0][4] = OP[0][5]*t34+OP[1][5]*t48-OP[2][5]*t56-OP[6][5]*t39+t61*t160-t68*t158+t163*(t64+t65-t79-t80); +A0[0][5] = t91; +A0[0][6] = t94; +A0[0][7] = t97; +A0[0][0] = -t34*t115-t48*t118+t56*t121+t39*(t164+t165-OP[1][6]*t105-OP[2][6]*t109); +A0[0][0] = dayNoise*t122+t101*t115-t105*t118-t109*t121+t39*(t166+t167-OP[1][7]*t105-OP[2][7]*t109); +A0[0][1] = -t115*t128+t118*t134-t121*t140+t39*(t168+t169-OP[1][8]*t105-OP[2][8]*t109); +A0[0][2] = -OP[0][3]*t101-OP[7][3]*t39+OP[1][3]*t105+OP[2][3]*t109-t115*t147+t121*t143+t118*t196; +A0[0][3] = -OP[0][4]*t101-OP[7][4]*t39+OP[1][4]*t105+OP[2][4]*t109+t115*t152-t121*t149-t118*t155; +A0[0][4] = -OP[0][5]*t101-OP[7][5]*t39+OP[1][5]*t105+OP[2][5]*t109-t115*t160+t118*t158-t121*t163; +A0[0][5] = -t164-t165+OP[1][6]*t105+OP[2][6]*t109; +A0[0][6] = -t166-t167+OP[1][7]*t105+OP[2][7]*t109; +A0[0][7] = -t168-t169+OP[1][8]*t105+OP[2][8]*t109; +A0[1][0] = -t34*t175-t48*t178+t56*t181+t39*(t190+t191-OP[0][6]*t128-OP[2][6]*t140); +A0[1][0] = t101*t175-t105*t178-t109*t181+t39*(t192+t193-OP[0][7]*t128-OP[2][7]*t140); +A0[1][1] = dazNoise*t122-t128*t175+t134*t178-t140*t181+t39*(t194+t195-OP[0][8]*t128-OP[2][8]*t140); +A0[1][2] = -OP[8][3]*t39+OP[0][3]*t128-OP[1][3]*t134+OP[2][3]*t140-t147*t175+t143*t181+t178*t196; +A0[1][3] = -OP[8][4]*t39+OP[0][4]*t128-OP[1][4]*t134+OP[2][4]*t140+t152*t175-t149*t181-t155*t178; +A0[1][4] = -OP[8][5]*t39+OP[0][5]*t128-OP[1][5]*t134+OP[2][5]*t140-t160*t175+t158*t178-t163*t181; +A0[1][5] = -t190-t191+OP[0][6]*t128+OP[2][6]*t140; +A0[1][6] = -t192-t193+OP[0][7]*t128+OP[2][7]*t140; +A0[1][7] = -t194-t195+OP[0][8]*t128+OP[2][8]*t140; +A0[2][0] = -t39*(OP[3][6]+t217-OP[2][6]*t143-OP[1][6]*t196)+t34*t199+t48*t201-t56*t203; +A0[2][0] = -t39*(OP[3][7]+t218-OP[2][7]*t143-OP[1][7]*t196)-t101*t199+t105*t201+t109*t203; +A0[2][1] = -t39*(OP[3][8]+t219-OP[2][8]*t143-OP[1][8]*t196)+t128*t199-t134*t201+t140*t203; +A0[2][2] = OP[3][3]+OP[0][3]*t147-OP[2][3]*t143+OP[1][3]*t210-t143*t203+t147*t212+t210*t214+dvxNoise*(t70*t70)+dvyNoise*(t77*t77)+dvzNoise*(t75*t75); +A0[2][3] = OP[3][4]+t232+OP[0][4]*t147-OP[2][4]*t143+OP[1][4]*t210-t152*t212+t149*t216+t155*t214-dvyNoise*t77*t81-dvzNoise*t75*t83; +A0[2][4] = OP[3][5]+t254+OP[0][5]*t147-OP[2][5]*t143+OP[1][5]*t210-t158*t214+t160*t212+t163*t216-dvxNoise*t70*t88-dvyNoise*t77*t87; +A0[2][5] = OP[3][6]+t217-OP[2][6]*t143+OP[1][6]*t210; +A0[2][6] = OP[3][7]+t218-OP[2][7]*t143+OP[1][7]*t210; +A0[2][7] = OP[3][8]+t219-OP[2][8]*t143+OP[1][8]*t210; +A0[3][0] = t34*t222+t48*t225-t39*t235-t56*t228; +A0[3][0] = -t39*t238-t101*t222+t105*t225+t109*t228; +A0[3][1] = -t39*t241+t128*t222-t134*t225+t140*t228; +A0[3][2] = OP[4][3]+t232-OP[0][3]*t152+OP[1][3]*t155+OP[2][3]*t149+t147*t222-t143*t228+t210*t225-dvyNoise*t77*t81-dvzNoise*t75*t83; +A0[3][3] = OP[4][4]-OP[0][4]*t152+OP[1][4]*t155+OP[2][4]*t149-t152*t222+t149*t228+t155*t225+dvxNoise*(t84*t84)+dvyNoise*(t81*t81)+dvzNoise*(t83*t83); +A0[3][4] = OP[4][5]+t255-OP[0][5]*t152+OP[1][5]*t155+OP[2][5]*t149+t160*t222-t158*t225+t163*t228-dvxNoise*t84*t88-dvzNoise*t83*t85; +A0[3][5] = t235; +A0[3][6] = t238; +A0[3][7] = t241; +A0[4][0] = t34*t244+t48*t247-t39*t258-t56*t250; +A0[4][0] = -t39*t261-t101*t244+t105*t247+t109*t250; +A0[4][1] = -t39*t264+t128*t244-t134*t247+t140*t250; +A0[4][2] = OP[5][3]+t254+OP[0][3]*t160-OP[1][3]*t158+OP[2][3]*t163+t147*t244-t143*t250+t210*t247-dvxNoise*t70*t88-dvyNoise*t77*t87; +A0[4][3] = OP[5][4]+t255+OP[0][4]*t160-OP[1][4]*t158+OP[2][4]*t163-t152*t244+t149*t250+t155*t247-dvxNoise*t84*t88-dvzNoise*t83*t85; +A0[4][4] = OP[5][5]+OP[0][5]*t160-OP[1][5]*t158+OP[2][5]*t163+t160*t244-t158*t247+t163*t250+dvxNoise*(t88*t88)+dvyNoise*(t87*t87)+dvzNoise*(t85*t85); +A0[4][5] = t258; +A0[4][6] = t261; +A0[4][7] = t264; +A0[5][0] = -t265+OP[6][0]*t34+OP[6][1]*t48-OP[6][2]*t56; +A0[5][0] = -t266-OP[6][0]*t101+OP[6][1]*t105+OP[6][2]*t109; +A0[5][1] = -t267+OP[6][0]*t128-OP[6][1]*t134+OP[6][2]*t140; +A0[5][2] = OP[6][3]-OP[6][2]*t143+OP[6][0]*t147+OP[6][1]*t210; +A0[5][3] = OP[6][4]+OP[6][2]*t149-OP[6][0]*t152+OP[6][1]*t155; +A0[5][4] = OP[6][5]-OP[6][1]*t158+OP[6][0]*t160+OP[6][2]*t163; +A0[5][5] = OP[6][6]; +A0[5][6] = OP[6][7]; +A0[5][7] = OP[6][8]; +A0[6][0] = -t164+OP[7][0]*t34+OP[7][1]*t48-OP[7][2]*t56; +A0[6][0] = -t166-OP[7][0]*t101+OP[7][1]*t105+OP[7][2]*t109; +A0[6][1] = -t168+OP[7][0]*t128-OP[7][1]*t134+OP[7][2]*t140; +A0[6][2] = OP[7][3]-OP[7][2]*t143+OP[7][0]*t147+OP[7][1]*t210; +A0[6][3] = OP[7][4]+OP[7][2]*t149-OP[7][0]*t152+OP[7][1]*t155; +A0[6][4] = OP[7][5]-OP[7][1]*t158+OP[7][0]*t160+OP[7][2]*t163; +A0[6][5] = OP[7][6]; +A0[6][6] = OP[7][7]; +A0[6][7] = OP[7][8]; +A0[7][0] = -t190+OP[8][0]*t34+OP[8][1]*t48-OP[8][2]*t56; +A0[7][0] = -t192-OP[8][0]*t101+OP[8][1]*t105+OP[8][2]*t109; +A0[7][1] = -t194+OP[8][0]*t128-OP[8][1]*t134+OP[8][2]*t140; +A0[7][2] = OP[8][3]-OP[8][2]*t143+OP[8][0]*t147+OP[8][1]*t210; +A0[7][3] = OP[8][4]+OP[8][2]*t149-OP[8][0]*t152+OP[8][1]*t155; +A0[7][4] = OP[8][5]-OP[8][1]*t158+OP[8][0]*t160+OP[8][2]*t163; +A0[7][5] = OP[8][6]; +A0[7][6] = OP[8][7]; +A0[7][7] = OP[8][8]; diff --git a/libraries/AP_NavEKF/Models/GimbalEstimatorExample/FixAutoGenCCode.m b/libraries/AP_NavEKF/Models/GimbalEstimatorExample/FixAutoGenCCode.m new file mode 100644 index 0000000000..50e1041990 --- /dev/null +++ b/libraries/AP_NavEKF/Models/GimbalEstimatorExample/FixAutoGenCCode.m @@ -0,0 +1,94 @@ +function FixAutoGenCCode(fileName) +%% Initialize variables +delimiter = ''; + +%% Format string for each line of text: +% column1: text (%s) +% For more information, see the TEXTSCAN documentation. +formatSpec = '%s%[^\n\r]'; + +%% Open the text file. +fileID = fopen(strcat(fileName,'.c'),'r'); + +%% Read columns of data according to format string. +% This call is based on the structure of the file used to generate this +% code. If an error occurs for a different file, try regenerating the code +% from the Import Tool. +dataArray = textscan(fileID, formatSpec, 'Delimiter', delimiter, 'ReturnOnError', false); + +%% Close the text file. +fclose(fileID); + +%% Create output variable +SymbolicOutput = [dataArray{1:end-1}]; + +%% Clear temporary variables +clearvars filename delimiter formatSpec fileID dataArray ans; + +%% Convert 1 based indexes in symbolic array variables +for lineIndex = 1:length(SymbolicOutput) + SymbolicOutput(lineIndex) = regexprep(SymbolicOutput(lineIndex), '_l_', '('); + SymbolicOutput(lineIndex) = regexprep(SymbolicOutput(lineIndex), '_c_', ','); + SymbolicOutput(lineIndex) = regexprep(SymbolicOutput(lineIndex), '_r_', ')'); +end + +% replace 2-D left indexes +for arrayIndex = 1:99 + strIndex = int2str(arrayIndex); + strRep = sprintf('[%d,',(arrayIndex-1)); + strPat = strcat('\(',strIndex,'\,'); + for lineIndex = 1:length(SymbolicOutput) + str = char(SymbolicOutput(lineIndex)); + SymbolicOutput(lineIndex) = {regexprep(str, strPat, strRep)}; + end +end + +% replace 2-D right indexes +for arrayIndex = 1:99 + strIndex = int2str(arrayIndex); + strRep = sprintf(',%d]',(arrayIndex-1)); + strPat = strcat('\,',strIndex,'\)'); + for lineIndex = 1:length(SymbolicOutput) + str = char(SymbolicOutput(lineIndex)); + SymbolicOutput(lineIndex) = {regexprep(str, strPat, strRep)}; + end +end + +% replace commas +for lineIndex = 1:length(SymbolicOutput) + str = char(SymbolicOutput(lineIndex)); + SymbolicOutput(lineIndex) = {regexprep(str, '\,', '][')}; +end + +%% add float declarations in front of temporary variables +expression = 't(\w*) ='; +replace = 'float t$1 ='; +for lineIndex = 1:length(SymbolicOutput) + SymbolicOutput(lineIndex) = regexprep(SymbolicOutput(lineIndex),expression,replace); +end + +%% replace (1.0/2.0) with 0.5f +expression = '\(1.0/2.0\)'; +replace = '0.5f'; +for lineIndex = 1:length(SymbolicOutput) + SymbolicOutput(lineIndex) = regexprep(SymbolicOutput(lineIndex),expression,replace); +end + +%% replace 2.0 +expression = '2\.0'; +replace = '2.0f'; +for lineIndex = 1:length(SymbolicOutput) + SymbolicOutput(lineIndex) = regexprep(SymbolicOutput(lineIndex),expression,replace); +end + +%% Write to file +fileName = strcat(fileName,'.cpp'); +fid = fopen(fileName,'wt'); +for lineIndex = 1:length(SymbolicOutput) + fprintf(fid,char(SymbolicOutput(lineIndex))); + fprintf(fid,'\n'); +end +fclose(fid); +clear all; + +end diff --git a/libraries/AP_NavEKF/Models/GimbalEstimatorExample/FuseMagnetometer.m b/libraries/AP_NavEKF/Models/GimbalEstimatorExample/FuseMagnetometer.m new file mode 100644 index 0000000000..5548d8c424 --- /dev/null +++ b/libraries/AP_NavEKF/Models/GimbalEstimatorExample/FuseMagnetometer.m @@ -0,0 +1,91 @@ +function [... + nextQuat, ... % quaternion state vector after fusion of measurements + nextStates, ... % state vector after fusion of measurements + nextP, ... % state covariance matrix after fusion of corrections + innovation, ... % Declination innovation - rad + varInnov] ... % + = FuseMagnetometer( ... + quat, ... % predicted quaternion states + states, ... % predicted states + P, ... % predicted covariance + magData, ... % body frame magnetic flux measurements + decl, ... % magnetic field declination from true north + gPhi, gPsi, gTheta) % gimbal yaw, roll, pitch angles + +q0 = quat(1); +q1 = quat(2); +q2 = quat(3); +q3 = quat(4); + +magX = magData(1); +magY = magData(2); +magZ = magData(3); + +R_MAG = 0.1745^2; + +% Calculate observation Jacobian +H = calcH_MAG(gPhi,gPsi,gTheta,magX,magY,magZ,q0,q1,q2,q3); +% Calculate innovation variance and Kalman gains +% Take advantage of the fact that only the first 3 elements in H are non zero +varInnov = (H(1,1:3)*P(1:3,1:3)*transpose(H(1,1:3)) + R_MAG); +Kfusion = (P(:,1:3)*transpose(H(1,1:3)))/varInnov; + +% Calculate the innovation +innovation = calcMagAng(decl,gPhi,gPsi,gTheta,magX,magY,magZ,q0,q1,q2,q3); + +if (innovation > pi) + innovation = innovation - 2*pi; +elseif (innovation < -pi) + innovation = innovation + 2*pi; +end +if (innovation > 0.5) + innovation = 0.5; +elseif (innovation < -0.5) + innovation = -0.5; +end + +% correct the state vector +states(1:3) = 0; +states = states - Kfusion * innovation; + +% the first 3 states represent the angular misalignment vector. This is +% is used to correct the estimate quaternion +% Convert the error rotation vector to its equivalent quaternion +% error = truth - estimate +rotationMag = sqrt(states(1)^2 + states(2)^2 + states(3)^2); +if rotationMag<1e-6 + deltaQuat = single([1;0;0;0]); +else + deltaQuat = [cos(0.5*rotationMag); [states(1);states(2);states(3)]/rotationMag*sin(0.5*rotationMag)]; +end + +% Update the quaternion states by rotating from the previous attitude through +% the delta angle rotation quaternion +nextQuat = [quat(1)*deltaQuat(1)-transpose(quat(2:4))*deltaQuat(2:4); quat(1)*deltaQuat(2:4) + deltaQuat(1)*quat(2:4) + cross(quat(2:4),deltaQuat(2:4))]; + +% normalise the updated quaternion states +quatMag = sqrt(nextQuat(1)^2 + nextQuat(2)^2 + nextQuat(3)^2 + nextQuat(4)^2); +if (quatMag > 1e-6) + nextQuat = nextQuat / quatMag; +end + +% correct the covariance P = P - K*H*P +% Take advantage of the fact that only the first 3 elements in H are non zero +P = P - Kfusion*H(1,1:3)*P(1:3,:); + +% Force symmetry on the covariance matrix to prevent ill-conditioning +% of the matrix which would cause the filter to blow-up +P = 0.5*(P + transpose(P)); + +% ensure diagonals are positive +for i=1:9 + if P(i,i) < 0 + P(i,i) = 0; + end +end + +% Set default output for states and covariance +nextP = P; +nextStates = states; + +end \ No newline at end of file diff --git a/libraries/AP_NavEKF/Models/GimbalEstimatorExample/FuseVelocity.m b/libraries/AP_NavEKF/Models/GimbalEstimatorExample/FuseVelocity.m new file mode 100644 index 0000000000..4818428a5e --- /dev/null +++ b/libraries/AP_NavEKF/Models/GimbalEstimatorExample/FuseVelocity.m @@ -0,0 +1,72 @@ +function [... + quat, ... % quaternion state vector after fusion of measurements + states, ... % state vector after fusion of measurements + tiltErr, ... % angle error + P, ... % state covariance matrix after fusion of corrections + innovation,... % NED velocity innovations (m/s) + varInnov] ... % NED velocity innovation variance ((m/s)^2) + = FuseVelocity( ... + quat, ... % predicted quaternion states from the INS + states, ... % predicted states from the INS + P, ... % predicted covariance + measVel) % NED velocity measurements (m/s) + +R_OBS = 0.5^2; +innovation = zeros(1,3); +varInnov = zeros(1,3); +% Fuse measurements sequentially +angErrVec = [0;0;0]; +for obsIndex = 1:3 + stateIndex = 3 + obsIndex; + % Calculate the velocity measurement innovation + innovation(obsIndex) = states(stateIndex) - measVel(obsIndex); + + % Calculate the Kalman Gain taking advantage of direct state observation + H = zeros(1,9); + H(1,stateIndex) = 1; + varInnov(obsIndex) = P(stateIndex,stateIndex) + R_OBS; + K = P(:,stateIndex)/varInnov(obsIndex); + + % Calculate state corrections + xk = K * innovation(obsIndex); + + % Apply the state corrections + states(1:3) = 0; + states = states - xk; + + % Store tilt error estimate for external monitoring + angErrVec = angErrVec + states(1:3); + + % the first 3 states represent the angular misalignment vector. This is + % is used to correct the estimated quaternion + % Convert the error rotation vector to its equivalent quaternion + % truth = estimate + error + rotationMag = sqrt(states(1)^2 + states(2)^2 + states(3)^2); + if rotationMag > 1e-12 + deltaQuat = [cos(0.5*rotationMag); [states(1);states(2);states(3)]/rotationMag*sin(0.5*rotationMag)]; + % Update the quaternion states by rotating from the previous attitude through + % the error quaternion + quat = QuatMult(quat,deltaQuat); + % re-normalise the quaternion + quatMag = sqrt(quat(1)^2 + quat(2)^2 + quat(3)^2 + quat(4)^2); + quat = quat / quatMag; + end + + % Update the covariance + P = P - K*P(stateIndex,:); + + % Force symmetry on the covariance matrix to prevent ill-conditioning + P = 0.5*(P + transpose(P)); + + % ensure diagonals are positive + for i=1:9 + if P(i,i) < 0 + P(i,i) = 0; + end + end + +end + +tiltErr = sqrt(dot(angErrVec(1:2),angErrVec(1:2))); + +end \ No newline at end of file diff --git a/libraries/AP_NavEKF/Models/GimbalEstimatorExample/GenerateEquations.m b/libraries/AP_NavEKF/Models/GimbalEstimatorExample/GenerateEquations.m new file mode 100644 index 0000000000..66185dd98a --- /dev/null +++ b/libraries/AP_NavEKF/Models/GimbalEstimatorExample/GenerateEquations.m @@ -0,0 +1,241 @@ +% IMPORTANT - This script requires the Matlab symbolic toolbox + +% Author: Paul Riseborough +% Last Modified: 16 Feb 2015 + +% Derivation of a 3-axis gimbal attitude estimator using a local NED earth Tangent +% Frame. Based on use of a rotation vector for attitude estimation as described +% here: + +% Mark E. Pittelkau. "Rotation Vector in Attitude Estimation", +% Journal of Guidance, Control, and Dynamics, Vol. 26, No. 6 (2003), +% pp. 855-860. + +% The gimbal is assumed to have the following characteristics: + +% A three axis gimbal having a fixed top plate mounted to the vehicle body with a magnetometer +% Yaw, roll and pitch degrees of freedom (yaw, roll, pitch Euler sequence) +% with angle measurements on each gimbal axis +% IMU measuring delta angles and delta velocites mounted on the +% camera/sensor assembly +% When the gimbal joints are all at zero degrees, the sensor assembly X,Y,Z +% axis is aligned with the top plate X,Y,Z axis + +% State vector: +% error rotation vector - X,Y,Z (rad) +% Velocity - North, East, Down (m/s) +% Delta Angle bias - X,Y,Z (rad) +% Delta Velocity Bias - X,Y,Z (m/s) + +% Observations: +% NED velocity - N,E,D (m/s) +% sensor fixed magnetic field vector of base - X,Y,Z + + +% Time varying parameters: +% XYZ delta angle measurements in sensor axes - rad +% XYZ delta velocity measurements in sensor axes - m/sec +% yaw, roll, pitch gimbal rotation angles + +%% define symbolic variables and constants +clear all; + +% specify if we want to incorporate accerometer bias estimation into the +% filter, 0 = no, 1 = yes +f_accBiasEst = 0; + +syms dax day daz real % IMU delta angle measurements in sensor axes - rad +syms dvx dvy dvz real % IMU delta velocity measurements in sensor axes - m/sec +syms q0 q1 q2 q3 real % quaternions defining attitude of sensor axes relative to local NED +syms vn ve vd real % NED velocity - m/sec +syms dax_b day_b daz_b real % delta angle bias - rad +syms dvx_b dvy_b dvz_b real % delta velocity bias - m/sec +syms dt real % IMU time step - sec +syms gravity real % gravity - m/sec^2 +syms daxNoise dayNoise dazNoise dvxNoise dvyNoise dvzNoise real; % IMU delta angle and delta velocity measurement noise +syms vwn vwe real; % NE wind velocity - m/sec +syms magX magY magZ real; % XYZ top plate magnetic field measurements - milligauss +syms magN magE magD real; % NED earth fixed magnetic field components - milligauss +syms R_VN R_VE R_VD real % variances for NED velocity measurements - (m/sec)^2 +syms R_MAG real % variance for magnetic flux measurements - milligauss^2 +syms rotErr1 rotErr2 rotErr3 real; % error rotation vector +syms decl real; % earth magnetic field declination from true north +syms gPsi gPhi gTheta real; % gimbal joint angles yaw, roll, pitch (rad) + +%% define the process equations + +% define the measured Delta angle and delta velocity vectors +dAngMeas = [dax; day; daz]; +dVelMeas = [dvx; dvy; dvz]; + +% define the delta angle bias errors +dAngBias = [dax_b; day_b; daz_b]; + +% define the delta velocity bias errors +if (f_accBiasEst > 0) + dVelBias = [dvx_b; dvy_b; dvz_b]; +else + dVelBias = [0; 0; 0]; +end + +% define the quaternion rotation vector for the state estimate +estQuat = [q0;q1;q2;q3]; + +% define the attitude error rotation vector, where error = truth - estimate +errRotVec = [rotErr1;rotErr2;rotErr3]; + +% define the attitude error quaternion using a first order linearisation +errQuat = [1;0.5*errRotVec]; + +% Define the truth quaternion as the estimate + error +truthQuat = QuatMult(estQuat, errQuat); + +% derive the truth sensor to nav direction cosine matrix +Tsn = Quat2Tbn(truthQuat); + +% define the truth delta angle +% ignore coning acompensation as these effects are negligible in terms of +% covariance growth for our application and grade of sensor +dAngTruth = dAngMeas - dAngBias - [daxNoise;dayNoise;dazNoise]; + +% Define the truth delta velocity +dVelTruth = dVelMeas - dVelBias - [dvxNoise;dvyNoise;dvzNoise]; + +% define the attitude update equations +% use a first order expansion of rotation to calculate the quaternion increment +% acceptable for propagation of covariances +deltaQuat = [1; + 0.5*dAngTruth(1); + 0.5*dAngTruth(2); + 0.5*dAngTruth(3); + ]; +truthQuatNew = QuatMult(truthQuat,deltaQuat); +% calculate the updated attitude error quaternion with respect to the previous estimate +errQuatNew = QuatDivide(truthQuatNew,estQuat); +% change to a rotaton vector - this is the error rotation vector updated state +errRotNew = 2 * [errQuatNew(2);errQuatNew(3);errQuatNew(4)]; + +% define the velocity update equations +% ignore coriolis terms for linearisation purposes +vNew = [vn;ve;vd] + [0;0;gravity]*dt + Tsn*dVelTruth; + +% define the IMU bias error update equations +dabNew = dAngBias; +dvbNew = dVelBias; + +% Define the state vector & number of states +if (f_accBiasEst > 0) + stateVector = [errRotVec;vn;ve;vd;dAngBias;dVelBias]; +else + stateVector = [errRotVec;vn;ve;vd;dAngBias]; +end +nStates=numel(stateVector); + +save 'symeqns.mat'; + +%% derive the filter Jacobians + +% Define the control (disturbance) vector. Error growth in the inertial +% solution is assumed to be driven by 'noise' in the delta angles and +% velocities, after bias effects have been removed. This is OK becasue we +% have sensor bias accounted for in the state equations. +distVector = [daxNoise;dayNoise;dazNoise;dvxNoise;dvyNoise;dvzNoise]; + +% derive the control(disturbance) influence matrix +if (f_accBiasEst > 0) + predictedState = [errRotNew;vNew;dabNew;dvbNew]; +else + predictedState = [errRotNew;vNew;dabNew]; +end +G = jacobian(predictedState, distVector); +G = subs(G, {'rotErr1', 'rotErr2', 'rotErr3'}, {0,0,0}); + +% derive the state error matrix +distMatrix = diag(distVector); +Q = G*distMatrix*transpose(G); +%matlabFunction(Q,'file','calcQ.m'); + +% derive the state transition matrix +vNew = subs(vNew,{'daxNoise','dayNoise','dazNoise','dvxNoise','dvyNoise','dvzNoise'}, {0,0,0,0,0,0}); +errRotNew = subs(errRotNew,{'daxNoise','dayNoise','dazNoise','dvxNoise','dvyNoise','dvzNoise'}, {0,0,0,0,0,0}); +% Define the state vector & number of states +if (f_accBiasEst) + predictedState = [errRotNew;vNew;dabNew;dvbNew]; +else + predictedState = [errRotNew;vNew;dabNew]; +end +F = jacobian(predictedState, stateVector); +F = subs(F, {'rotErr1', 'rotErr2', 'rotErr3'}, {0,0,0}); +%matlabFunction(F,'file','calcF.m'); + +%% Derive the predicted covariance +% This reduces the number of floating point operations by a factor of 4 or +% more compared to using the standard matrix operations in code +% define a symbolic covariance matrix using strings to represent +% '_l_' to represent '( ' +% '_c_' to represent , +% '_r_' to represent ')' +% these can be substituted later to create executable code +for rowIndex = 1:nStates + for colIndex = 1:nStates + eval(['syms OP_l_',num2str(rowIndex),'_c_',num2str(colIndex), '_r_ real']); + eval(['P(',num2str(rowIndex),',',num2str(colIndex), ') = OP_l_',num2str(rowIndex),'_c_',num2str(colIndex),'_r_;']); + end +end +% Derive the predicted covariance matrix using the standard equation +PP = F*P*transpose(F) + Q; +%matlabFunction(PP,'file','calcP.m'); +ccode(PP,'file','calcP.c'); +FixCode('calcP'); + +% free up memory +clear all; +reset(symengine); + +%% derive equations for fusion of magnetic deviation measurement + +load('symeqns.mat'); + +% Define rotation from magnetometer to yaw gimbal +T3 = [ cos(gPsi) sin(gPsi) 0; ... + -sin(gPsi) cos(gPsi) 0; ... + 0 0 1]; +% Define rotation from yaw gimbal to roll gimbal +T1 = [ 1 0 0; ... + 0 cos(gPhi) sin(gPhi); ... + 0 -sin(gPhi) cos(gPhi)]; +% Define rotation from roll gimbal to pitch gimbal +T2 = [ cos(gTheta) 0 -sin(gTheta); ... + 0 1 0; ... + sin(gTheta) 0 cos(gTheta)]; +% Define rotation from magnetometer to sensor using a 312 rotation sequence +Tms = T2*T1*T3; +% Define rotation from magnetometer to nav axes +Tmn = Tsn*Tms; + +save 'symeqns.mat'; + +% rotate magentic field measured at top plate into nav axes +magMeasNED = Tmn*[magX;magY;magZ]; +% the predicted measurement is the angle wrt magnetic north of the horizontal +% component of the measured field +angMeas = tan(magMeasNED(2)/magMeasNED(1)) - decl; +H_MAG = jacobian(angMeas,stateVector); % measurement Jacobian +H_MAG = subs(H_MAG, {'rotErr1', 'rotErr2', 'rotErr3'}, {0,0,0}); +H_MAG = H_MAG(1:3); +H_MAG = simplify(H_MAG); +% matlabFunction(H_MAG,'file','calcH_MAG.m'); +ccode(H_MAG,'file','calcH_MAG.c'); +FixCode('calcH_MAG'); + +% free up memory +clear all; +reset(symengine); + +%% generate helper functions + +load 'symeqns.mat'; + +matlabFunction(Tms,'file','calcTms.m'); +Tmn = subs(Tmn, {'rotErr1', 'rotErr2', 'rotErr3'}, {0,0,0}); +matlabFunction(Tmn,'file','calcTmn.m'); diff --git a/libraries/AP_NavEKF/Models/GimbalEstimatorExample/PlotData.m b/libraries/AP_NavEKF/Models/GimbalEstimatorExample/PlotData.m new file mode 100644 index 0000000000..705ab5b1e8 --- /dev/null +++ b/libraries/AP_NavEKF/Models/GimbalEstimatorExample/PlotData.m @@ -0,0 +1,65 @@ +%% plot gyro bias estimates +figure; +plot(EKFlogs.time,EKFlogs.states(7:9,:)/dtSlow*180/pi); +grid on; +ylabel('Gyro Bias Estimate (deg/sec)'); +xlabel('time (sec)'); +hold on; +plot([min(time),max(time)],[gyroBias,gyroBias]*180/pi); +hold off; + +%% plot velocity +figure; +plot(EKFlogs.time,EKFlogs.states(4:6,:)); +grid on; +ylabel('Velocity (m/sec)'); +xlabel('time (sec)'); + +%% calculate and plot tilt correction magnitude +figure; +plot(EKFlogs.time,EKFlogs.tiltCorr); +grid on; +ylabel('Tilt Correction Magnitude (rad)'); +xlabel('time (sec)'); + +%% plot velocity innovations +figure; +subplot(3,1,1);plot(EKFlogs.time,[EKFlogs.velInnov(1,:);sqrt(EKFlogs.velInnovVar(1,:));-sqrt(EKFlogs.velInnovVar(1,:))]'); +grid on; +ylabel('VelN Innovations (m)'); +subplot(3,1,2);plot(EKFlogs.time,[EKFlogs.velInnov(2,:);sqrt(EKFlogs.velInnovVar(2,:));-sqrt(EKFlogs.velInnovVar(2,:))]'); +grid on; +ylabel('VelE Innovations (m)'); +subplot(3,1,3);plot(EKFlogs.time,[EKFlogs.velInnov(3,:);sqrt(EKFlogs.velInnovVar(3,:));-sqrt(EKFlogs.velInnovVar(3,:))]'); +grid on; +ylabel('VelD Innovations (m)'); +xlabel('time (sec)'); + +%% plot compass innovations +figure; +plot(EKFlogs.time,[EKFlogs.decInnov;sqrt(EKFlogs.decInnovVar);-sqrt(EKFlogs.decInnovVar)]'); +grid on; +ylabel('Compass Innovations (rad)'); +xlabel('time (sec)'); + +%% plot Euler angle estimates +figure; +subplot(3,1,1);plot(gimbal.time,gimbal.euler(1,:)*180/pi); +ylabel('Roll (deg)');grid on; +subplot(3,1,2);plot(gimbal.time,gimbal.euler(2,:)*180/pi); +ylabel('Pitch (deg)');grid on; +subplot(3,1,3);plot(gimbal.time,gimbal.euler(3,:)*180/pi); +ylabel('Yaw (deg)'); +grid on; +xlabel('time (sec)'); + +%% plot Euler angle error estimates +figure; +subplot(3,1,1);plot(gimbal.time,gimbal.eulerError(1,:)*180/pi); +ylabel('Roll Error (deg)');grid on; +subplot(3,1,2);plot(gimbal.time,gimbal.eulerError(2,:)*180/pi); +ylabel('Pitch Error (deg)');grid on; +subplot(3,1,3);plot(gimbal.time,gimbal.eulerError(3,:)*180/pi); +ylabel('Yaw Error (deg)'); +grid on; +xlabel('time (sec)'); \ No newline at end of file diff --git a/libraries/AP_NavEKF/Models/GimbalEstimatorExample/PredictCovariance.m b/libraries/AP_NavEKF/Models/GimbalEstimatorExample/PredictCovariance.m new file mode 100644 index 0000000000..94e871aeb6 --- /dev/null +++ b/libraries/AP_NavEKF/Models/GimbalEstimatorExample/PredictCovariance.m @@ -0,0 +1,61 @@ +function P = PredictCovariance(deltaAngle, ... + deltaVelocity, ... + quat, ... + states,... + P, ... % Previous state covariance matrix + dt) ... % IMU and prediction time step + +% Set filter state process noise other than IMU errors, which are already +% built into the derived covariance predition equations. +% This process noise determines the rate of estimation of IMU bias errors +dAngBiasSigma = dt*dt*5E-4; % delta angle bias process noise (rad) +processNoise = [0*ones(1,6), dAngBiasSigma*[1 1 1]]; + +% Specify the estimated errors on the IMU delta angles and delta velocities +% Allow for 0.5 deg/sec of gyro error +daxNoise = (dt*0.5*pi/180)^2; +dayNoise = (dt*0.5*pi/180)^2; +dazNoise = (dt*0.5*pi/180)^2; +% Allow for 0.5 m/s/s of accelerometer error +dvxNoise = (dt*0.5)^2; +dvyNoise = (dt*0.5)^2; +dvzNoise = (dt*0.5)^2; + +dvx = deltaVelocity(1); +dvy = deltaVelocity(2); +dvz = deltaVelocity(3); +dax = deltaAngle(1); +day = deltaAngle(2); +daz = deltaAngle(3); + +q0 = quat(1); +q1 = quat(2); +q2 = quat(3); +q3 = quat(4); + +dax_b = states(7); +day_b = states(8); +daz_b = states(9); + +% Predicted covariance +F = calcF(dax,dax_b,day,day_b,daz,daz_b,dvx,dvy,dvz,q0,q1,q2,q3); +Q = calcQ(daxNoise,dayNoise,dazNoise,dvxNoise,dvyNoise,dvzNoise,q0,q1,q2,q3); +P = F*P*transpose(F) + Q; + +% Add the general process noise +for i = 1:9 + P(i,i) = P(i,i) + processNoise(i)^2; +end + +% Force symmetry on the covariance matrix to prevent ill-conditioning +% of the matrix which would cause the filter to blow-up +P = 0.5*(P + transpose(P)); + +% ensure diagonals are positive +for i=1:9 + if P(i,i) < 0 + P(i,i) = 0; + end +end + +end \ No newline at end of file diff --git a/libraries/AP_NavEKF/Models/GimbalEstimatorExample/PredictCovarianceOptimised.m b/libraries/AP_NavEKF/Models/GimbalEstimatorExample/PredictCovarianceOptimised.m new file mode 100644 index 0000000000..a6675b6e1a --- /dev/null +++ b/libraries/AP_NavEKF/Models/GimbalEstimatorExample/PredictCovarianceOptimised.m @@ -0,0 +1,404 @@ +function nextP = PredictCovarianceOptimised(deltaAngle, ... + deltaVelocity, ... + quat, ... + states,... + P, ... % Previous state covariance matrix + dt) ... % IMU and prediction time step + +% Set filter state process noise other than IMU errors, which are already +% built into the derived covariance predition equations. +% This process noise determines the rate of estimation of IMU bias errors +dAngBiasSigma = dt*dt*5E-4; % delta angle bias process noise (rad) +processNoise = [0*ones(1,6), dAngBiasSigma*[1 1 1]]; + +% Specify the estimated errors on the IMU delta angles and delta velocities +% Allow for 0.5 deg/sec of gyro error +daxNoise = (dt*0.5*pi/180)^2; +dayNoise = (dt*0.5*pi/180)^2; +dazNoise = (dt*0.5*pi/180)^2; +% Allow for 0.5 m/s/s of accelerometer error +dvxNoise = (dt*0.5)^2; +dvyNoise = (dt*0.5)^2; +dvzNoise = (dt*0.5)^2; + +dvx = deltaVelocity(1); +dvy = deltaVelocity(2); +dvz = deltaVelocity(3); +dax = deltaAngle(1); +day = deltaAngle(2); +daz = deltaAngle(3); + +q0 = quat(1); +q1 = quat(2); +q2 = quat(3); +q3 = quat(4); + +dax_b = states(7); +day_b = states(8); +daz_b = states(9); + +t1365 = dax*0.5; +t1366 = dax_b*0.5; +t1367 = t1365-t1366; +t1368 = day*0.5; +t1369 = day_b*0.5; +t1370 = t1368-t1369; +t1371 = daz*0.5; +t1372 = daz_b*0.5; +t1373 = t1371-t1372; +t1374 = q2*t1367*0.5; +t1375 = q1*t1370*0.5; +t1376 = q0*t1373*0.5; +t1377 = q2*0.5; +t1378 = q3*t1367*0.5; +t1379 = q1*t1373*0.5; +t1380 = q1*0.5; +t1381 = q0*t1367*0.5; +t1382 = q3*t1370*0.5; +t1383 = q0*0.5; +t1384 = q2*t1370*0.5; +t1385 = q3*t1373*0.5; +t1386 = q0*t1370*0.5; +t1387 = q3*0.5; +t1388 = q1*t1367*0.5; +t1389 = q2*t1373*0.5; +t1390 = t1374+t1375+t1376-t1387; +t1391 = t1377+t1378+t1379-t1386; +t1392 = q2*t1391*2.0; +t1393 = t1380+t1381+t1382-t1389; +t1394 = q1*t1393*2.0; +t1395 = t1383+t1384+t1385-t1388; +t1396 = q0*t1395*2.0; +t1403 = q3*t1390*2.0; +t1397 = t1392+t1394+t1396-t1403; +t1398 = q0^2; +t1399 = q1^2; +t1400 = q2^2; +t1401 = q3^2; +t1402 = t1398+t1399+t1400+t1401; +t1404 = t1374+t1375-t1376+t1387; +t1405 = t1377-t1378+t1379+t1386; +t1406 = q1*t1405*2.0; +t1407 = -t1380+t1381+t1382+t1389; +t1408 = q2*t1407*2.0; +t1409 = t1383-t1384+t1385+t1388; +t1410 = q3*t1409*2.0; +t1420 = q0*t1404*2.0; +t1411 = t1406+t1408+t1410-t1420; +t1412 = -t1377+t1378+t1379+t1386; +t1413 = q0*t1412*2.0; +t1414 = t1374-t1375+t1376+t1387; +t1415 = t1383+t1384-t1385+t1388; +t1416 = q2*t1415*2.0; +t1417 = t1380-t1381+t1382+t1389; +t1418 = q3*t1417*2.0; +t1421 = q1*t1414*2.0; +t1419 = t1413+t1416+t1418-t1421; +t1422 = P(1,1)*t1397; +t1423 = P(2,1)*t1411; +t1429 = P(7,1)*t1402; +t1430 = P(3,1)*t1419; +t1424 = t1422+t1423-t1429-t1430; +t1425 = P(1,2)*t1397; +t1426 = P(2,2)*t1411; +t1427 = P(1,3)*t1397; +t1428 = P(2,3)*t1411; +t1434 = P(7,2)*t1402; +t1435 = P(3,2)*t1419; +t1431 = t1425+t1426-t1434-t1435; +t1442 = P(7,3)*t1402; +t1443 = P(3,3)*t1419; +t1432 = t1427+t1428-t1442-t1443; +t1433 = t1398+t1399-t1400-t1401; +t1436 = q0*q2*2.0; +t1437 = q1*q3*2.0; +t1438 = t1436+t1437; +t1439 = q0*q3*2.0; +t1441 = q1*q2*2.0; +t1440 = t1439-t1441; +t1444 = t1398-t1399+t1400-t1401; +t1445 = q0*q1*2.0; +t1449 = q2*q3*2.0; +t1446 = t1445-t1449; +t1447 = t1439+t1441; +t1448 = t1398-t1399-t1400+t1401; +t1450 = t1445+t1449; +t1451 = t1436-t1437; +t1452 = P(1,7)*t1397; +t1453 = P(2,7)*t1411; +t1628 = P(7,7)*t1402; +t1454 = t1452+t1453-t1628-P(3,7)*t1419; +t1455 = P(1,8)*t1397; +t1456 = P(2,8)*t1411; +t1629 = P(7,8)*t1402; +t1457 = t1455+t1456-t1629-P(3,8)*t1419; +t1458 = P(1,9)*t1397; +t1459 = P(2,9)*t1411; +t1630 = P(7,9)*t1402; +t1460 = t1458+t1459-t1630-P(3,9)*t1419; +t1461 = q0*t1390*2.0; +t1462 = q1*t1391*2.0; +t1463 = q3*t1395*2.0; +t1473 = q2*t1393*2.0; +t1464 = t1461+t1462+t1463-t1473; +t1465 = q0*t1409*2.0; +t1466 = q2*t1405*2.0; +t1467 = q3*t1404*2.0; +t1474 = q1*t1407*2.0; +t1468 = t1465+t1466+t1467-t1474; +t1469 = q1*t1415*2.0; +t1470 = q2*t1414*2.0; +t1471 = q3*t1412*2.0; +t1475 = q0*t1417*2.0; +t1472 = t1469+t1470+t1471-t1475; +t1476 = P(8,1)*t1402; +t1477 = P(1,1)*t1464; +t1486 = P(2,1)*t1468; +t1487 = P(3,1)*t1472; +t1478 = t1476+t1477-t1486-t1487; +t1479 = P(8,2)*t1402; +t1480 = P(1,2)*t1464; +t1492 = P(2,2)*t1468; +t1493 = P(3,2)*t1472; +t1481 = t1479+t1480-t1492-t1493; +t1482 = P(8,3)*t1402; +t1483 = P(1,3)*t1464; +t1498 = P(2,3)*t1468; +t1499 = P(3,3)*t1472; +t1484 = t1482+t1483-t1498-t1499; +t1485 = t1402^2; +t1488 = q1*t1390*2.0; +t1489 = q2*t1395*2.0; +t1490 = q3*t1393*2.0; +t1533 = q0*t1391*2.0; +t1491 = t1488+t1489+t1490-t1533; +t1494 = q0*t1407*2.0; +t1495 = q1*t1409*2.0; +t1496 = q2*t1404*2.0; +t1534 = q3*t1405*2.0; +t1497 = t1494+t1495+t1496-t1534; +t1500 = q0*t1415*2.0; +t1501 = q1*t1417*2.0; +t1502 = q3*t1414*2.0; +t1535 = q2*t1412*2.0; +t1503 = t1500+t1501+t1502-t1535; +t1504 = dvy*t1433; +t1505 = dvx*t1440; +t1506 = t1504+t1505; +t1507 = dvx*t1438; +t1508 = dvy*t1438; +t1509 = dvz*t1440; +t1510 = t1508+t1509; +t1511 = dvx*t1444; +t1551 = dvy*t1447; +t1512 = t1511-t1551; +t1513 = dvz*t1444; +t1514 = dvy*t1446; +t1515 = t1513+t1514; +t1516 = dvx*t1446; +t1517 = dvz*t1447; +t1518 = t1516+t1517; +t1519 = dvx*t1448; +t1520 = dvz*t1451; +t1521 = t1519+t1520; +t1522 = dvy*t1448; +t1552 = dvz*t1450; +t1523 = t1522-t1552; +t1524 = dvx*t1450; +t1525 = dvy*t1451; +t1526 = t1524+t1525; +t1527 = P(8,7)*t1402; +t1528 = P(1,7)*t1464; +t1529 = P(8,8)*t1402; +t1530 = P(1,8)*t1464; +t1531 = P(8,9)*t1402; +t1532 = P(1,9)*t1464; +t1536 = P(9,1)*t1402; +t1537 = P(2,1)*t1497; +t1545 = P(1,1)*t1491; +t1546 = P(3,1)*t1503; +t1538 = t1536+t1537-t1545-t1546; +t1539 = P(9,2)*t1402; +t1540 = P(2,2)*t1497; +t1547 = P(1,2)*t1491; +t1548 = P(3,2)*t1503; +t1541 = t1539+t1540-t1547-t1548; +t1542 = P(9,3)*t1402; +t1543 = P(2,3)*t1497; +t1549 = P(1,3)*t1491; +t1550 = P(3,3)*t1503; +t1544 = t1542+t1543-t1549-t1550; +t1553 = P(9,7)*t1402; +t1554 = P(2,7)*t1497; +t1555 = P(9,8)*t1402; +t1556 = P(2,8)*t1497; +t1557 = P(9,9)*t1402; +t1558 = P(2,9)*t1497; +t1560 = dvz*t1433; +t1559 = t1507-t1560; +t1561 = P(1,1)*t1510; +t1567 = P(3,1)*t1506; +t1568 = P(2,1)*t1559; +t1562 = P(4,1)+t1561-t1567-t1568; +t1563 = P(1,2)*t1510; +t1569 = P(3,2)*t1506; +t1570 = P(2,2)*t1559; +t1564 = P(4,2)+t1563-t1569-t1570; +t1565 = P(1,3)*t1510; +t1571 = P(3,3)*t1506; +t1572 = P(2,3)*t1559; +t1566 = P(4,3)+t1565-t1571-t1572; +t1573 = -t1507+t1560; +t1574 = P(2,1)*t1573; +t1575 = P(4,1)+t1561-t1567+t1574; +t1576 = P(2,2)*t1573; +t1577 = P(4,2)+t1563-t1569+t1576; +t1578 = P(2,3)*t1573; +t1579 = P(4,3)+t1565-t1571+t1578; +t1580 = P(1,7)*t1510; +t1581 = P(1,8)*t1510; +t1582 = P(1,9)*t1510; +t1583 = P(2,1)*t1518; +t1584 = P(3,1)*t1512; +t1592 = P(1,1)*t1515; +t1585 = P(5,1)+t1583+t1584-t1592; +t1586 = P(2,2)*t1518; +t1587 = P(3,2)*t1512; +t1593 = P(1,2)*t1515; +t1588 = P(5,2)+t1586+t1587-t1593; +t1589 = P(2,3)*t1518; +t1590 = P(3,3)*t1512; +t1594 = P(1,3)*t1515; +t1591 = P(5,3)+t1589+t1590-t1594; +t1595 = dvxNoise*t1433*t1447; +t1596 = P(2,7)*t1518; +t1597 = P(3,7)*t1512; +t1598 = P(5,7)+t1596+t1597-P(1,7)*t1515; +t1599 = P(2,8)*t1518; +t1600 = P(3,8)*t1512; +t1601 = P(5,8)+t1599+t1600-P(1,8)*t1515; +t1602 = P(2,9)*t1518; +t1603 = P(3,9)*t1512; +t1604 = P(5,9)+t1602+t1603-P(1,9)*t1515; +t1605 = P(3,1)*t1526; +t1606 = P(1,1)*t1523; +t1614 = P(2,1)*t1521; +t1607 = P(6,1)+t1605+t1606-t1614; +t1608 = P(3,2)*t1526; +t1609 = P(1,2)*t1523; +t1615 = P(2,2)*t1521; +t1610 = P(6,2)+t1608+t1609-t1615; +t1611 = P(3,3)*t1526; +t1612 = P(1,3)*t1523; +t1616 = P(2,3)*t1521; +t1613 = P(6,3)+t1611+t1612-t1616; +t1617 = dvzNoise*t1438*t1448; +t1618 = dvyNoise*t1444*t1450; +t1619 = P(3,7)*t1526; +t1620 = P(1,7)*t1523; +t1621 = P(6,7)+t1619+t1620-P(2,7)*t1521; +t1622 = P(3,8)*t1526; +t1623 = P(1,8)*t1523; +t1624 = P(6,8)+t1622+t1623-P(2,8)*t1521; +t1625 = P(3,9)*t1526; +t1626 = P(1,9)*t1523; +t1627 = P(6,9)+t1625+t1626-P(2,9)*t1521; +nextP(1,1) = daxNoise*t1485+t1397*t1424+t1411*t1431-t1419*t1432-t1402*t1454; +nextP(2,1) = -t1397*t1478-t1411*t1481+t1419*t1484+t1402*(t1527+t1528-P(2,7)*t1468-P(3,7)*t1472); +nextP(3,1) = -t1397*t1538-t1411*t1541+t1419*t1544+t1402*(t1553+t1554-P(1,7)*t1491-P(3,7)*t1503); +nextP(4,1) = -t1402*(P(4,7)+t1580-P(3,7)*t1506-P(2,7)*t1559)+t1397*t1562+t1411*t1564-t1419*t1566; +nextP(5,1) = t1397*t1585+t1411*t1588-t1402*t1598-t1419*t1591; +nextP(6,1) = t1397*t1607+t1411*t1610-t1402*t1621-t1419*t1613; +nextP(7,1) = -t1628+P(7,1)*t1397+P(7,2)*t1411-P(7,3)*t1419; +nextP(8,1) = -t1527+P(8,1)*t1397+P(8,2)*t1411-P(8,3)*t1419; +nextP(9,1) = -t1553+P(9,1)*t1397+P(9,2)*t1411-P(9,3)*t1419; +nextP(1,2) = -t1402*t1457-t1424*t1464+t1431*t1468+t1432*t1472; +nextP(2,2) = dayNoise*t1485+t1464*t1478-t1468*t1481-t1472*t1484+t1402*(t1529+t1530-P(2,8)*t1468-P(3,8)*t1472); +nextP(3,2) = t1464*t1538-t1468*t1541-t1472*t1544+t1402*(t1555+t1556-P(1,8)*t1491-P(3,8)*t1503); +nextP(4,2) = -t1402*(P(4,8)+t1581-P(3,8)*t1506-P(2,8)*t1559)-t1464*t1562+t1468*t1564+t1472*t1566; +nextP(5,2) = -t1402*t1601-t1464*t1585+t1468*t1588+t1472*t1591; +nextP(6,2) = -t1402*t1624-t1464*t1607+t1468*t1610+t1472*t1613; +nextP(7,2) = -t1629-P(7,1)*t1464+P(7,2)*t1468+P(7,3)*t1472; +nextP(8,2) = -t1529-P(8,1)*t1464+P(8,2)*t1468+P(8,3)*t1472; +nextP(9,2) = -t1555-P(9,1)*t1464+P(9,2)*t1468+P(9,3)*t1472; +nextP(1,3) = -t1402*t1460-t1431*t1497+t1432*t1503+t1491*(t1422+t1423-t1429-t1430); +nextP(2,3) = -t1478*t1491+t1481*t1497-t1484*t1503+t1402*(t1531+t1532-P(2,9)*t1468-P(3,9)*t1472); +nextP(3,3) = dazNoise*t1485-t1491*t1538+t1497*t1541-t1503*t1544+t1402*(t1557+t1558-P(1,9)*t1491-P(3,9)*t1503); +nextP(4,3) = -t1402*(P(4,9)+t1582-P(3,9)*t1506-P(2,9)*t1559)+t1491*t1562-t1497*t1564+t1503*t1566; +nextP(5,3) = -t1402*t1604+t1491*t1585-t1497*t1588+t1503*t1591; +nextP(6,3) = -t1402*t1627+t1491*t1607-t1497*t1610+t1503*t1613; +nextP(7,3) = -t1630+P(7,1)*t1491-P(7,2)*t1497+P(7,3)*t1503; +nextP(8,3) = -t1531+P(8,1)*t1491-P(8,2)*t1497+P(8,3)*t1503; +nextP(9,3) = -t1557+P(9,1)*t1491-P(9,2)*t1497+P(9,3)*t1503; +nextP(1,4) = P(1,4)*t1397+P(2,4)*t1411-P(3,4)*t1419-P(7,4)*t1402-t1432*t1506+t1510*(t1422+t1423-t1429-t1430)-t1559*(t1425+t1426-t1434-t1435); +nextP(2,4) = -P(1,4)*t1464-P(8,4)*t1402+P(2,4)*t1468+P(3,4)*t1472-t1478*t1510+t1484*t1506+t1481*t1559; +nextP(3,4) = -P(9,4)*t1402+P(1,4)*t1491-P(2,4)*t1497+P(3,4)*t1503-t1510*t1538+t1506*t1544+t1541*t1559; +nextP(4,4) = P(4,4)+P(1,4)*t1510-P(3,4)*t1506+P(2,4)*t1573-t1506*t1566+t1510*t1575+t1573*t1577+dvxNoise*t1433^2+dvyNoise*t1440^2+dvzNoise*t1438^2; +nextP(5,4) = P(5,4)+t1595-P(1,4)*t1515+P(2,4)*t1518+P(3,4)*t1512+t1510*t1585-t1506*t1591+t1573*t1588-dvyNoise*t1440*t1444-dvzNoise*t1438*t1446; +nextP(6,4) = P(6,4)+t1617+P(1,4)*t1523-P(2,4)*t1521+P(3,4)*t1526+t1510*t1607-t1506*t1613+t1573*t1610-dvxNoise*t1433*t1451-dvyNoise*t1440*t1450; +nextP(7,4) = P(7,4)-P(7,3)*t1506+P(7,1)*t1510+P(7,2)*t1573; +nextP(8,4) = P(8,4)-P(8,3)*t1506+P(8,1)*t1510+P(8,2)*t1573; +nextP(9,4) = P(9,4)-P(9,3)*t1506+P(9,1)*t1510+P(9,2)*t1573; +nextP(1,5) = P(1,5)*t1397+P(2,5)*t1411-P(3,5)*t1419-P(7,5)*t1402-t1424*t1515+t1432*t1512+t1518*(t1425+t1426-t1434-t1435); +nextP(2,5) = -P(1,5)*t1464-P(8,5)*t1402+P(2,5)*t1468+P(3,5)*t1472+t1478*t1515-t1484*t1512-t1481*t1518; +nextP(3,5) = -P(9,5)*t1402+P(1,5)*t1491-P(2,5)*t1497+P(3,5)*t1503+t1515*t1538-t1512*t1544-t1518*t1541; +nextP(4,5) = P(4,5)+t1595+P(1,5)*t1510-P(3,5)*t1506+P(2,5)*t1573-t1515*t1575+t1512*t1579+t1518*t1577-dvyNoise*t1440*t1444-dvzNoise*t1438*t1446; +nextP(5,5) = P(5,5)-P(1,5)*t1515+P(2,5)*t1518+P(3,5)*t1512-t1515*t1585+t1512*t1591+t1518*t1588+dvxNoise*t1447^2+dvyNoise*t1444^2+dvzNoise*t1446^2; +nextP(6,5) = P(6,5)+t1618+P(1,5)*t1523-P(2,5)*t1521+P(3,5)*t1526-t1515*t1607+t1512*t1613+t1518*t1610-dvxNoise*t1447*t1451-dvzNoise*t1446*t1448; +nextP(7,5) = P(7,5)+P(7,3)*t1512-P(7,1)*t1515+P(7,2)*t1518; +nextP(8,5) = P(8,5)+P(8,3)*t1512-P(8,1)*t1515+P(8,2)*t1518; +nextP(9,5) = P(9,5)+P(9,3)*t1512-P(9,1)*t1515+P(9,2)*t1518; +nextP(1,6) = P(1,6)*t1397+P(2,6)*t1411-P(3,6)*t1419-P(7,6)*t1402+t1424*t1523-t1431*t1521+t1526*(t1427+t1428-t1442-t1443); +nextP(2,6) = -P(1,6)*t1464-P(8,6)*t1402+P(2,6)*t1468+P(3,6)*t1472-t1478*t1523+t1481*t1521-t1484*t1526; +nextP(3,6) = -P(9,6)*t1402+P(1,6)*t1491-P(2,6)*t1497+P(3,6)*t1503-t1523*t1538+t1521*t1541-t1526*t1544; +nextP(4,6) = P(4,6)+t1617+P(1,6)*t1510-P(3,6)*t1506+P(2,6)*t1573-t1521*t1577+t1523*t1575+t1526*t1579-dvxNoise*t1433*t1451-dvyNoise*t1440*t1450; +nextP(5,6) = P(5,6)+t1618-P(1,6)*t1515+P(2,6)*t1518+P(3,6)*t1512+t1523*t1585-t1521*t1588+t1526*t1591-dvxNoise*t1447*t1451-dvzNoise*t1446*t1448; +nextP(6,6) = P(6,6)+P(1,6)*t1523-P(2,6)*t1521+P(3,6)*t1526+t1523*t1607-t1521*t1610+t1526*t1613+dvxNoise*t1451^2+dvyNoise*t1450^2+dvzNoise*t1448^2; +nextP(7,6) = P(7,6)-P(7,2)*t1521+P(7,1)*t1523+P(7,3)*t1526; +nextP(8,6) = P(8,6)-P(8,2)*t1521+P(8,1)*t1523+P(8,3)*t1526; +nextP(9,6) = P(9,6)-P(9,2)*t1521+P(9,1)*t1523+P(9,3)*t1526; +nextP(1,7) = t1454; +nextP(2,7) = -t1527-t1528+P(2,7)*t1468+P(3,7)*t1472; +nextP(3,7) = -t1553-t1554+P(1,7)*t1491+P(3,7)*t1503; +nextP(4,7) = P(4,7)+t1580-P(3,7)*t1506+P(2,7)*t1573; +nextP(5,7) = t1598; +nextP(6,7) = t1621; +nextP(7,7) = P(7,7); +nextP(8,7) = P(8,7); +nextP(9,7) = P(9,7); +nextP(1,8) = t1457; +nextP(2,8) = -t1529-t1530+P(2,8)*t1468+P(3,8)*t1472; +nextP(3,8) = -t1555-t1556+P(1,8)*t1491+P(3,8)*t1503; +nextP(4,8) = P(4,8)+t1581-P(3,8)*t1506+P(2,8)*t1573; +nextP(5,8) = t1601; +nextP(6,8) = t1624; +nextP(7,8) = P(7,8); +nextP(8,8) = P(8,8); +nextP(9,8) = P(9,8); +nextP(1,9) = t1460; +nextP(2,9) = -t1531-t1532+P(2,9)*t1468+P(3,9)*t1472; +nextP(3,9) = -t1557-t1558+P(1,9)*t1491+P(3,9)*t1503; +nextP(4,9) = P(4,9)+t1582-P(3,9)*t1506+P(2,9)*t1573; +nextP(5,9) = t1604; +nextP(6,9) = t1627; +nextP(7,9) = P(7,9); +nextP(8,9) = P(8,9); +nextP(9,9) = P(9,9); + +% Add the general process noise +for i = 1:9 + nextP(i,i) = nextP(i,i) + processNoise(i)^2; +end + +% Force symmetry on the covariance matrix to prevent ill-conditioning +% of the matrix which would cause the filter to blow-up +P = 0.5*(P + transpose(P)); + +% ensure diagonals are positive +for i=1:9 + if P(i,i) < 0 + P(i,i) = 0; + end +end + +end \ No newline at end of file diff --git a/libraries/AP_NavEKF/Models/GimbalEstimatorExample/PredictStates.m b/libraries/AP_NavEKF/Models/GimbalEstimatorExample/PredictStates.m new file mode 100644 index 0000000000..e685925dff --- /dev/null +++ b/libraries/AP_NavEKF/Models/GimbalEstimatorExample/PredictStates.m @@ -0,0 +1,55 @@ +function [quat, states, Tbn, correctedDelAng, correctedDelVel] = PredictStates( ... + quat, ... % previous quaternion states 4x1 + states, ... % previous states (3x1 rotation error, 3x1 velocity, 3x1 gyro bias) + dAng, ... % IMU delta angles, 3x1 (rad) + dVel, ... % IMU delta velocities 3x1 (m/s) + dt) % time since last IMU measurement (sec) + +% Define parameters used for previous angular rates and acceleration shwich +% are used for trapezoidal integration +% define persistent variables for previous delta angle and velocity which +% are required for sculling and coning error corrections +persistent prevDelAng; +if isempty(prevDelAng) + prevDelAng = dAng; +end +persistent prevDelVel; +if isempty(prevDelVel) + prevDelVel = dVel; +end + +% Remove sensor bias errors +dAng = dAng - states(7:9); + +% Apply rotational and skulling corrections +correctedDelVel= dVel + ... + 0.5*cross(prevDelAng + dAng , prevDelVel + dVel) + 1/6*cross(prevDelAng + dAng , cross(prevDelAng + dAng , prevDelVel + dVel)) + ... % rotational correction + 1/12*(cross(prevDelAng , dVel) + cross(prevDelVel , dAng)); % sculling correction + +% Apply corrections for coning errors +correctedDelAng = dAng - 1/12*cross(prevDelAng , dAng); + +% Save current measurements +prevDelAng = dAng; +prevDelVel = dVel; + +% Convert the rotation vector to its equivalent quaternion +deltaQuat = RotToQuat(correctedDelAng); + +% Update the quaternions by rotating from the previous attitude through +% the delta angle rotation quaternion +quat = QuatMult(quat,deltaQuat); + +% Normalise the quaternions +quat = NormQuat(quat); + +% Calculate the body to nav cosine matrix +Tbn = Quat2Tbn(quat); + +% transform body delta velocities to delta velocities in the nav frame +delVelNav = Tbn * correctedDelVel + [0;0;9.807]*dt; + +% Sum delta velocities to get velocity +states(4:6) = states(4:6) + delVelNav(1:3); + +end \ No newline at end of file diff --git a/libraries/AP_NavEKF/Models/GimbalEstimatorExample/RunSimulation.m b/libraries/AP_NavEKF/Models/GimbalEstimatorExample/RunSimulation.m new file mode 100644 index 0000000000..26d16e2dcd --- /dev/null +++ b/libraries/AP_NavEKF/Models/GimbalEstimatorExample/RunSimulation.m @@ -0,0 +1,203 @@ +%% Set initial conditions +clear all; +dtSlow = 1/50; +dtFast = 1/1000; +rateMult = round(dtSlow/dtFast); +duration = 60; +indexLimitSlow = round(duration/dtSlow); +indexLimitFast = indexLimitSlow*rateMult; + +% create data logging variables +gimbal.time = zeros(1,indexLimitFast); +gimbal.euler = zeros(3,indexLimitFast); +gimbal.eulerTruth = zeros(3,indexLimitFast); +gimbal.eulerError = zeros(3,indexLimitFast); + +% Use a random initial truth orientation +phiInit = 0.1*randn; +thetaInit = 0.1*randn; +psiInit = 2*pi*rand - pi; +quatTruth = EulToQuat([phiInit,thetaInit,psiInit]);% [1;0.05*randn;0.05*randn;2*(rand-0.5)]; +quatLength = sqrt(quatTruth(1)^2 + quatTruth(2)^2 + quatTruth(3)^2 + quatTruth(4)^2); +quatTruth = quatTruth / quatLength; +TsnTruth = Quat2Tbn(quatTruth); + +% define the earths truth magnetic field +declTruth = 10*pi/180; +magEarthTruth = [0.25*cos(declTruth);0.25*sin(declTruth);-0.5]; + +% define the declination parameter assuming 2deg RMS error - this would be +% obtained from the main EKF to take advantage of in-flight learning +declParam = declTruth + 2*pi/180*randn; + +% define the magnetometer bias errors +magMeasBias = 0.02*[randn;randn;randn]; + +% Define IMU bias errors and noise +gyroBias = 1*pi/180*[randn;randn;randn]; +accBias = 0.05*[randn;randn;randn]; +gyroNoise = 0.01; +accNoise = 0.05; + +% define the state covariances with the exception of the quaternion covariances +Sigma_velNED = 0.5; % 1 sigma uncertainty in horizontal velocity components +Sigma_dAngBias = 1*pi/180*dtSlow; % 1 Sigma uncertainty in delta angle bias +Sigma_angErr = 1; % 1 Sigma uncertainty in angular misalignment (rad) +covariance = single(diag([Sigma_angErr*[1;1;1];Sigma_velNED*[1;1;1];Sigma_dAngBias*[1;1;1]]).^2); + +% Initialise truth trajectory variables +% fly a CCW circle with constant gimbal angles +gPsiInit = 20*pi/180; % gimbal yaw +gThetaInit = 0; % gimbal pitch +gPhiInit = 0; % gimbal roll +psiTruth = psiInit; +radius = 20; +gndSpd = 5; +trackAngTruth = -pi; +centripAccelMag = gndSpd/radius*gndSpd; +gravAccel = [0;0;-9.81]; + +%% Main Loop +hdgAlignedEKF=0; +hdgAlignedGimbal=0; +slowIndex = 0; +delAngFast = [0;0;0]; +delVelFast = [0;0;0]; +delAngSlow = [0;0;0]; +delVelSlow = [0;0;0]; +prevAngRateMeas = [0;0;0]; +prevAccelMeas = [0;0;0]; +quatFast = [1;0;0;0]; +quatFastSaved = quatFast; +angRateBiasEKF = [0;0;0]; +quatEKF = [1;0;0;0]; +for fastIndex = 1:indexLimitFast % 1000 Hz gimbal prediction loop + time = dtFast*fastIndex; + % Calculate Truth Data + % Need to replace this with a full kinematic model or test data + % calculate truth angular rates - we don't start maneouvring until + % heading alignment is complete + psiRateTruth = gndSpd/radius*hdgAlignedEKF; + angRateTruth = [0;0;psiRateTruth]; % constant yaw rate + + % calculate yaw and track angles + psiTruth = psiTruth + psiRateTruth*dtFast; + trackAngTruth = trackAngTruth + psiRateTruth*dtFast; + + % Cacluate truth quternion + quatTruth = EulToQuat([phiInit,thetaInit,psiTruth]); + + % Calculate truth rotaton from sensor to NED + TsnTruth = Quat2Tbn(quatTruth); + + % calculate truth accel vector + centripAccel = centripAccelMag*[-sin(trackAngTruth);cos(trackAngTruth);0]; + accelTruth = transpose(TsnTruth)*(gravAccel + centripAccel); + + % calculate truth velocity vector + truthVel = gndSpd*[cos(trackAngTruth);sin(trackAngTruth);0]; + + % synthesise sensor measurements + % Synthesise IMU measurements, adding bias and noise + angRateMeas = angRateTruth + gyroBias + gyroNoise*[randn;randn;randn]; + accelMeas = accelTruth + accBias + accNoise*[randn;randn;randn]; + + % synthesise velocity measurements + measVel = truthVel; + + % synthesise gimbal angles + gPhi = 0; + gTheta = 0; + gPsi = gPsiInit; + + % Define rotation from magnetometer to sensor using a 312 rotation sequence + TmsTruth = calcTms(gPhi,gPsi,gTheta); + + % calculate rotation from NED to magnetometer axes Tnm = Tsm * Tns + TnmTruth = transpose(TmsTruth) * transpose(TsnTruth); + + % synthesise magnetometer measurements adding sensor bias + magMeas = TnmTruth*magEarthTruth + magMeasBias; + + % integrate the IMU measurements to produce delta angles and velocities + % using a trapezoidal integrator + if isempty(prevAngRateMeas) + prevAngRateMeas = angRateMeas; + end + if isempty(prevAccelMeas) + prevAccelMeas = accelMeas; + end + delAngFast = delAngFast + 0.5*(angRateMeas + prevAngRateMeas)*dtFast; + delVelFast = delVelFast + 0.5*(accelMeas + prevAccelMeas)*dtFast; + prevAngRateMeas = angRateMeas; + prevAccelMeas = accelMeas; + + % Run an attitude prediction calculation at 1000Hz + % Convert the rotation vector to its equivalent quaternion + % using a first order approximation after applying the correction for + % gyro bias using bias estimates from the EKF + deltaQuat = [1;0.5*(angRateMeas - angRateBiasEKF)*dtFast]; + % Update the quaternions by rotating from the previous attitude through + % the delta angle rotation quaternion + quatFast = QuatMult(quatFast,deltaQuat); + % Normalise the quaternions + quatFast = NormQuat(quatFast); + % log the high rate data + eulLogFast(:,fastIndex) = QuatToEul(quatFast); + + % every 20msec we send them to the EKF computer and reset + % the total + % we also save a copy of the quaternion from our high rate prediction + if (rem(fastIndex,rateMult) == 0) + delAngSlow = delAngFast; + delVelSlow = delVelFast; + delAngFast = [0;0;0]; + delVelFast = [0;0;0]; + quatFastSaved = quatFast; + end + + % run the 50Hz EKF loop but do so 5 msec behind the + % data transmission to simulate the effect of transmission and + % computational delays + if (rem(fastIndex,rateMult) == 5) + slowIndex = slowIndex + 1; + [quatEKF,angRateBiasEKF,EKFlogs,hdgAlignedEKF] = calcEKF(delAngSlow,delVelSlow,measVel,gPhi,gPsi,gTheta,magMeas,declParam,time,dtSlow,slowIndex,indexLimitSlow); + end + + % Correct Gimbal attitude usng EKF data + % Assume the gimbal controller receive the EKF solution 10 msec after + % it sent the sensor data + if (rem(fastIndex,rateMult) == 10) + % calculate the quaternion from the EKF corrected attitude to the + % attitude calculated using the local fast prediction algorithm + deltaQuatFast = QuatDivide(quatEKF,quatFastSaved); + % apply this correction to the fast solution at the current time + % step (this can be applied across several steps to smooth the + % output if required) + quatFast = QuatMult(quatFast,deltaQuatFast); + % normalise the resultant quaternion + quatFast = NormQuat(quatFast); + % flag when the gimbals own heading is aligned + hdgAlignedGimbal = hdgAlignedEKF; + end + + % Log gimbal data + gimbal.time(fastIndex) = time; + gimbal.euler(:,fastIndex) = QuatToEul(quatFast); + gimbal.eulerTruth(:,fastIndex) = QuatToEul(quatTruth); + if (hdgAlignedGimbal) + gimbal.eulerError(:,fastIndex) = gimbal.euler(:,fastIndex) - gimbal.eulerTruth(:,fastIndex); + if (gimbal.eulerError(3,fastIndex) > pi) + gimbal.eulerError(3,fastIndex) = gimbal.eulerError(3,fastIndex) - 2*pi; + elseif (gimbal.eulerError(3,fastIndex) < -pi) + gimbal.eulerError(3,fastIndex) = gimbal.eulerError(3,fastIndex) + 2*pi; + end + else + gimbal.eulerError(:,fastIndex) = [NaN;NaN;NaN]; + end + +end + +%% Generate Plots +close all; +PlotData; \ No newline at end of file diff --git a/libraries/AP_NavEKF/Models/GimbalEstimatorExample/calcEKF.m b/libraries/AP_NavEKF/Models/GimbalEstimatorExample/calcEKF.m new file mode 100644 index 0000000000..888f30d3cb --- /dev/null +++ b/libraries/AP_NavEKF/Models/GimbalEstimatorExample/calcEKF.m @@ -0,0 +1,96 @@ +function [quatOut,angRateBiasOut,logOut,headingAlignedOut] = calcEKF(delAngSlow,delVelSlow,measVel,gPhi,gPsi,gTheta,magMeas,declParam,time,dtSlow,frameIndex,maxFrameIndex) + +persistent velocityAligned; +if isempty(velocityAligned) + velocityAligned = 0; +end + +persistent quat; +if isempty(quat) + quat = [1;0;0;0]; +end + +persistent states; +if isempty(states) + states = zeros(9,1); +end + +persistent covariance; +if isempty(covariance) + % define the state covariances with the exception of the quaternion covariances + Sigma_velNED = 0.5; % 1 sigma uncertainty in horizontal velocity components + Sigma_dAngBias = 1*pi/180*dtSlow; % 1 Sigma uncertainty in delta angle bias + Sigma_angErr = 1; % 1 Sigma uncertainty in angular misalignment (rad) + covariance = single(diag([Sigma_angErr*[1;1;1];Sigma_velNED*[1;1;1];Sigma_dAngBias*[1;1;1]]).^2); +end + +persistent headingAligned +if isempty(headingAligned) + headingAligned = 0; +end + +persistent log; +if isempty(log) + % create data logging variables + log.time = zeros(1,maxFrameIndex); + log.states = zeros(9,maxFrameIndex); + log.quat = zeros(4,maxFrameIndex); + log.euler = zeros(3,maxFrameIndex); + log.tiltCorr = zeros(1,maxFrameIndex); + log.velInnov = zeros(3,maxFrameIndex); + log.decInnov = zeros(1,maxFrameIndex); + log.velInnovVar = log.velInnov; + log.decInnovVar = log.decInnov; +end + +% predict states +[quat, states, Tsn, delAngCorrected, delVelCorrected] = PredictStates(quat,states,delAngSlow,delVelSlow,dtSlow); + +% log state prediction data +log.states(:,frameIndex) = states; +log.quat(:,frameIndex) = quat; +log.euler(:,frameIndex) = QuatToEul(quat); + +% predict covariance matrix +covariance = PredictCovarianceOptimised(delAngCorrected,delVelCorrected,quat,states,covariance,dtSlow); + +if (velocityAligned == 0) + % initialise velocity states + states(4:6) = measVel; + velocityAligned = 1; +else + % fuse velocity measurements + [quat,states,tiltCorrection,covariance,velInnov,velInnovVar] = FuseVelocity(quat,states,covariance,measVel); + % log velocity fusion data + log.velInnov(:,frameIndex) = velInnov; + log.velInnovVar(:,frameIndex) = velInnovVar; + log.tiltCorr(1,frameIndex) = tiltCorrection; +end + + +% Align the heading once there has been enough time for the filter to +% settle and the tilt corrections have dropped below a threshold +if (((time > 5.0 && tiltCorrection < 1e-4) || (time > 30.0)) && headingAligned==0) + % calculate the initial heading using magnetometer, gimbal, + % estimated tilt and declination + quat = AlignHeading(gPhi,gPsi,gTheta,Tsn,magMeas,quat,declParam); + headingAligned = 1; +end + +% fuse magnetometer measurements and log fusion data +if (headingAligned == 1) + [quat,states,covariance,decInnov,decInnovVar] = FuseMagnetometer(quat,states,covariance,magMeas,declParam,gPhi,gPsi,gTheta); + log.decInnov(:,frameIndex) = decInnov; + log.decInnovVar(:,frameIndex) = decInnovVar; +end + +% time stamp the log data +log.time(frameIndex) = time; + +% write to the output data +quatOut = quat; +angRateBiasOut = states(7:9)/dtSlow; +logOut = log; +headingAlignedOut = headingAligned; + +end \ No newline at end of file diff --git a/libraries/AP_NavEKF/Models/GimbalEstimatorExample/calcF.c b/libraries/AP_NavEKF/Models/GimbalEstimatorExample/calcF.c new file mode 100644 index 0000000000..e69de29bb2 diff --git a/libraries/AP_NavEKF/Models/GimbalEstimatorExample/calcF.cpp b/libraries/AP_NavEKF/Models/GimbalEstimatorExample/calcF.cpp new file mode 100644 index 0000000000..e69de29bb2 diff --git a/libraries/AP_NavEKF/Models/GimbalEstimatorExample/calcF.m b/libraries/AP_NavEKF/Models/GimbalEstimatorExample/calcF.m new file mode 100644 index 0000000000..14c2d76d28 --- /dev/null +++ b/libraries/AP_NavEKF/Models/GimbalEstimatorExample/calcF.m @@ -0,0 +1,68 @@ +function F = calcF(dax,dax_b,day,day_b,daz,daz_b,dvx,dvx_b,dvy,dvy_b,dvz,dvz_b,q0,q1,q2,q3) +%CALCF +% F = CALCF(DAX,DAX_B,DAY,DAY_B,DAZ,DAZ_B,DVX,DVX_B,DVY,DVY_B,DVZ,DVZ_B,Q0,Q1,Q2,Q3) + +% This function was generated by the Symbolic Math Toolbox version 6.1. +% 15-Feb-2015 15:45:52 + +t2 = dax.*(1.0./2.0); +t3 = dax_b.*(1.0./2.0); +t4 = t2-t3; +t5 = day.*(1.0./2.0); +t6 = day_b.*(1.0./2.0); +t7 = t5-t6; +t8 = daz.*(1.0./2.0); +t9 = daz_b.*(1.0./2.0); +t10 = t8-t9; +t11 = q2.*t4.*(1.0./2.0); +t12 = q1.*t7.*(1.0./2.0); +t13 = q0.*t10.*(1.0./2.0); +t14 = q2.*(1.0./2.0); +t15 = q3.*t4.*(1.0./2.0); +t16 = q1.*t10.*(1.0./2.0); +t17 = q1.*(1.0./2.0); +t18 = q0.*t4.*(1.0./2.0); +t19 = q3.*t7.*(1.0./2.0); +t20 = q0.*(1.0./2.0); +t21 = q2.*t7.*(1.0./2.0); +t22 = q3.*t10.*(1.0./2.0); +t23 = q0.*t7.*(1.0./2.0); +t24 = q3.*(1.0./2.0); +t25 = q1.*t4.*(1.0./2.0); +t26 = q2.*t10.*(1.0./2.0); +t27 = t20-t21+t22+t25; +t28 = -t17+t18+t19+t26; +t29 = t14-t15+t16+t23; +t30 = t11+t12-t13+t24; +t31 = t17-t18+t19+t26; +t32 = t20+t21-t22+t25; +t33 = t11-t12+t13+t24; +t34 = -t14+t15+t16+t23; +t35 = q0.^2; +t36 = q1.^2; +t37 = q2.^2; +t38 = q3.^2; +t39 = -t35-t36-t37-t38; +t40 = t14+t15+t16-t23; +t41 = t11+t12+t13-t24; +t42 = t20+t21+t22-t25; +t43 = t17+t18+t19-t26; +t44 = dvz-dvz_b; +t45 = q0.*q2.*2.0; +t46 = q1.*q3.*2.0; +t47 = t45+t46; +t48 = dvy-dvy_b; +t49 = t35+t36-t37-t38; +t50 = dvx-dvx_b; +t51 = q0.*q3.*2.0; +t53 = q1.*q2.*2.0; +t52 = t51-t53; +t54 = q0.*q1.*2.0; +t58 = q2.*q3.*2.0; +t55 = t54-t58; +t56 = t35-t36+t37-t38; +t57 = t51+t53; +t59 = t35-t36-t37+t38; +t60 = t54+t58; +t61 = t45-t46; +F = reshape([q3.*(q3.*(-1.0./2.0)+t11+t12+t13).*-2.0+q2.*(t14+t15+t16-q0.*t7.*(1.0./2.0)).*2.0+q1.*(t17+t18+t19-q2.*t10.*(1.0./2.0)).*2.0+q0.*(t20+t21+t22-q1.*t4.*(1.0./2.0)).*2.0,q0.*t41.*-2.0-q1.*t40.*2.0+q2.*t43.*2.0-q3.*t42.*2.0,q0.*t40.*-2.0+q1.*t41.*2.0+q2.*t42.*2.0+q3.*t43.*2.0,t47.*t48+t44.*t52,-t44.*t56-t48.*t55,-t44.*t60+t48.*t59,0.0,0.0,0.0,0.0,0.0,0.0,q0.*t30.*-2.0+q1.*t29.*2.0+q2.*t28.*2.0+q3.*t27.*2.0,q0.*t27.*2.0-q1.*t28.*2.0+q2.*t29.*2.0+q3.*t30.*2.0,q0.*t28.*-2.0-q1.*t27.*2.0-q2.*t30.*2.0+q3.*t29.*2.0,t44.*t49-t47.*t50,t44.*t57+t50.*t55,-t44.*t61-t50.*t59,0.0,0.0,0.0,0.0,0.0,0.0,q0.*t34.*-2.0+q1.*t33.*2.0-q2.*t32.*2.0-q3.*t31.*2.0,q0.*t31.*-2.0+q1.*t32.*2.0+q2.*t33.*2.0+q3.*t34.*2.0,q0.*t32.*2.0+q1.*t31.*2.0-q2.*t34.*2.0+q3.*t33.*2.0,-t48.*t49-t50.*t52,-t48.*t57+t50.*t56,t48.*t61+t50.*t60,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,1.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,1.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,1.0,0.0,0.0,0.0,0.0,0.0,0.0,t39,0.0,0.0,0.0,0.0,0.0,1.0,0.0,0.0,0.0,0.0,0.0,0.0,t39,0.0,0.0,0.0,0.0,0.0,1.0,0.0,0.0,0.0,0.0,0.0,0.0,t39,0.0,0.0,0.0,0.0,0.0,1.0,0.0,0.0,0.0,0.0,0.0,0.0,-t35-t36+t37+t38,-t51-t53,t61,0.0,0.0,0.0,1.0,0.0,0.0,0.0,0.0,0.0,t52,-t35+t36-t37+t38,-t54-t58,0.0,0.0,0.0,0.0,1.0,0.0,0.0,0.0,0.0,-t45-t46,t55,-t35+t36+t37-t38,0.0,0.0,0.0,0.0,0.0,1.0],[12, 12]); diff --git a/libraries/AP_NavEKF/Models/GimbalEstimatorExample/calcH_MAG.c b/libraries/AP_NavEKF/Models/GimbalEstimatorExample/calcH_MAG.c new file mode 100644 index 0000000000..4ac70413dc --- /dev/null +++ b/libraries/AP_NavEKF/Models/GimbalEstimatorExample/calcH_MAG.c @@ -0,0 +1,75 @@ + t2 = cos(gPhi); + t3 = cos(gTheta); + t4 = sin(gPhi); + t5 = sin(gTheta); + t6 = q0*q0; + t7 = q1*q1; + t8 = q2*q2; + t9 = q3*q3; + t10 = t6+t7-t8-t9; + t11 = sin(gPsi); + t12 = cos(gPsi); + t13 = q0*q2*2.0; + t14 = q1*q3*2.0; + t15 = t13+t14; + t16 = q0*q3*2.0; + t18 = q1*q2*2.0; + t17 = t16-t18; + t19 = t3*t11; + t20 = t4*t5*t12; + t21 = t19+t20; + t22 = t16+t18; + t23 = t5*t11; + t41 = t3*t4*t12; + t24 = t23-t41; + t25 = q0*q1*2.0; + t31 = q2*q3*2.0; + t26 = t25-t31; + t27 = t6-t7+t8-t9; + t28 = t5*t12; + t29 = t3*t4*t11; + t30 = t28+t29; + t32 = t3*t12; + t46 = t4*t5*t11; + t33 = t32-t46; + t35 = t4*t17; + t36 = t2*t5*t10; + t37 = t2*t3*t15; + t38 = t35+t36-t37; + t39 = magZ*t38; + t40 = t10*t21; + t42 = t15*t24; + t43 = t2*t12*t17; + t44 = t40+t42-t43; + t45 = magY*t44; + t47 = t10*t33; + t48 = t15*t30; + t49 = t2*t11*t17; + t50 = t47+t48+t49; + t51 = magX*t50; + t52 = -t39+t45+t51; + t53 = 1.0/t52; + t54 = t4*t27; + t55 = t2*t3*t26; + t56 = t2*t5*t22; + t57 = -t54+t55+t56; + t58 = magZ*t57; + t59 = t21*t22; + t60 = t24*t26; + t61 = t2*t12*t27; + t62 = t59-t60+t61; + t63 = magY*t62; + t64 = t26*t30; + t65 = t22*t33; + t66 = t2*t11*t27; + t67 = t64-t65+t66; + t68 = magX*t67; + t69 = t58-t63+t68; + t70 = t53*t69; + t34 = tan(t70); + t71 = t34*t34; + t72 = t71+1.0; + t73 = 1.0/(t52*t52); + A0[0][0] = -t72*(t53*(magZ*(t4*t26+t2*t3*t27)+magY*(t24*t27+t2*t12*t26)+magX*(t27*t30-t2*t11*t26))-t69*t73*(magZ*(t4*t15+t2*t3*t17)+magY*(t17*t24+t2*t12*t15)+magX*(t17*t30-t2*t11*t15))); + A0[0][1] = t72*(t53*(magZ*(t2*t3*t22-t2*t5*t26)+magY*(t22*t24+t21*t26)+magX*(t22*t30+t26*t33))+t69*t73*(magZ*(t2*t3*t10+t2*t5*t15)+magY*(t10*t24-t15*t21)+magX*(t10*t30-t15*t33))); + A0[0][2] = t72*(t53*(-magZ*(t4*t22+t2*t5*t27)+magY*(t21*t27-t2*t12*t22)+magX*(t27*t33+t2*t11*t22))-t69*t73*(magZ*(t4*t10-t2*t5*t17)+magY*(t17*t21+t2*t10*t12)+magX*(t17*t33-t2*t10*t11))); diff --git a/libraries/AP_NavEKF/Models/GimbalEstimatorExample/calcH_MAG.cpp b/libraries/AP_NavEKF/Models/GimbalEstimatorExample/calcH_MAG.cpp new file mode 100644 index 0000000000..3c7739e202 --- /dev/null +++ b/libraries/AP_NavEKF/Models/GimbalEstimatorExample/calcH_MAG.cpp @@ -0,0 +1,75 @@ +float t2 = cos(gPhi); +float t3 = cos(gTheta); +float t4 = sin(gPhi); +float t5 = sin(gTheta); +float t6 = q0*q0; +float t7 = q1*q1; +float t8 = q2*q2; +float t9 = q3*q3; +float t10 = t6+t7-t8-t9; +float t11 = sin(gPsi); +float t12 = cos(gPsi); +float t13 = q0*q2*2.0f; +float t14 = q1*q3*2.0f; +float t15 = t13+t14; +float t16 = q0*q3*2.0f; +float t18 = q1*q2*2.0f; +float t17 = t16-t18; +float t19 = t3*t11; +float t20 = t4*t5*t12; +float t21 = t19+t20; +float t22 = t16+t18; +float t23 = t5*t11; +float t41 = t3*t4*t12; +float t24 = t23-t41; +float t25 = q0*q1*2.0f; +float t31 = q2*q3*2.0f; +float t26 = t25-t31; +float t27 = t6-t7+t8-t9; +float t28 = t5*t12; +float t29 = t3*t4*t11; +float t30 = t28+t29; +float t32 = t3*t12; +float t46 = t4*t5*t11; +float t33 = t32-t46; +float t35 = t4*t17; +float t36 = t2*t5*t10; +float t37 = t2*t3*t15; +float t38 = t35+t36-t37; +float t39 = magZ*t38; +float t40 = t10*t21; +float t42 = t15*t24; +float t43 = t2*t12*t17; +float t44 = t40+t42-t43; +float t45 = magY*t44; +float t47 = t10*t33; +float t48 = t15*t30; +float t49 = t2*t11*t17; +float t50 = t47+t48+t49; +float t51 = magX*t50; +float t52 = -t39+t45+t51; +float t53 = 1.0/t52; +float t54 = t4*t27; +float t55 = t2*t3*t26; +float t56 = t2*t5*t22; +float t57 = -t54+t55+t56; +float t58 = magZ*t57; +float t59 = t21*t22; +float t60 = t24*t26; +float t61 = t2*t12*t27; +float t62 = t59-t60+t61; +float t63 = magY*t62; +float t64 = t26*t30; +float t65 = t22*t33; +float t66 = t2*t11*t27; +float t67 = t64-t65+t66; +float t68 = magX*t67; +float t69 = t58-t63+t68; +float t70 = t53*t69; +float t34 = tan(t70); +float t71 = t34*t34; +float t72 = t71+1.0; +float t73 = 1.0/(t52*t52); +A0[0][0] = -t72*(t53*(magZ*(t4*t26+t2*t3*t27)+magY*(t24*t27+t2*t12*t26)+magX*(t27*t30-t2*t11*t26))-t69*t73*(magZ*(t4*t15+t2*t3*t17)+magY*(t17*t24+t2*t12*t15)+magX*(t17*t30-t2*t11*t15))); +A0[0][1] = t72*(t53*(magZ*(t2*t3*t22-t2*t5*t26)+magY*(t22*t24+t21*t26)+magX*(t22*t30+t26*t33))+t69*t73*(magZ*(t2*t3*t10+t2*t5*t15)+magY*(t10*t24-t15*t21)+magX*(t10*t30-t15*t33))); +A0[0][2] = t72*(t53*(-magZ*(t4*t22+t2*t5*t27)+magY*(t21*t27-t2*t12*t22)+magX*(t27*t33+t2*t11*t22))-t69*t73*(magZ*(t4*t10-t2*t5*t17)+magY*(t17*t21+t2*t10*t12)+magX*(t17*t33-t2*t10*t11))); diff --git a/libraries/AP_NavEKF/Models/GimbalEstimatorExample/calcH_MAG.m b/libraries/AP_NavEKF/Models/GimbalEstimatorExample/calcH_MAG.m new file mode 100644 index 0000000000..3b8243fa42 --- /dev/null +++ b/libraries/AP_NavEKF/Models/GimbalEstimatorExample/calcH_MAG.m @@ -0,0 +1,80 @@ +function H_MAG = calcH_MAG(gPhi,gPsi,gTheta,magX,magY,magZ,q0,q1,q2,q3) +%CALCH_MAG +% H_MAG = CALCH_MAG(GPHI,GPSI,GTHETA,MAGX,MAGY,MAGZ,Q0,Q1,Q2,Q3) + +% This function was generated by the Symbolic Math Toolbox version 6.1. +% 15-Feb-2015 16:00:09 + +t2 = cos(gPhi); +t3 = cos(gTheta); +t4 = sin(gPhi); +t5 = sin(gTheta); +t6 = q0.^2; +t7 = q1.^2; +t8 = q2.^2; +t9 = q3.^2; +t10 = t6+t7-t8-t9; +t11 = sin(gPsi); +t12 = cos(gPsi); +t13 = q0.*q2.*2.0; +t14 = q1.*q3.*2.0; +t15 = t13+t14; +t16 = q0.*q3.*2.0; +t18 = q1.*q2.*2.0; +t17 = t16-t18; +t19 = t3.*t11; +t20 = t4.*t5.*t12; +t21 = t19+t20; +t22 = t16+t18; +t23 = t5.*t11; +t41 = t3.*t4.*t12; +t24 = t23-t41; +t25 = q0.*q1.*2.0; +t31 = q2.*q3.*2.0; +t26 = t25-t31; +t27 = t6-t7+t8-t9; +t28 = t5.*t12; +t29 = t3.*t4.*t11; +t30 = t28+t29; +t32 = t3.*t12; +t46 = t4.*t5.*t11; +t33 = t32-t46; +t35 = t4.*t17; +t36 = t2.*t5.*t10; +t37 = t2.*t3.*t15; +t38 = t35+t36-t37; +t39 = magZ.*t38; +t40 = t10.*t21; +t42 = t15.*t24; +t43 = t2.*t12.*t17; +t44 = t40+t42-t43; +t45 = magY.*t44; +t47 = t10.*t33; +t48 = t15.*t30; +t49 = t2.*t11.*t17; +t50 = t47+t48+t49; +t51 = magX.*t50; +t52 = -t39+t45+t51; +t53 = 1.0./t52; +t54 = t4.*t27; +t55 = t2.*t3.*t26; +t56 = t2.*t5.*t22; +t57 = -t54+t55+t56; +t58 = magZ.*t57; +t59 = t21.*t22; +t60 = t24.*t26; +t61 = t2.*t12.*t27; +t62 = t59-t60+t61; +t63 = magY.*t62; +t64 = t26.*t30; +t65 = t22.*t33; +t66 = t2.*t11.*t27; +t67 = t64-t65+t66; +t68 = magX.*t67; +t69 = t58-t63+t68; +t70 = t53.*t69; +t34 = tan(t70); +t71 = t34.^2; +t72 = t71+1.0; +t73 = 1.0./t52.^2; +H_MAG = [-t72.*(t53.*(magZ.*(t4.*t26+t2.*t3.*t27)+magY.*(t24.*t27+t2.*t12.*t26)+magX.*(t27.*t30-t2.*t11.*t26))-t69.*t73.*(magZ.*(t4.*t15+t2.*t3.*t17)+magY.*(t17.*t24+t2.*t12.*t15)+magX.*(t17.*t30-t2.*t11.*t15))),t72.*(t53.*(magZ.*(t2.*t3.*t22-t2.*t5.*t26)+magY.*(t22.*t24+t21.*t26)+magX.*(t22.*t30+t26.*t33))+t69.*t73.*(magZ.*(t2.*t3.*t10+t2.*t5.*t15)+magY.*(t10.*t24-t15.*t21)+magX.*(t10.*t30-t15.*t33))),t72.*(t53.*(-magZ.*(t4.*t22+t2.*t5.*t27)+magY.*(t21.*t27-t2.*t12.*t22)+magX.*(t27.*t33+t2.*t11.*t22))-t69.*t73.*(magZ.*(t4.*t10-t2.*t5.*t17)+magY.*(t17.*t21+t2.*t10.*t12)+magX.*(t17.*t33-t2.*t10.*t11))),0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0]; diff --git a/libraries/AP_NavEKF/Models/GimbalEstimatorExample/calcMagAng.m b/libraries/AP_NavEKF/Models/GimbalEstimatorExample/calcMagAng.m new file mode 100644 index 0000000000..00f52f0682 --- /dev/null +++ b/libraries/AP_NavEKF/Models/GimbalEstimatorExample/calcMagAng.m @@ -0,0 +1,18 @@ +function angMeas = calcMagAng(decl,gPhi,gPsi,gTheta,magX,magY,magZ,q0,q1,q2,q3) +%CALCMAGANG +% ANGMEAS = CALCMAGANG(DECL,GPHI,GPSI,GTHETA,MAGX,MAGY,MAGZ,Q0,Q1,Q2,Q3) + +% This function was generated by the Symbolic Math Toolbox version 5.8. +% 14-Jan-2015 16:51:18 + +% Define rotation from magnetometer to sensor using a 312 rotation sequence +Tms = calcTms(gPhi,gPsi,gTheta); +% Define rotation from sensor to NED +Tsn = Quat2Tbn([q0;q1;q2;q3]); +% Define rotation from magnetometer to NED axes +Tmn = Tsn*Tms; +% rotate magentic field measured at top plate into nav axes +magMeasNED = Tmn*[magX;magY;magZ]; +% the predicted measurement is the angle wrt magnetic north of the horizontal +% component of the measured field +angMeas = atan2(magMeasNED(2),magMeasNED(1)) - decl; \ No newline at end of file diff --git a/libraries/AP_NavEKF/Models/GimbalEstimatorExample/calcP.c b/libraries/AP_NavEKF/Models/GimbalEstimatorExample/calcP.c new file mode 100644 index 0000000000..f12270cb07 --- /dev/null +++ b/libraries/AP_NavEKF/Models/GimbalEstimatorExample/calcP.c @@ -0,0 +1,556 @@ + t2 = dax*(1.0/2.0); + t3 = dax_b*(1.0/2.0); + t4 = t2-t3; + t5 = day*(1.0/2.0); + t6 = day_b*(1.0/2.0); + t7 = t5-t6; + t8 = daz*(1.0/2.0); + t9 = daz_b*(1.0/2.0); + t10 = t8-t9; + t11 = q2*t4*(1.0/2.0); + t12 = q1*t7*(1.0/2.0); + t13 = q0*t10*(1.0/2.0); + t14 = q2*(1.0/2.0); + t15 = q3*t4*(1.0/2.0); + t16 = q1*t10*(1.0/2.0); + t17 = q1*(1.0/2.0); + t18 = q0*t4*(1.0/2.0); + t19 = q3*t7*(1.0/2.0); + t20 = q0*(1.0/2.0); + t21 = q2*t7*(1.0/2.0); + t22 = q3*t10*(1.0/2.0); + t23 = q0*t7*(1.0/2.0); + t24 = q3*(1.0/2.0); + t25 = q1*t4*(1.0/2.0); + t26 = q2*t10*(1.0/2.0); + t27 = t11+t12+t13-t24; + t28 = t14+t15+t16-t23; + t29 = q2*t28*2.0; + t30 = t17+t18+t19-t26; + t31 = q1*t30*2.0; + t32 = t20+t21+t22-t25; + t33 = q0*t32*2.0; + t40 = q3*t27*2.0; + t34 = t29+t31+t33-t40; + t35 = q0*q0; + t36 = q1*q1; + t37 = q2*q2; + t38 = q3*q3; + t39 = t35+t36+t37+t38; + t41 = t11+t12-t13+t24; + t42 = t14-t15+t16+t23; + t43 = q1*t42*2.0; + t44 = -t17+t18+t19+t26; + t45 = q2*t44*2.0; + t46 = t20-t21+t22+t25; + t47 = q3*t46*2.0; + t57 = q0*t41*2.0; + t48 = t43+t45+t47-t57; + t49 = -t14+t15+t16+t23; + t50 = q0*t49*2.0; + t51 = t11-t12+t13+t24; + t52 = t20+t21-t22+t25; + t53 = q2*t52*2.0; + t54 = t17-t18+t19+t26; + t55 = q3*t54*2.0; + t58 = q1*t51*2.0; + t56 = t50+t53+t55-t58; + t59 = OP_l_1_c_1_r_*t34; + t60 = OP_l_2_c_1_r_*t48; + t66 = OP_l_7_c_1_r_*t39; + t67 = OP_l_3_c_1_r_*t56; + t61 = t59+t60-t66-t67; + t62 = OP_l_1_c_2_r_*t34; + t63 = OP_l_2_c_2_r_*t48; + t64 = OP_l_1_c_3_r_*t34; + t65 = OP_l_2_c_3_r_*t48; + t72 = OP_l_7_c_2_r_*t39; + t73 = OP_l_3_c_2_r_*t56; + t68 = t62+t63-t72-t73; + t69 = t35+t36-t37-t38; + t86 = OP_l_7_c_3_r_*t39; + t87 = OP_l_3_c_3_r_*t56; + t70 = t64+t65-t86-t87; + t71 = dvx-dvx_b; + t74 = q0*q3*2.0; + t81 = q1*q2*2.0; + t75 = t74-t81; + t76 = q0*q2*2.0; + t77 = q1*q3*2.0; + t78 = t76+t77; + t79 = dvy-dvy_b; + t80 = dvz-dvz_b; + t82 = OP_l_1_c_11_r_*t34; + t83 = OP_l_2_c_11_r_*t48; + t103 = OP_l_7_c_11_r_*t39; + t104 = OP_l_3_c_11_r_*t56; + t84 = t82+t83-t103-t104; + t85 = t35-t36+t37-t38; + t88 = t74+t81; + t89 = OP_l_1_c_10_r_*t34; + t90 = OP_l_2_c_10_r_*t48; + t100 = OP_l_7_c_10_r_*t39; + t101 = OP_l_3_c_10_r_*t56; + t91 = t89+t90-t100-t101; + t92 = q0*q1*2.0; + t96 = q2*q3*2.0; + t93 = t92-t96; + t94 = OP_l_1_c_12_r_*t34; + t95 = OP_l_2_c_12_r_*t48; + t114 = OP_l_7_c_12_r_*t39; + t115 = OP_l_3_c_12_r_*t56; + t97 = t94+t95-t114-t115; + t98 = t35-t36-t37+t38; + t99 = t76-t77; + t102 = t92+t96; + t105 = OP_l_1_c_7_r_*t34; + t106 = OP_l_2_c_7_r_*t48; + t411 = OP_l_7_c_7_r_*t39; + t107 = t105+t106-t411-OP_l_3_c_7_r_*t56; + t108 = OP_l_1_c_8_r_*t34; + t109 = OP_l_2_c_8_r_*t48; + t412 = OP_l_7_c_8_r_*t39; + t110 = t108+t109-t412-OP_l_3_c_8_r_*t56; + t111 = OP_l_1_c_9_r_*t34; + t112 = OP_l_2_c_9_r_*t48; + t413 = OP_l_7_c_9_r_*t39; + t113 = t111+t112-t413-OP_l_3_c_9_r_*t56; + t116 = q0*t27*2.0; + t117 = q1*t28*2.0; + t118 = q3*t32*2.0; + t128 = q2*t30*2.0; + t119 = t116+t117+t118-t128; + t120 = q0*t46*2.0; + t121 = q2*t42*2.0; + t122 = q3*t41*2.0; + t129 = q1*t44*2.0; + t123 = t120+t121+t122-t129; + t124 = q1*t52*2.0; + t125 = q2*t51*2.0; + t126 = q3*t49*2.0; + t130 = q0*t54*2.0; + t127 = t124+t125+t126-t130; + t131 = OP_l_8_c_1_r_*t39; + t132 = OP_l_1_c_1_r_*t119; + t141 = OP_l_2_c_1_r_*t123; + t142 = OP_l_3_c_1_r_*t127; + t133 = t131+t132-t141-t142; + t134 = OP_l_8_c_2_r_*t39; + t135 = OP_l_1_c_2_r_*t119; + t147 = OP_l_2_c_2_r_*t123; + t148 = OP_l_3_c_2_r_*t127; + t136 = t134+t135-t147-t148; + t137 = OP_l_8_c_3_r_*t39; + t138 = OP_l_1_c_3_r_*t119; + t153 = OP_l_2_c_3_r_*t123; + t154 = OP_l_3_c_3_r_*t127; + t139 = t137+t138-t153-t154; + t140 = t39*t39; + t143 = q1*t27*2.0; + t144 = q2*t32*2.0; + t145 = q3*t30*2.0; + t204 = q0*t28*2.0; + t146 = t143+t144+t145-t204; + t149 = q0*t44*2.0; + t150 = q1*t46*2.0; + t151 = q2*t41*2.0; + t205 = q3*t42*2.0; + t152 = t149+t150+t151-t205; + t155 = q0*t52*2.0; + t156 = q1*t54*2.0; + t157 = q3*t51*2.0; + t206 = q2*t49*2.0; + t158 = t155+t156+t157-t206; + t159 = t69*t79; + t160 = t71*t75; + t161 = t159+t160; + t162 = t69*t80; + t222 = t71*t78; + t163 = t162-t222; + t164 = t78*t79; + t165 = t75*t80; + t166 = t164+t165; + t167 = OP_l_8_c_11_r_*t39; + t168 = OP_l_1_c_11_r_*t119; + t193 = OP_l_2_c_11_r_*t123; + t194 = OP_l_3_c_11_r_*t127; + t169 = t167+t168-t193-t194; + t170 = t71*t85; + t226 = t79*t88; + t171 = t170-t226; + t172 = t80*t85; + t173 = t79*t93; + t174 = t172+t173; + t175 = OP_l_8_c_10_r_*t39; + t176 = OP_l_1_c_10_r_*t119; + t191 = OP_l_2_c_10_r_*t123; + t192 = OP_l_3_c_10_r_*t127; + t177 = t175+t176-t191-t192; + t178 = OP_l_8_c_12_r_*t39; + t179 = OP_l_1_c_12_r_*t119; + t184 = OP_l_2_c_12_r_*t123; + t185 = OP_l_3_c_12_r_*t127; + t180 = t178+t179-t184-t185; + t181 = t71*t93; + t182 = t80*t88; + t183 = t181+t182; + t186 = t71*t98; + t187 = t80*t99; + t188 = t186+t187; + t189 = t79*t98; + t233 = t80*t102; + t190 = t189-t233; + t195 = t71*t102; + t196 = t79*t99; + t197 = t195+t196; + t198 = OP_l_8_c_7_r_*t39; + t199 = OP_l_1_c_7_r_*t119; + t200 = OP_l_8_c_8_r_*t39; + t201 = OP_l_1_c_8_r_*t119; + t202 = OP_l_8_c_9_r_*t39; + t203 = OP_l_1_c_9_r_*t119; + t207 = OP_l_9_c_1_r_*t39; + t208 = OP_l_2_c_1_r_*t152; + t216 = OP_l_1_c_1_r_*t146; + t217 = OP_l_3_c_1_r_*t158; + t209 = t207+t208-t216-t217; + t210 = OP_l_9_c_2_r_*t39; + t211 = OP_l_2_c_2_r_*t152; + t218 = OP_l_1_c_2_r_*t146; + t219 = OP_l_3_c_2_r_*t158; + t212 = t210+t211-t218-t219; + t213 = OP_l_9_c_3_r_*t39; + t214 = OP_l_2_c_3_r_*t152; + t220 = OP_l_1_c_3_r_*t146; + t221 = OP_l_3_c_3_r_*t158; + t215 = t213+t214-t220-t221; + t223 = OP_l_1_c_11_r_*t146; + t224 = OP_l_3_c_11_r_*t158; + t236 = OP_l_9_c_11_r_*t39; + t237 = OP_l_2_c_11_r_*t152; + t225 = t223+t224-t236-t237; + t227 = OP_l_1_c_10_r_*t146; + t228 = OP_l_3_c_10_r_*t158; + t234 = OP_l_9_c_10_r_*t39; + t235 = OP_l_2_c_10_r_*t152; + t229 = t227+t228-t234-t235; + t230 = OP_l_1_c_12_r_*t146; + t231 = OP_l_3_c_12_r_*t158; + t244 = OP_l_9_c_12_r_*t39; + t245 = OP_l_2_c_12_r_*t152; + t232 = t230+t231-t244-t245; + t238 = OP_l_9_c_7_r_*t39; + t239 = OP_l_2_c_7_r_*t152; + t240 = OP_l_9_c_8_r_*t39; + t241 = OP_l_2_c_8_r_*t152; + t242 = OP_l_9_c_9_r_*t39; + t243 = OP_l_2_c_9_r_*t152; + t246 = OP_l_2_c_1_r_*t163; + t247 = OP_l_11_c_1_r_*t75; + t248 = OP_l_1_c_1_r_*t166; + t258 = OP_l_10_c_1_r_*t69; + t259 = OP_l_3_c_1_r_*t161; + t260 = OP_l_12_c_1_r_*t78; + t249 = OP_l_4_c_1_r_+t246+t247+t248-t258-t259-t260; + t250 = OP_l_2_c_2_r_*t163; + t251 = OP_l_11_c_2_r_*t75; + t252 = OP_l_1_c_2_r_*t166; + t261 = OP_l_10_c_2_r_*t69; + t262 = OP_l_3_c_2_r_*t161; + t263 = OP_l_12_c_2_r_*t78; + t253 = OP_l_4_c_2_r_+t250+t251+t252-t261-t262-t263; + t254 = OP_l_2_c_3_r_*t163; + t255 = OP_l_11_c_3_r_*t75; + t256 = OP_l_1_c_3_r_*t166; + t264 = OP_l_10_c_3_r_*t69; + t265 = OP_l_3_c_3_r_*t161; + t266 = OP_l_12_c_3_r_*t78; + t257 = OP_l_4_c_3_r_+t254+t255+t256-t264-t265-t266; + t267 = OP_l_2_c_10_r_*t163; + t268 = OP_l_11_c_10_r_*t75; + t269 = OP_l_1_c_10_r_*t166; + t279 = OP_l_10_c_10_r_*t69; + t280 = OP_l_3_c_10_r_*t161; + t281 = OP_l_12_c_10_r_*t78; + t270 = OP_l_4_c_10_r_+t267+t268+t269-t279-t280-t281; + t271 = OP_l_2_c_12_r_*t163; + t272 = OP_l_11_c_12_r_*t75; + t273 = OP_l_1_c_12_r_*t166; + t285 = OP_l_10_c_12_r_*t69; + t286 = OP_l_3_c_12_r_*t161; + t287 = OP_l_12_c_12_r_*t78; + t274 = OP_l_4_c_12_r_+t271+t272+t273-t285-t286-t287; + t275 = OP_l_2_c_11_r_*t163; + t276 = OP_l_11_c_11_r_*t75; + t277 = OP_l_1_c_11_r_*t166; + t282 = OP_l_10_c_11_r_*t69; + t283 = OP_l_3_c_11_r_*t161; + t284 = OP_l_12_c_11_r_*t78; + t278 = OP_l_4_c_11_r_+t275+t276+t277-t282-t283-t284; + t288 = OP_l_2_c_7_r_*t163; + t289 = OP_l_11_c_7_r_*t75; + t290 = OP_l_1_c_7_r_*t166; + t291 = OP_l_4_c_7_r_+t288+t289+t290-OP_l_10_c_7_r_*t69-OP_l_3_c_7_r_*t161-OP_l_12_c_7_r_*t78; + t292 = OP_l_2_c_8_r_*t163; + t293 = OP_l_11_c_8_r_*t75; + t294 = OP_l_1_c_8_r_*t166; + t295 = OP_l_4_c_8_r_+t292+t293+t294-OP_l_10_c_8_r_*t69-OP_l_3_c_8_r_*t161-OP_l_12_c_8_r_*t78; + t296 = OP_l_2_c_9_r_*t163; + t297 = OP_l_11_c_9_r_*t75; + t298 = OP_l_1_c_9_r_*t166; + t299 = OP_l_4_c_9_r_+t296+t297+t298-OP_l_10_c_9_r_*t69-OP_l_3_c_9_r_*t161-OP_l_12_c_9_r_*t78; + t300 = OP_l_3_c_1_r_*t171; + t301 = OP_l_12_c_1_r_*t93; + t302 = OP_l_2_c_1_r_*t183; + t312 = OP_l_11_c_1_r_*t85; + t313 = OP_l_1_c_1_r_*t174; + t314 = OP_l_10_c_1_r_*t88; + t303 = OP_l_5_c_1_r_+t300+t301+t302-t312-t313-t314; + t304 = OP_l_3_c_2_r_*t171; + t305 = OP_l_12_c_2_r_*t93; + t306 = OP_l_2_c_2_r_*t183; + t315 = OP_l_11_c_2_r_*t85; + t316 = OP_l_1_c_2_r_*t174; + t317 = OP_l_10_c_2_r_*t88; + t307 = OP_l_5_c_2_r_+t304+t305+t306-t315-t316-t317; + t308 = OP_l_3_c_3_r_*t171; + t309 = OP_l_12_c_3_r_*t93; + t310 = OP_l_2_c_3_r_*t183; + t318 = OP_l_11_c_3_r_*t85; + t319 = OP_l_1_c_3_r_*t174; + t320 = OP_l_10_c_3_r_*t88; + t311 = OP_l_5_c_3_r_+t308+t309+t310-t318-t319-t320; + t321 = dvxNoise*t69*t88; + t322 = OP_l_3_c_10_r_*t171; + t323 = OP_l_12_c_10_r_*t93; + t324 = OP_l_2_c_10_r_*t183; + t334 = OP_l_11_c_10_r_*t85; + t335 = OP_l_1_c_10_r_*t174; + t336 = OP_l_10_c_10_r_*t88; + t325 = OP_l_5_c_10_r_+t322+t323+t324-t334-t335-t336; + t326 = OP_l_3_c_12_r_*t171; + t327 = OP_l_12_c_12_r_*t93; + t328 = OP_l_2_c_12_r_*t183; + t340 = OP_l_11_c_12_r_*t85; + t341 = OP_l_1_c_12_r_*t174; + t342 = OP_l_10_c_12_r_*t88; + t329 = OP_l_5_c_12_r_+t326+t327+t328-t340-t341-t342; + t330 = OP_l_3_c_11_r_*t171; + t331 = OP_l_12_c_11_r_*t93; + t332 = OP_l_2_c_11_r_*t183; + t337 = OP_l_11_c_11_r_*t85; + t338 = OP_l_1_c_11_r_*t174; + t339 = OP_l_10_c_11_r_*t88; + t333 = OP_l_5_c_11_r_+t330+t331+t332-t337-t338-t339; + t343 = OP_l_3_c_7_r_*t171; + t344 = OP_l_12_c_7_r_*t93; + t345 = OP_l_2_c_7_r_*t183; + t346 = OP_l_5_c_7_r_+t343+t344+t345-OP_l_1_c_7_r_*t174-OP_l_10_c_7_r_*t88-OP_l_11_c_7_r_*t85; + t347 = OP_l_3_c_8_r_*t171; + t348 = OP_l_12_c_8_r_*t93; + t349 = OP_l_2_c_8_r_*t183; + t350 = OP_l_5_c_8_r_+t347+t348+t349-OP_l_1_c_8_r_*t174-OP_l_10_c_8_r_*t88-OP_l_11_c_8_r_*t85; + t351 = OP_l_3_c_9_r_*t171; + t352 = OP_l_12_c_9_r_*t93; + t353 = OP_l_2_c_9_r_*t183; + t354 = OP_l_5_c_9_r_+t351+t352+t353-OP_l_1_c_9_r_*t174-OP_l_10_c_9_r_*t88-OP_l_11_c_9_r_*t85; + t355 = OP_l_1_c_1_r_*t190; + t356 = OP_l_10_c_1_r_*t99; + t357 = OP_l_3_c_1_r_*t197; + t367 = OP_l_12_c_1_r_*t98; + t368 = OP_l_2_c_1_r_*t188; + t369 = OP_l_11_c_1_r_*t102; + t358 = OP_l_6_c_1_r_+t355+t356+t357-t367-t368-t369; + t359 = OP_l_1_c_2_r_*t190; + t360 = OP_l_10_c_2_r_*t99; + t361 = OP_l_3_c_2_r_*t197; + t370 = OP_l_12_c_2_r_*t98; + t371 = OP_l_2_c_2_r_*t188; + t372 = OP_l_11_c_2_r_*t102; + t362 = OP_l_6_c_2_r_+t359+t360+t361-t370-t371-t372; + t363 = OP_l_1_c_3_r_*t190; + t364 = OP_l_10_c_3_r_*t99; + t365 = OP_l_3_c_3_r_*t197; + t373 = OP_l_12_c_3_r_*t98; + t374 = OP_l_2_c_3_r_*t188; + t375 = OP_l_11_c_3_r_*t102; + t366 = OP_l_6_c_3_r_+t363+t364+t365-t373-t374-t375; + t376 = dvzNoise*t78*t98; + t377 = OP_l_1_c_10_r_*t190; + t378 = OP_l_10_c_10_r_*t99; + t379 = OP_l_3_c_10_r_*t197; + t390 = OP_l_12_c_10_r_*t98; + t391 = OP_l_2_c_10_r_*t188; + t392 = OP_l_11_c_10_r_*t102; + t380 = OP_l_6_c_10_r_+t377+t378+t379-t390-t391-t392; + t381 = OP_l_1_c_12_r_*t190; + t382 = OP_l_10_c_12_r_*t99; + t383 = OP_l_3_c_12_r_*t197; + t396 = OP_l_12_c_12_r_*t98; + t397 = OP_l_2_c_12_r_*t188; + t398 = OP_l_11_c_12_r_*t102; + t384 = OP_l_6_c_12_r_+t381+t382+t383-t396-t397-t398; + t385 = OP_l_1_c_11_r_*t190; + t386 = OP_l_10_c_11_r_*t99; + t387 = OP_l_3_c_11_r_*t197; + t393 = OP_l_12_c_11_r_*t98; + t394 = OP_l_2_c_11_r_*t188; + t395 = OP_l_11_c_11_r_*t102; + t388 = OP_l_6_c_11_r_+t385+t386+t387-t393-t394-t395; + t389 = dvyNoise*t85*t102; + t399 = OP_l_1_c_7_r_*t190; + t400 = OP_l_10_c_7_r_*t99; + t401 = OP_l_3_c_7_r_*t197; + t402 = OP_l_6_c_7_r_+t399+t400+t401-OP_l_2_c_7_r_*t188-OP_l_11_c_7_r_*t102-OP_l_12_c_7_r_*t98; + t403 = OP_l_1_c_8_r_*t190; + t404 = OP_l_10_c_8_r_*t99; + t405 = OP_l_3_c_8_r_*t197; + t406 = OP_l_6_c_8_r_+t403+t404+t405-OP_l_2_c_8_r_*t188-OP_l_11_c_8_r_*t102-OP_l_12_c_8_r_*t98; + t407 = OP_l_1_c_9_r_*t190; + t408 = OP_l_10_c_9_r_*t99; + t409 = OP_l_3_c_9_r_*t197; + t410 = OP_l_6_c_9_r_+t407+t408+t409-OP_l_2_c_9_r_*t188-OP_l_11_c_9_r_*t102-OP_l_12_c_9_r_*t98; + A0[0][0] = daxNoise*t140+t34*t61+t48*t68-t56*t70-t39*t107; + A0[0][1] = -t39*t110-t61*t119+t68*t123+t70*t127; + A0[0][2] = -t39*t113-t68*t152+t70*t158+t146*(t59+t60-t66-t67); + A0[0][3] = OP_l_1_c_4_r_*t34+OP_l_2_c_4_r_*t48-OP_l_3_c_4_r_*t56-OP_l_7_c_4_r_*t39+t75*t84-t69*t91-t78*t97-t70*t161+t166*(t59+t60-t66-t67)+t163*(t62+t63-t72-t73); + A0[0][4] = OP_l_1_c_5_r_*t34+OP_l_2_c_5_r_*t48-OP_l_3_c_5_r_*t56-OP_l_7_c_5_r_*t39-t84*t85-t88*t91+t93*t97-t61*t174+t70*t171+t183*(t62+t63-t72-t73); + A0[0][5] = OP_l_1_c_6_r_*t34+OP_l_2_c_6_r_*t48-OP_l_3_c_6_r_*t56-OP_l_7_c_6_r_*t39-t84*t102-t97*t98+t61*t190-t68*t188+t99*(t89+t90-t100-t101)+t197*(t64+t65-t86-t87); + A0[0][6] = t107; + A0[0][7] = t110; + A0[0][8] = t113; + A0[0][9] = t91; + A0[0][10] = t84; + A0[0][11] = t97; + A0[1][0] = -t34*t133-t48*t136+t56*t139+t39*(t198+t199-OP_l_2_c_7_r_*t123-OP_l_3_c_7_r_*t127); + A0[1][1] = dayNoise*t140+t119*t133-t123*t136-t127*t139+t39*(t200+t201-OP_l_2_c_8_r_*t123-OP_l_3_c_8_r_*t127); + A0[1][2] = -t133*t146+t136*t152-t139*t158+t39*(t202+t203-OP_l_2_c_9_r_*t123-OP_l_3_c_9_r_*t127); + A0[1][3] = -OP_l_8_c_4_r_*t39-OP_l_1_c_4_r_*t119+OP_l_2_c_4_r_*t123+OP_l_3_c_4_r_*t127-t75*t169+t69*t177+t78*t180-t133*t166-t136*t163+t139*t161; + A0[1][4] = -OP_l_8_c_5_r_*t39-OP_l_1_c_5_r_*t119+OP_l_2_c_5_r_*t123+OP_l_3_c_5_r_*t127+t85*t169+t88*t177-t93*t180+t133*t174-t139*t171-t136*t183; + A0[1][5] = -OP_l_8_c_6_r_*t39-OP_l_1_c_6_r_*t119+OP_l_2_c_6_r_*t123+OP_l_3_c_6_r_*t127+t102*t169-t99*t177+t98*t180-t133*t190+t136*t188-t139*t197; + A0[1][6] = -t198-t199+OP_l_2_c_7_r_*t123+OP_l_3_c_7_r_*t127; + A0[1][7] = -t200-t201+OP_l_2_c_8_r_*t123+OP_l_3_c_8_r_*t127; + A0[1][8] = -t202-t203+OP_l_2_c_9_r_*t123+OP_l_3_c_9_r_*t127; + A0[1][9] = -t175-t176+t191+t192; + A0[1][10] = -t167-t168+t193+t194; + A0[1][11] = -t178-t179+t184+t185; + A0[2][0] = -t34*t209-t48*t212+t56*t215+t39*(t238+t239-OP_l_1_c_7_r_*t146-OP_l_3_c_7_r_*t158); + A0[2][1] = t119*t209-t123*t212-t127*t215+t39*(t240+t241-OP_l_1_c_8_r_*t146-OP_l_3_c_8_r_*t158); + A0[2][2] = dazNoise*t140-t146*t209+t152*t212-t158*t215+t39*(t242+t243-OP_l_1_c_9_r_*t146-OP_l_3_c_9_r_*t158); + A0[2][3] = -OP_l_9_c_4_r_*t39+OP_l_1_c_4_r_*t146-OP_l_2_c_4_r_*t152+OP_l_3_c_4_r_*t158-t69*t229+t75*t225-t78*t232-t163*t212-t166*t209+t161*t215; + A0[2][4] = -OP_l_9_c_5_r_*t39+OP_l_1_c_5_r_*t146-OP_l_2_c_5_r_*t152+OP_l_3_c_5_r_*t158-t85*t225-t88*t229+t93*t232+t174*t209-t171*t215-t183*t212; + A0[2][5] = -OP_l_9_c_6_r_*t39+OP_l_1_c_6_r_*t146-OP_l_2_c_6_r_*t152+OP_l_3_c_6_r_*t158-t102*t225-t98*t232-t190*t209+t188*t212-t197*t215+t99*(t227+t228-t234-t235); + A0[2][6] = -t238-t239+OP_l_1_c_7_r_*t146+OP_l_3_c_7_r_*t158; + A0[2][7] = -t240-t241+OP_l_1_c_8_r_*t146+OP_l_3_c_8_r_*t158; + A0[2][8] = -t242-t243+OP_l_1_c_9_r_*t146+OP_l_3_c_9_r_*t158; + A0[2][9] = t229; + A0[2][10] = t225; + A0[2][11] = t232; + A0[3][0] = t34*t249+t48*t253-t56*t257-t39*t291; + A0[3][1] = -t39*t295-t119*t249+t123*t253+t127*t257; + A0[3][2] = -t39*t299+t146*t249-t152*t253+t158*t257; + A0[3][3] = OP_l_4_c_4_r_-OP_l_10_c_4_r_*t69+OP_l_1_c_4_r_*t166+OP_l_2_c_4_r_*t163+OP_l_11_c_4_r_*t75-OP_l_3_c_4_r_*t161-OP_l_12_c_4_r_*t78-t69*t270-t78*t274+t75*t278+t166*t249+t163*t253-t161*t257+dvxNoise*(t69*t69)+dvyNoise*(t75*t75)+dvzNoise*(t78*t78); + A0[3][4] = OP_l_4_c_5_r_+t321-OP_l_10_c_5_r_*t69+OP_l_1_c_5_r_*t166+OP_l_2_c_5_r_*t163+OP_l_11_c_5_r_*t75-OP_l_3_c_5_r_*t161-OP_l_12_c_5_r_*t78-t88*t270-t85*t278+t93*t274-t174*t249+t171*t257+t183*t253-dvyNoise*t75*t85-dvzNoise*t78*t93; + A0[3][5] = OP_l_4_c_6_r_+t376-OP_l_10_c_6_r_*t69+OP_l_1_c_6_r_*t166+OP_l_2_c_6_r_*t163+OP_l_11_c_6_r_*t75-OP_l_3_c_6_r_*t161-OP_l_12_c_6_r_*t78+t99*t270-t98*t274-t102*t278+t190*t249-t188*t253+t197*t257-dvxNoise*t69*t99-dvyNoise*t75*t102; + A0[3][6] = t291; + A0[3][7] = t295; + A0[3][8] = t299; + A0[3][9] = t270; + A0[3][10] = t278; + A0[3][11] = t274; + A0[4][0] = t34*t303+t48*t307-t56*t311-t39*t346; + A0[4][1] = -t39*t350-t119*t303+t123*t307+t127*t311; + A0[4][2] = -t39*t354+t146*t303-t152*t307+t158*t311; + A0[4][3] = OP_l_5_c_4_r_+t321-OP_l_1_c_4_r_*t174-OP_l_10_c_4_r_*t88-OP_l_11_c_4_r_*t85+OP_l_3_c_4_r_*t171+OP_l_2_c_4_r_*t183+OP_l_12_c_4_r_*t93-t69*t325-t78*t329+t75*t333+t166*t303+t163*t307-t161*t311-dvyNoise*t75*t85-dvzNoise*t78*t93; + A0[4][4] = OP_l_5_c_5_r_-OP_l_1_c_5_r_*t174-OP_l_10_c_5_r_*t88-OP_l_11_c_5_r_*t85+OP_l_3_c_5_r_*t171+OP_l_2_c_5_r_*t183+OP_l_12_c_5_r_*t93-t88*t325-t85*t333+t93*t329-t174*t303+t171*t311+t183*t307+dvxNoise*(t88*t88)+dvyNoise*(t85*t85)+dvzNoise*(t93*t93); + A0[4][5] = OP_l_5_c_6_r_+t389-OP_l_1_c_6_r_*t174-OP_l_10_c_6_r_*t88-OP_l_11_c_6_r_*t85+OP_l_3_c_6_r_*t171+OP_l_2_c_6_r_*t183+OP_l_12_c_6_r_*t93+t99*t325-t98*t329-t102*t333+t190*t303-t188*t307+t197*t311-dvxNoise*t88*t99-dvzNoise*t93*t98; + A0[4][6] = t346; + A0[4][7] = t350; + A0[4][8] = t354; + A0[4][9] = t325; + A0[4][10] = t333; + A0[4][11] = t329; + A0[5][0] = t34*t358+t48*t362-t56*t366-t39*t402; + A0[5][1] = -t39*t406-t119*t358+t123*t362+t127*t366; + A0[5][2] = -t39*t410+t146*t358-t152*t362+t158*t366; + A0[5][3] = OP_l_6_c_4_r_+t376+OP_l_10_c_4_r_*t99+OP_l_1_c_4_r_*t190-OP_l_2_c_4_r_*t188-OP_l_11_c_4_r_*t102-OP_l_12_c_4_r_*t98+OP_l_3_c_4_r_*t197-t69*t380-t78*t384+t75*t388+t166*t358+t163*t362-t161*t366-dvxNoise*t69*t99-dvyNoise*t75*t102; + A0[5][4] = OP_l_6_c_5_r_+t389+OP_l_10_c_5_r_*t99+OP_l_1_c_5_r_*t190-OP_l_2_c_5_r_*t188-OP_l_11_c_5_r_*t102-OP_l_12_c_5_r_*t98+OP_l_3_c_5_r_*t197-t88*t380-t85*t388+t93*t384-t174*t358+t171*t366+t183*t362-dvxNoise*t88*t99-dvzNoise*t93*t98; + A0[5][5] = OP_l_6_c_6_r_+OP_l_10_c_6_r_*t99+OP_l_1_c_6_r_*t190-OP_l_2_c_6_r_*t188-OP_l_11_c_6_r_*t102-OP_l_12_c_6_r_*t98+OP_l_3_c_6_r_*t197+t99*t380-t98*t384-t102*t388+t190*t358-t188*t362+t197*t366+dvxNoise*(t99*t99)+dvyNoise*(t102*t102)+dvzNoise*(t98*t98); + A0[5][6] = t402; + A0[5][7] = t406; + A0[5][8] = t410; + A0[5][9] = t380; + A0[5][10] = t388; + A0[5][11] = t384; + A0[6][0] = -t411+OP_l_7_c_1_r_*t34+OP_l_7_c_2_r_*t48-OP_l_7_c_3_r_*t56; + A0[6][1] = -t412-OP_l_7_c_1_r_*t119+OP_l_7_c_2_r_*t123+OP_l_7_c_3_r_*t127; + A0[6][2] = -t413+OP_l_7_c_1_r_*t146-OP_l_7_c_2_r_*t152+OP_l_7_c_3_r_*t158; + A0[6][3] = OP_l_7_c_4_r_-OP_l_7_c_3_r_*t161+OP_l_7_c_2_r_*t163+OP_l_7_c_1_r_*t166-OP_l_7_c_10_r_*t69+OP_l_7_c_11_r_*t75-OP_l_7_c_12_r_*t78; + A0[6][4] = OP_l_7_c_5_r_+OP_l_7_c_3_r_*t171-OP_l_7_c_1_r_*t174+OP_l_7_c_2_r_*t183-OP_l_7_c_11_r_*t85-OP_l_7_c_10_r_*t88+OP_l_7_c_12_r_*t93; + A0[6][5] = OP_l_7_c_6_r_-OP_l_7_c_2_r_*t188+OP_l_7_c_1_r_*t190+OP_l_7_c_3_r_*t197+OP_l_7_c_10_r_*t99-OP_l_7_c_12_r_*t98-OP_l_7_c_11_r_*t102; + A0[6][6] = OP_l_7_c_7_r_; + A0[6][7] = OP_l_7_c_8_r_; + A0[6][8] = OP_l_7_c_9_r_; + A0[6][9] = OP_l_7_c_10_r_; + A0[6][10] = OP_l_7_c_11_r_; + A0[6][11] = OP_l_7_c_12_r_; + A0[7][0] = -t198+OP_l_8_c_1_r_*t34+OP_l_8_c_2_r_*t48-OP_l_8_c_3_r_*t56; + A0[7][1] = -t200-OP_l_8_c_1_r_*t119+OP_l_8_c_2_r_*t123+OP_l_8_c_3_r_*t127; + A0[7][2] = -t202+OP_l_8_c_1_r_*t146-OP_l_8_c_2_r_*t152+OP_l_8_c_3_r_*t158; + A0[7][3] = OP_l_8_c_4_r_-OP_l_8_c_3_r_*t161+OP_l_8_c_2_r_*t163+OP_l_8_c_1_r_*t166-OP_l_8_c_10_r_*t69+OP_l_8_c_11_r_*t75-OP_l_8_c_12_r_*t78; + A0[7][4] = OP_l_8_c_5_r_+OP_l_8_c_3_r_*t171-OP_l_8_c_1_r_*t174+OP_l_8_c_2_r_*t183-OP_l_8_c_11_r_*t85-OP_l_8_c_10_r_*t88+OP_l_8_c_12_r_*t93; + A0[7][5] = OP_l_8_c_6_r_-OP_l_8_c_2_r_*t188+OP_l_8_c_1_r_*t190+OP_l_8_c_3_r_*t197+OP_l_8_c_10_r_*t99-OP_l_8_c_12_r_*t98-OP_l_8_c_11_r_*t102; + A0[7][6] = OP_l_8_c_7_r_; + A0[7][7] = OP_l_8_c_8_r_; + A0[7][8] = OP_l_8_c_9_r_; + A0[7][9] = OP_l_8_c_10_r_; + A0[7][10] = OP_l_8_c_11_r_; + A0[7][11] = OP_l_8_c_12_r_; + A0[8][0] = -t238+OP_l_9_c_1_r_*t34+OP_l_9_c_2_r_*t48-OP_l_9_c_3_r_*t56; + A0[8][1] = -t240-OP_l_9_c_1_r_*t119+OP_l_9_c_2_r_*t123+OP_l_9_c_3_r_*t127; + A0[8][2] = -t242+OP_l_9_c_1_r_*t146-OP_l_9_c_2_r_*t152+OP_l_9_c_3_r_*t158; + A0[8][3] = OP_l_9_c_4_r_-OP_l_9_c_3_r_*t161+OP_l_9_c_2_r_*t163+OP_l_9_c_1_r_*t166-OP_l_9_c_10_r_*t69+OP_l_9_c_11_r_*t75-OP_l_9_c_12_r_*t78; + A0[8][4] = OP_l_9_c_5_r_+OP_l_9_c_3_r_*t171-OP_l_9_c_1_r_*t174+OP_l_9_c_2_r_*t183-OP_l_9_c_11_r_*t85-OP_l_9_c_10_r_*t88+OP_l_9_c_12_r_*t93; + A0[8][5] = OP_l_9_c_6_r_-OP_l_9_c_2_r_*t188+OP_l_9_c_1_r_*t190+OP_l_9_c_3_r_*t197+OP_l_9_c_10_r_*t99-OP_l_9_c_12_r_*t98-OP_l_9_c_11_r_*t102; + A0[8][6] = OP_l_9_c_7_r_; + A0[8][7] = OP_l_9_c_8_r_; + A0[8][8] = OP_l_9_c_9_r_; + A0[8][9] = OP_l_9_c_10_r_; + A0[8][10] = OP_l_9_c_11_r_; + A0[8][11] = OP_l_9_c_12_r_; + A0[9][0] = OP_l_10_c_1_r_*t34-OP_l_10_c_7_r_*t39+OP_l_10_c_2_r_*t48-OP_l_10_c_3_r_*t56; + A0[9][1] = -OP_l_10_c_8_r_*t39-OP_l_10_c_1_r_*t119+OP_l_10_c_2_r_*t123+OP_l_10_c_3_r_*t127; + A0[9][2] = -OP_l_10_c_9_r_*t39+OP_l_10_c_1_r_*t146-OP_l_10_c_2_r_*t152+OP_l_10_c_3_r_*t158; + A0[9][3] = OP_l_10_c_4_r_-t279-OP_l_10_c_3_r_*t161+OP_l_10_c_2_r_*t163+OP_l_10_c_1_r_*t166+OP_l_10_c_11_r_*t75-OP_l_10_c_12_r_*t78; + A0[9][4] = OP_l_10_c_5_r_-t336+OP_l_10_c_3_r_*t171-OP_l_10_c_1_r_*t174+OP_l_10_c_2_r_*t183-OP_l_10_c_11_r_*t85+OP_l_10_c_12_r_*t93; + A0[9][5] = OP_l_10_c_6_r_+t378-OP_l_10_c_2_r_*t188+OP_l_10_c_1_r_*t190+OP_l_10_c_3_r_*t197-OP_l_10_c_12_r_*t98-OP_l_10_c_11_r_*t102; + A0[9][6] = OP_l_10_c_7_r_; + A0[9][7] = OP_l_10_c_8_r_; + A0[9][8] = OP_l_10_c_9_r_; + A0[9][9] = OP_l_10_c_10_r_; + A0[9][10] = OP_l_10_c_11_r_; + A0[9][11] = OP_l_10_c_12_r_; + A0[10][0] = OP_l_11_c_1_r_*t34-OP_l_11_c_7_r_*t39+OP_l_11_c_2_r_*t48-OP_l_11_c_3_r_*t56; + A0[10][1] = -OP_l_11_c_8_r_*t39-OP_l_11_c_1_r_*t119+OP_l_11_c_2_r_*t123+OP_l_11_c_3_r_*t127; + A0[10][2] = -OP_l_11_c_9_r_*t39+OP_l_11_c_1_r_*t146-OP_l_11_c_2_r_*t152+OP_l_11_c_3_r_*t158; + A0[10][3] = OP_l_11_c_4_r_+t276-OP_l_11_c_3_r_*t161+OP_l_11_c_2_r_*t163+OP_l_11_c_1_r_*t166-OP_l_11_c_10_r_*t69-OP_l_11_c_12_r_*t78; + A0[10][4] = OP_l_11_c_5_r_-t337+OP_l_11_c_3_r_*t171-OP_l_11_c_1_r_*t174+OP_l_11_c_2_r_*t183-OP_l_11_c_10_r_*t88+OP_l_11_c_12_r_*t93; + A0[10][5] = OP_l_11_c_6_r_-t395-OP_l_11_c_2_r_*t188+OP_l_11_c_1_r_*t190+OP_l_11_c_3_r_*t197+OP_l_11_c_10_r_*t99-OP_l_11_c_12_r_*t98; + A0[10][6] = OP_l_11_c_7_r_; + A0[10][7] = OP_l_11_c_8_r_; + A0[10][8] = OP_l_11_c_9_r_; + A0[10][9] = OP_l_11_c_10_r_; + A0[10][10] = OP_l_11_c_11_r_; + A0[10][11] = OP_l_11_c_12_r_; + A0[11][0] = OP_l_12_c_1_r_*t34-OP_l_12_c_7_r_*t39+OP_l_12_c_2_r_*t48-OP_l_12_c_3_r_*t56; + A0[11][1] = -OP_l_12_c_8_r_*t39-OP_l_12_c_1_r_*t119+OP_l_12_c_2_r_*t123+OP_l_12_c_3_r_*t127; + A0[11][2] = -OP_l_12_c_9_r_*t39+OP_l_12_c_1_r_*t146-OP_l_12_c_2_r_*t152+OP_l_12_c_3_r_*t158; + A0[11][3] = OP_l_12_c_4_r_-t287-OP_l_12_c_3_r_*t161+OP_l_12_c_2_r_*t163+OP_l_12_c_1_r_*t166-OP_l_12_c_10_r_*t69+OP_l_12_c_11_r_*t75; + A0[11][4] = OP_l_12_c_5_r_+t327+OP_l_12_c_3_r_*t171-OP_l_12_c_1_r_*t174+OP_l_12_c_2_r_*t183-OP_l_12_c_11_r_*t85-OP_l_12_c_10_r_*t88; + A0[11][5] = OP_l_12_c_6_r_-t396-OP_l_12_c_2_r_*t188+OP_l_12_c_1_r_*t190+OP_l_12_c_3_r_*t197+OP_l_12_c_10_r_*t99-OP_l_12_c_11_r_*t102; + A0[11][6] = OP_l_12_c_7_r_; + A0[11][7] = OP_l_12_c_8_r_; + A0[11][8] = OP_l_12_c_9_r_; + A0[11][9] = OP_l_12_c_10_r_; + A0[11][10] = OP_l_12_c_11_r_; + A0[11][11] = OP_l_12_c_12_r_; diff --git a/libraries/AP_NavEKF/Models/GimbalEstimatorExample/calcP.cpp b/libraries/AP_NavEKF/Models/GimbalEstimatorExample/calcP.cpp new file mode 100644 index 0000000000..86afdb442d --- /dev/null +++ b/libraries/AP_NavEKF/Models/GimbalEstimatorExample/calcP.cpp @@ -0,0 +1,556 @@ +float t2 = dax*0.5f; +float t3 = dax_b*0.5f; +float t4 = t2-t3; +float t5 = day*0.5f; +float t6 = day_b*0.5f; +float t7 = t5-t6; +float t8 = daz*0.5f; +float t9 = daz_b*0.5f; +float t10 = t8-t9; +float t11 = q2*t4*0.5f; +float t12 = q1*t7*0.5f; +float t13 = q0*t10*0.5f; +float t14 = q2*0.5f; +float t15 = q3*t4*0.5f; +float t16 = q1*t10*0.5f; +float t17 = q1*0.5f; +float t18 = q0*t4*0.5f; +float t19 = q3*t7*0.5f; +float t20 = q0*0.5f; +float t21 = q2*t7*0.5f; +float t22 = q3*t10*0.5f; +float t23 = q0*t7*0.5f; +float t24 = q3*0.5f; +float t25 = q1*t4*0.5f; +float t26 = q2*t10*0.5f; +float t27 = t11+t12+t13-t24; +float t28 = t14+t15+t16-t23; +float t29 = q2*t28*2.0f; +float t30 = t17+t18+t19-t26; +float t31 = q1*t30*2.0f; +float t32 = t20+t21+t22-t25; +float t33 = q0*t32*2.0f; +float t40 = q3*t27*2.0f; +float t34 = t29+t31+t33-t40; +float t35 = q0*q0; +float t36 = q1*q1; +float t37 = q2*q2; +float t38 = q3*q3; +float t39 = t35+t36+t37+t38; +float t41 = t11+t12-t13+t24; +float t42 = t14-t15+t16+t23; +float t43 = q1*t42*2.0f; +float t44 = -t17+t18+t19+t26; +float t45 = q2*t44*2.0f; +float t46 = t20-t21+t22+t25; +float t47 = q3*t46*2.0f; +float t57 = q0*t41*2.0f; +float t48 = t43+t45+t47-t57; +float t49 = -t14+t15+t16+t23; +float t50 = q0*t49*2.0f; +float t51 = t11-t12+t13+t24; +float t52 = t20+t21-t22+t25; +float t53 = q2*t52*2.0f; +float t54 = t17-t18+t19+t26; +float t55 = q3*t54*2.0f; +float t58 = q1*t51*2.0f; +float t56 = t50+t53+t55-t58; +float t59 = OP[0][0]*t34; +float t60 = OP[1][0]*t48; +float t66 = OP[6][0]*t39; +float t67 = OP[2][0]*t56; +float t61 = t59+t60-t66-t67; +float t62 = OP[0][1]*t34; +float t63 = OP[1][1]*t48; +float t64 = OP[0][2]*t34; +float t65 = OP[1][2]*t48; +float t72 = OP[6][1]*t39; +float t73 = OP[2][1]*t56; +float t68 = t62+t63-t72-t73; +float t69 = t35+t36-t37-t38; +float t86 = OP[6][2]*t39; +float t87 = OP[2][2]*t56; +float t70 = t64+t65-t86-t87; +float t71 = dvx-dvx_b; +float t74 = q0*q3*2.0f; +float t81 = q1*q2*2.0f; +float t75 = t74-t81; +float t76 = q0*q2*2.0f; +float t77 = q1*q3*2.0f; +float t78 = t76+t77; +float t79 = dvy-dvy_b; +float t80 = dvz-dvz_b; +float t82 = OP[0][10]*t34; +float t83 = OP[1][10]*t48; +float t103 = OP[6][10]*t39; +float t104 = OP[2][10]*t56; +float t84 = t82+t83-t103-t104; +float t85 = t35-t36+t37-t38; +float t88 = t74+t81; +float t89 = OP[0][9]*t34; +float t90 = OP[1][9]*t48; +float t100 = OP[6][9]*t39; +float t101 = OP[2][9]*t56; +float t91 = t89+t90-t100-t101; +float t92 = q0*q1*2.0f; +float t96 = q2*q3*2.0f; +float t93 = t92-t96; +float t94 = OP[0][11]*t34; +float t95 = OP[1][11]*t48; +float t114 = OP[6][11]*t39; +float t115 = OP[2][11]*t56; +float t97 = t94+t95-t114-t115; +float t98 = t35-t36-t37+t38; +float t99 = t76-t77; +float t102 = t92+t96; +float t105 = OP[0][6]*t34; +float t106 = OP[1][6]*t48; +float t411 = OP[6][6]*t39; +float t107 = t105+t106-t411-OP[2][6]*t56; +float t108 = OP[0][7]*t34; +float t109 = OP[1][7]*t48; +float t412 = OP[6][7]*t39; +float t110 = t108+t109-t412-OP[2][7]*t56; +float t111 = OP[0][8]*t34; +float t112 = OP[1][8]*t48; +float t413 = OP[6][8]*t39; +float t113 = t111+t112-t413-OP[2][8]*t56; +float t116 = q0*t27*2.0f; +float t117 = q1*t28*2.0f; +float t118 = q3*t32*2.0f; +float t128 = q2*t30*2.0f; +float t119 = t116+t117+t118-t128; +float t120 = q0*t46*2.0f; +float t121 = q2*t42*2.0f; +float t122 = q3*t41*2.0f; +float t129 = q1*t44*2.0f; +float t123 = t120+t121+t122-t129; +float t124 = q1*t52*2.0f; +float t125 = q2*t51*2.0f; +float t126 = q3*t49*2.0f; +float t130 = q0*t54*2.0f; +float t127 = t124+t125+t126-t130; +float t131 = OP[7][0]*t39; +float t132 = OP[0][0]*t119; +float t141 = OP[1][0]*t123; +float t142 = OP[2][0]*t127; +float t133 = t131+t132-t141-t142; +float t134 = OP[7][1]*t39; +float t135 = OP[0][1]*t119; +float t147 = OP[1][1]*t123; +float t148 = OP[2][1]*t127; +float t136 = t134+t135-t147-t148; +float t137 = OP[7][2]*t39; +float t138 = OP[0][2]*t119; +float t153 = OP[1][2]*t123; +float t154 = OP[2][2]*t127; +float t139 = t137+t138-t153-t154; +float t140 = t39*t39; +float t143 = q1*t27*2.0f; +float t144 = q2*t32*2.0f; +float t145 = q3*t30*2.0f; +float t204 = q0*t28*2.0f; +float t146 = t143+t144+t145-t204; +float t149 = q0*t44*2.0f; +float t150 = q1*t46*2.0f; +float t151 = q2*t41*2.0f; +float t205 = q3*t42*2.0f; +float t152 = t149+t150+t151-t205; +float t155 = q0*t52*2.0f; +float t156 = q1*t54*2.0f; +float t157 = q3*t51*2.0f; +float t206 = q2*t49*2.0f; +float t158 = t155+t156+t157-t206; +float t159 = t69*t79; +float t160 = t71*t75; +float t161 = t159+t160; +float t162 = t69*t80; +float t222 = t71*t78; +float t163 = t162-t222; +float t164 = t78*t79; +float t165 = t75*t80; +float t166 = t164+t165; +float t167 = OP[7][10]*t39; +float t168 = OP[0][10]*t119; +float t193 = OP[1][10]*t123; +float t194 = OP[2][10]*t127; +float t169 = t167+t168-t193-t194; +float t170 = t71*t85; +float t226 = t79*t88; +float t171 = t170-t226; +float t172 = t80*t85; +float t173 = t79*t93; +float t174 = t172+t173; +float t175 = OP[7][9]*t39; +float t176 = OP[0][9]*t119; +float t191 = OP[1][9]*t123; +float t192 = OP[2][9]*t127; +float t177 = t175+t176-t191-t192; +float t178 = OP[7][11]*t39; +float t179 = OP[0][11]*t119; +float t184 = OP[1][11]*t123; +float t185 = OP[2][11]*t127; +float t180 = t178+t179-t184-t185; +float t181 = t71*t93; +float t182 = t80*t88; +float t183 = t181+t182; +float t186 = t71*t98; +float t187 = t80*t99; +float t188 = t186+t187; +float t189 = t79*t98; +float t233 = t80*t102; +float t190 = t189-t233; +float t195 = t71*t102; +float t196 = t79*t99; +float t197 = t195+t196; +float t198 = OP[7][6]*t39; +float t199 = OP[0][6]*t119; +float t200 = OP[7][7]*t39; +float t201 = OP[0][7]*t119; +float t202 = OP[7][8]*t39; +float t203 = OP[0][8]*t119; +float t207 = OP[8][0]*t39; +float t208 = OP[1][0]*t152; +float t216 = OP[0][0]*t146; +float t217 = OP[2][0]*t158; +float t209 = t207+t208-t216-t217; +float t210 = OP[8][1]*t39; +float t211 = OP[1][1]*t152; +float t218 = OP[0][1]*t146; +float t219 = OP[2][1]*t158; +float t212 = t210+t211-t218-t219; +float t213 = OP[8][2]*t39; +float t214 = OP[1][2]*t152; +float t220 = OP[0][2]*t146; +float t221 = OP[2][2]*t158; +float t215 = t213+t214-t220-t221; +float t223 = OP[0][10]*t146; +float t224 = OP[2][10]*t158; +float t236 = OP[8][10]*t39; +float t237 = OP[1][10]*t152; +float t225 = t223+t224-t236-t237; +float t227 = OP[0][9]*t146; +float t228 = OP[2][9]*t158; +float t234 = OP[8][9]*t39; +float t235 = OP[1][9]*t152; +float t229 = t227+t228-t234-t235; +float t230 = OP[0][11]*t146; +float t231 = OP[2][11]*t158; +float t244 = OP[8][11]*t39; +float t245 = OP[1][11]*t152; +float t232 = t230+t231-t244-t245; +float t238 = OP[8][6]*t39; +float t239 = OP[1][6]*t152; +float t240 = OP[8][7]*t39; +float t241 = OP[1][7]*t152; +float t242 = OP[8][8]*t39; +float t243 = OP[1][8]*t152; +float t246 = OP[1][0]*t163; +float t247 = OP[10][0]*t75; +float t248 = OP[0][0]*t166; +float t258 = OP[9][0]*t69; +float t259 = OP[2][0]*t161; +float t260 = OP[11][0]*t78; +float t249 = OP[3][0]+t246+t247+t248-t258-t259-t260; +float t250 = OP[1][1]*t163; +float t251 = OP[10][1]*t75; +float t252 = OP[0][1]*t166; +float t261 = OP[9][1]*t69; +float t262 = OP[2][1]*t161; +float t263 = OP[11][1]*t78; +float t253 = OP[3][1]+t250+t251+t252-t261-t262-t263; +float t254 = OP[1][2]*t163; +float t255 = OP[10][2]*t75; +float t256 = OP[0][2]*t166; +float t264 = OP[9][2]*t69; +float t265 = OP[2][2]*t161; +float t266 = OP[11][2]*t78; +float t257 = OP[3][2]+t254+t255+t256-t264-t265-t266; +float t267 = OP[1][9]*t163; +float t268 = OP[10][9]*t75; +float t269 = OP[0][9]*t166; +float t279 = OP[9][9]*t69; +float t280 = OP[2][9]*t161; +float t281 = OP[11][9]*t78; +float t270 = OP[3][9]+t267+t268+t269-t279-t280-t281; +float t271 = OP[1][11]*t163; +float t272 = OP[10][11]*t75; +float t273 = OP[0][11]*t166; +float t285 = OP[9][11]*t69; +float t286 = OP[2][11]*t161; +float t287 = OP[11][11]*t78; +float t274 = OP[3][11]+t271+t272+t273-t285-t286-t287; +float t275 = OP[1][10]*t163; +float t276 = OP[10][10]*t75; +float t277 = OP[0][10]*t166; +float t282 = OP[9][10]*t69; +float t283 = OP[2][10]*t161; +float t284 = OP[11][10]*t78; +float t278 = OP[3][10]+t275+t276+t277-t282-t283-t284; +float t288 = OP[1][6]*t163; +float t289 = OP[10][6]*t75; +float t290 = OP[0][6]*t166; +float t291 = OP[3][6]+t288+t289+t290-OP[9][6]*t69-OP[2][6]*t161-OP[11][6]*t78; +float t292 = OP[1][7]*t163; +float t293 = OP[10][7]*t75; +float t294 = OP[0][7]*t166; +float t295 = OP[3][7]+t292+t293+t294-OP[9][7]*t69-OP[2][7]*t161-OP[11][7]*t78; +float t296 = OP[1][8]*t163; +float t297 = OP[10][8]*t75; +float t298 = OP[0][8]*t166; +float t299 = OP[3][8]+t296+t297+t298-OP[9][8]*t69-OP[2][8]*t161-OP[11][8]*t78; +float t300 = OP[2][0]*t171; +float t301 = OP[11][0]*t93; +float t302 = OP[1][0]*t183; +float t312 = OP[10][0]*t85; +float t313 = OP[0][0]*t174; +float t314 = OP[9][0]*t88; +float t303 = OP[4][0]+t300+t301+t302-t312-t313-t314; +float t304 = OP[2][1]*t171; +float t305 = OP[11][1]*t93; +float t306 = OP[1][1]*t183; +float t315 = OP[10][1]*t85; +float t316 = OP[0][1]*t174; +float t317 = OP[9][1]*t88; +float t307 = OP[4][1]+t304+t305+t306-t315-t316-t317; +float t308 = OP[2][2]*t171; +float t309 = OP[11][2]*t93; +float t310 = OP[1][2]*t183; +float t318 = OP[10][2]*t85; +float t319 = OP[0][2]*t174; +float t320 = OP[9][2]*t88; +float t311 = OP[4][2]+t308+t309+t310-t318-t319-t320; +float t321 = dvxNoise*t69*t88; +float t322 = OP[2][9]*t171; +float t323 = OP[11][9]*t93; +float t324 = OP[1][9]*t183; +float t334 = OP[10][9]*t85; +float t335 = OP[0][9]*t174; +float t336 = OP[9][9]*t88; +float t325 = OP[4][9]+t322+t323+t324-t334-t335-t336; +float t326 = OP[2][11]*t171; +float t327 = OP[11][11]*t93; +float t328 = OP[1][11]*t183; +float t340 = OP[10][11]*t85; +float t341 = OP[0][11]*t174; +float t342 = OP[9][11]*t88; +float t329 = OP[4][11]+t326+t327+t328-t340-t341-t342; +float t330 = OP[2][10]*t171; +float t331 = OP[11][10]*t93; +float t332 = OP[1][10]*t183; +float t337 = OP[10][10]*t85; +float t338 = OP[0][10]*t174; +float t339 = OP[9][10]*t88; +float t333 = OP[4][10]+t330+t331+t332-t337-t338-t339; +float t343 = OP[2][6]*t171; +float t344 = OP[11][6]*t93; +float t345 = OP[1][6]*t183; +float t346 = OP[4][6]+t343+t344+t345-OP[0][6]*t174-OP[9][6]*t88-OP[10][6]*t85; +float t347 = OP[2][7]*t171; +float t348 = OP[11][7]*t93; +float t349 = OP[1][7]*t183; +float t350 = OP[4][7]+t347+t348+t349-OP[0][7]*t174-OP[9][7]*t88-OP[10][7]*t85; +float t351 = OP[2][8]*t171; +float t352 = OP[11][8]*t93; +float t353 = OP[1][8]*t183; +float t354 = OP[4][8]+t351+t352+t353-OP[0][8]*t174-OP[9][8]*t88-OP[10][8]*t85; +float t355 = OP[0][0]*t190; +float t356 = OP[9][0]*t99; +float t357 = OP[2][0]*t197; +float t367 = OP[11][0]*t98; +float t368 = OP[1][0]*t188; +float t369 = OP[10][0]*t102; +float t358 = OP[5][0]+t355+t356+t357-t367-t368-t369; +float t359 = OP[0][1]*t190; +float t360 = OP[9][1]*t99; +float t361 = OP[2][1]*t197; +float t370 = OP[11][1]*t98; +float t371 = OP[1][1]*t188; +float t372 = OP[10][1]*t102; +float t362 = OP[5][1]+t359+t360+t361-t370-t371-t372; +float t363 = OP[0][2]*t190; +float t364 = OP[9][2]*t99; +float t365 = OP[2][2]*t197; +float t373 = OP[11][2]*t98; +float t374 = OP[1][2]*t188; +float t375 = OP[10][2]*t102; +float t366 = OP[5][2]+t363+t364+t365-t373-t374-t375; +float t376 = dvzNoise*t78*t98; +float t377 = OP[0][9]*t190; +float t378 = OP[9][9]*t99; +float t379 = OP[2][9]*t197; +float t390 = OP[11][9]*t98; +float t391 = OP[1][9]*t188; +float t392 = OP[10][9]*t102; +float t380 = OP[5][9]+t377+t378+t379-t390-t391-t392; +float t381 = OP[0][11]*t190; +float t382 = OP[9][11]*t99; +float t383 = OP[2][11]*t197; +float t396 = OP[11][11]*t98; +float t397 = OP[1][11]*t188; +float t398 = OP[10][11]*t102; +float t384 = OP[5][11]+t381+t382+t383-t396-t397-t398; +float t385 = OP[0][10]*t190; +float t386 = OP[9][10]*t99; +float t387 = OP[2][10]*t197; +float t393 = OP[11][10]*t98; +float t394 = OP[1][10]*t188; +float t395 = OP[10][10]*t102; +float t388 = OP[5][10]+t385+t386+t387-t393-t394-t395; +float t389 = dvyNoise*t85*t102; +float t399 = OP[0][6]*t190; +float t400 = OP[9][6]*t99; +float t401 = OP[2][6]*t197; +float t402 = OP[5][6]+t399+t400+t401-OP[1][6]*t188-OP[10][6]*t102-OP[11][6]*t98; +float t403 = OP[0][7]*t190; +float t404 = OP[9][7]*t99; +float t405 = OP[2][7]*t197; +float t406 = OP[5][7]+t403+t404+t405-OP[1][7]*t188-OP[10][7]*t102-OP[11][7]*t98; +float t407 = OP[0][8]*t190; +float t408 = OP[9][8]*t99; +float t409 = OP[2][8]*t197; +float t410 = OP[5][8]+t407+t408+t409-OP[1][8]*t188-OP[10][8]*t102-OP[11][8]*t98; +A0[0][0] = daxNoise*t140+t34*t61+t48*t68-t56*t70-t39*t107; +A0[0][1] = -t39*t110-t61*t119+t68*t123+t70*t127; +A0[0][2] = -t39*t113-t68*t152+t70*t158+t146*(t59+t60-t66-t67); +A0[0][3] = OP[0][3]*t34+OP[1][3]*t48-OP[2][3]*t56-OP[6][3]*t39+t75*t84-t69*t91-t78*t97-t70*t161+t166*(t59+t60-t66-t67)+t163*(t62+t63-t72-t73); +A0[0][4] = OP[0][4]*t34+OP[1][4]*t48-OP[2][4]*t56-OP[6][4]*t39-t84*t85-t88*t91+t93*t97-t61*t174+t70*t171+t183*(t62+t63-t72-t73); +A0[0][5] = OP[0][5]*t34+OP[1][5]*t48-OP[2][5]*t56-OP[6][5]*t39-t84*t102-t97*t98+t61*t190-t68*t188+t99*(t89+t90-t100-t101)+t197*(t64+t65-t86-t87); +A0[0][6] = t107; +A0[0][7] = t110; +A0[0][8] = t113; +A0[0][9] = t91; +A0[0][10] = t84; +A0[0][11] = t97; +A0[1][0] = -t34*t133-t48*t136+t56*t139+t39*(t198+t199-OP[1][6]*t123-OP[2][6]*t127); +A0[1][1] = dayNoise*t140+t119*t133-t123*t136-t127*t139+t39*(t200+t201-OP[1][7]*t123-OP[2][7]*t127); +A0[1][2] = -t133*t146+t136*t152-t139*t158+t39*(t202+t203-OP[1][8]*t123-OP[2][8]*t127); +A0[1][3] = -OP[7][3]*t39-OP[0][3]*t119+OP[1][3]*t123+OP[2][3]*t127-t75*t169+t69*t177+t78*t180-t133*t166-t136*t163+t139*t161; +A0[1][4] = -OP[7][4]*t39-OP[0][4]*t119+OP[1][4]*t123+OP[2][4]*t127+t85*t169+t88*t177-t93*t180+t133*t174-t139*t171-t136*t183; +A0[1][5] = -OP[7][5]*t39-OP[0][5]*t119+OP[1][5]*t123+OP[2][5]*t127+t102*t169-t99*t177+t98*t180-t133*t190+t136*t188-t139*t197; +A0[1][6] = -t198-t199+OP[1][6]*t123+OP[2][6]*t127; +A0[1][7] = -t200-t201+OP[1][7]*t123+OP[2][7]*t127; +A0[1][8] = -t202-t203+OP[1][8]*t123+OP[2][8]*t127; +A0[1][9] = -t175-t176+t191+t192; +A0[1][10] = -t167-t168+t193+t194; +A0[1][11] = -t178-t179+t184+t185; +A0[2][0] = -t34*t209-t48*t212+t56*t215+t39*(t238+t239-OP[0][6]*t146-OP[2][6]*t158); +A0[2][1] = t119*t209-t123*t212-t127*t215+t39*(t240+t241-OP[0][7]*t146-OP[2][7]*t158); +A0[2][2] = dazNoise*t140-t146*t209+t152*t212-t158*t215+t39*(t242+t243-OP[0][8]*t146-OP[2][8]*t158); +A0[2][3] = -OP[8][3]*t39+OP[0][3]*t146-OP[1][3]*t152+OP[2][3]*t158-t69*t229+t75*t225-t78*t232-t163*t212-t166*t209+t161*t215; +A0[2][4] = -OP[8][4]*t39+OP[0][4]*t146-OP[1][4]*t152+OP[2][4]*t158-t85*t225-t88*t229+t93*t232+t174*t209-t171*t215-t183*t212; +A0[2][5] = -OP[8][5]*t39+OP[0][5]*t146-OP[1][5]*t152+OP[2][5]*t158-t102*t225-t98*t232-t190*t209+t188*t212-t197*t215+t99*(t227+t228-t234-t235); +A0[2][6] = -t238-t239+OP[0][6]*t146+OP[2][6]*t158; +A0[2][7] = -t240-t241+OP[0][7]*t146+OP[2][7]*t158; +A0[2][8] = -t242-t243+OP[0][8]*t146+OP[2][8]*t158; +A0[2][9] = t229; +A0[2][10] = t225; +A0[2][11] = t232; +A0[3][0] = t34*t249+t48*t253-t56*t257-t39*t291; +A0[3][1] = -t39*t295-t119*t249+t123*t253+t127*t257; +A0[3][2] = -t39*t299+t146*t249-t152*t253+t158*t257; +A0[3][3] = OP[3][3]-OP[9][3]*t69+OP[0][3]*t166+OP[1][3]*t163+OP[10][3]*t75-OP[2][3]*t161-OP[11][3]*t78-t69*t270-t78*t274+t75*t278+t166*t249+t163*t253-t161*t257+dvxNoise*(t69*t69)+dvyNoise*(t75*t75)+dvzNoise*(t78*t78); +A0[3][4] = OP[3][4]+t321-OP[9][4]*t69+OP[0][4]*t166+OP[1][4]*t163+OP[10][4]*t75-OP[2][4]*t161-OP[11][4]*t78-t88*t270-t85*t278+t93*t274-t174*t249+t171*t257+t183*t253-dvyNoise*t75*t85-dvzNoise*t78*t93; +A0[3][5] = OP[3][5]+t376-OP[9][5]*t69+OP[0][5]*t166+OP[1][5]*t163+OP[10][5]*t75-OP[2][5]*t161-OP[11][5]*t78+t99*t270-t98*t274-t102*t278+t190*t249-t188*t253+t197*t257-dvxNoise*t69*t99-dvyNoise*t75*t102; +A0[3][6] = t291; +A0[3][7] = t295; +A0[3][8] = t299; +A0[3][9] = t270; +A0[3][10] = t278; +A0[3][11] = t274; +A0[4][0] = t34*t303+t48*t307-t56*t311-t39*t346; +A0[4][1] = -t39*t350-t119*t303+t123*t307+t127*t311; +A0[4][2] = -t39*t354+t146*t303-t152*t307+t158*t311; +A0[4][3] = OP[4][3]+t321-OP[0][3]*t174-OP[9][3]*t88-OP[10][3]*t85+OP[2][3]*t171+OP[1][3]*t183+OP[11][3]*t93-t69*t325-t78*t329+t75*t333+t166*t303+t163*t307-t161*t311-dvyNoise*t75*t85-dvzNoise*t78*t93; +A0[4][4] = OP[4][4]-OP[0][4]*t174-OP[9][4]*t88-OP[10][4]*t85+OP[2][4]*t171+OP[1][4]*t183+OP[11][4]*t93-t88*t325-t85*t333+t93*t329-t174*t303+t171*t311+t183*t307+dvxNoise*(t88*t88)+dvyNoise*(t85*t85)+dvzNoise*(t93*t93); +A0[4][5] = OP[4][5]+t389-OP[0][5]*t174-OP[9][5]*t88-OP[10][5]*t85+OP[2][5]*t171+OP[1][5]*t183+OP[11][5]*t93+t99*t325-t98*t329-t102*t333+t190*t303-t188*t307+t197*t311-dvxNoise*t88*t99-dvzNoise*t93*t98; +A0[4][6] = t346; +A0[4][7] = t350; +A0[4][8] = t354; +A0[4][9] = t325; +A0[4][10] = t333; +A0[4][11] = t329; +A0[5][0] = t34*t358+t48*t362-t56*t366-t39*t402; +A0[5][1] = -t39*t406-t119*t358+t123*t362+t127*t366; +A0[5][2] = -t39*t410+t146*t358-t152*t362+t158*t366; +A0[5][3] = OP[5][3]+t376+OP[9][3]*t99+OP[0][3]*t190-OP[1][3]*t188-OP[10][3]*t102-OP[11][3]*t98+OP[2][3]*t197-t69*t380-t78*t384+t75*t388+t166*t358+t163*t362-t161*t366-dvxNoise*t69*t99-dvyNoise*t75*t102; +A0[5][4] = OP[5][4]+t389+OP[9][4]*t99+OP[0][4]*t190-OP[1][4]*t188-OP[10][4]*t102-OP[11][4]*t98+OP[2][4]*t197-t88*t380-t85*t388+t93*t384-t174*t358+t171*t366+t183*t362-dvxNoise*t88*t99-dvzNoise*t93*t98; +A0[5][5] = OP[5][5]+OP[9][5]*t99+OP[0][5]*t190-OP[1][5]*t188-OP[10][5]*t102-OP[11][5]*t98+OP[2][5]*t197+t99*t380-t98*t384-t102*t388+t190*t358-t188*t362+t197*t366+dvxNoise*(t99*t99)+dvyNoise*(t102*t102)+dvzNoise*(t98*t98); +A0[5][6] = t402; +A0[5][7] = t406; +A0[5][8] = t410; +A0[5][9] = t380; +A0[5][10] = t388; +A0[5][11] = t384; +A0[6][0] = -t411+OP[6][0]*t34+OP[6][1]*t48-OP[6][2]*t56; +A0[6][1] = -t412-OP[6][0]*t119+OP[6][1]*t123+OP[6][2]*t127; +A0[6][2] = -t413+OP[6][0]*t146-OP[6][1]*t152+OP[6][2]*t158; +A0[6][3] = OP[6][3]-OP[6][2]*t161+OP[6][1]*t163+OP[6][0]*t166-OP[6][9]*t69+OP[6][10]*t75-OP[6][11]*t78; +A0[6][4] = OP[6][4]+OP[6][2]*t171-OP[6][0]*t174+OP[6][1]*t183-OP[6][10]*t85-OP[6][9]*t88+OP[6][11]*t93; +A0[6][5] = OP[6][5]-OP[6][1]*t188+OP[6][0]*t190+OP[6][2]*t197+OP[6][9]*t99-OP[6][11]*t98-OP[6][10]*t102; +A0[6][6] = OP[6][6]; +A0[6][7] = OP[6][7]; +A0[6][8] = OP[6][8]; +A0[6][9] = OP[6][9]; +A0[6][10] = OP[6][10]; +A0[6][11] = OP[6][11]; +A0[7][0] = -t198+OP[7][0]*t34+OP[7][1]*t48-OP[7][2]*t56; +A0[7][1] = -t200-OP[7][0]*t119+OP[7][1]*t123+OP[7][2]*t127; +A0[7][2] = -t202+OP[7][0]*t146-OP[7][1]*t152+OP[7][2]*t158; +A0[7][3] = OP[7][3]-OP[7][2]*t161+OP[7][1]*t163+OP[7][0]*t166-OP[7][9]*t69+OP[7][10]*t75-OP[7][11]*t78; +A0[7][4] = OP[7][4]+OP[7][2]*t171-OP[7][0]*t174+OP[7][1]*t183-OP[7][10]*t85-OP[7][9]*t88+OP[7][11]*t93; +A0[7][5] = OP[7][5]-OP[7][1]*t188+OP[7][0]*t190+OP[7][2]*t197+OP[7][9]*t99-OP[7][11]*t98-OP[7][10]*t102; +A0[7][6] = OP[7][6]; +A0[7][7] = OP[7][7]; +A0[7][8] = OP[7][8]; +A0[7][9] = OP[7][9]; +A0[7][10] = OP[7][10]; +A0[7][11] = OP[7][11]; +A0[8][0] = -t238+OP[8][0]*t34+OP[8][1]*t48-OP[8][2]*t56; +A0[8][1] = -t240-OP[8][0]*t119+OP[8][1]*t123+OP[8][2]*t127; +A0[8][2] = -t242+OP[8][0]*t146-OP[8][1]*t152+OP[8][2]*t158; +A0[8][3] = OP[8][3]-OP[8][2]*t161+OP[8][1]*t163+OP[8][0]*t166-OP[8][9]*t69+OP[8][10]*t75-OP[8][11]*t78; +A0[8][4] = OP[8][4]+OP[8][2]*t171-OP[8][0]*t174+OP[8][1]*t183-OP[8][10]*t85-OP[8][9]*t88+OP[8][11]*t93; +A0[8][5] = OP[8][5]-OP[8][1]*t188+OP[8][0]*t190+OP[8][2]*t197+OP[8][9]*t99-OP[8][11]*t98-OP[8][10]*t102; +A0[8][6] = OP[8][6]; +A0[8][7] = OP[8][7]; +A0[8][8] = OP[8][8]; +A0[8][9] = OP[8][9]; +A0[8][10] = OP[8][10]; +A0[8][11] = OP[8][11]; +A0[9][0] = OP[9][0]*t34-OP[9][6]*t39+OP[9][1]*t48-OP[9][2]*t56; +A0[9][1] = -OP[9][7]*t39-OP[9][0]*t119+OP[9][1]*t123+OP[9][2]*t127; +A0[9][2] = -OP[9][8]*t39+OP[9][0]*t146-OP[9][1]*t152+OP[9][2]*t158; +A0[9][3] = OP[9][3]-t279-OP[9][2]*t161+OP[9][1]*t163+OP[9][0]*t166+OP[9][10]*t75-OP[9][11]*t78; +A0[9][4] = OP[9][4]-t336+OP[9][2]*t171-OP[9][0]*t174+OP[9][1]*t183-OP[9][10]*t85+OP[9][11]*t93; +A0[9][5] = OP[9][5]+t378-OP[9][1]*t188+OP[9][0]*t190+OP[9][2]*t197-OP[9][11]*t98-OP[9][10]*t102; +A0[9][6] = OP[9][6]; +A0[9][7] = OP[9][7]; +A0[9][8] = OP[9][8]; +A0[9][9] = OP[9][9]; +A0[9][10] = OP[9][10]; +A0[9][11] = OP[9][11]; +A0[10][0] = OP[10][0]*t34-OP[10][6]*t39+OP[10][1]*t48-OP[10][2]*t56; +A0[10][1] = -OP[10][7]*t39-OP[10][0]*t119+OP[10][1]*t123+OP[10][2]*t127; +A0[10][2] = -OP[10][8]*t39+OP[10][0]*t146-OP[10][1]*t152+OP[10][2]*t158; +A0[10][3] = OP[10][3]+t276-OP[10][2]*t161+OP[10][1]*t163+OP[10][0]*t166-OP[10][9]*t69-OP[10][11]*t78; +A0[10][4] = OP[10][4]-t337+OP[10][2]*t171-OP[10][0]*t174+OP[10][1]*t183-OP[10][9]*t88+OP[10][11]*t93; +A0[10][5] = OP[10][5]-t395-OP[10][1]*t188+OP[10][0]*t190+OP[10][2]*t197+OP[10][9]*t99-OP[10][11]*t98; +A0[10][6] = OP[10][6]; +A0[10][7] = OP[10][7]; +A0[10][8] = OP[10][8]; +A0[10][9] = OP[10][9]; +A0[10][10] = OP[10][10]; +A0[10][11] = OP[10][11]; +A0[11][0] = OP[11][0]*t34-OP[11][6]*t39+OP[11][1]*t48-OP[11][2]*t56; +A0[11][1] = -OP[11][7]*t39-OP[11][0]*t119+OP[11][1]*t123+OP[11][2]*t127; +A0[11][2] = -OP[11][8]*t39+OP[11][0]*t146-OP[11][1]*t152+OP[11][2]*t158; +A0[11][3] = OP[11][3]-t287-OP[11][2]*t161+OP[11][1]*t163+OP[11][0]*t166-OP[11][9]*t69+OP[11][10]*t75; +A0[11][4] = OP[11][4]+t327+OP[11][2]*t171-OP[11][0]*t174+OP[11][1]*t183-OP[11][10]*t85-OP[11][9]*t88; +A0[11][5] = OP[11][5]-t396-OP[11][1]*t188+OP[11][0]*t190+OP[11][2]*t197+OP[11][9]*t99-OP[11][10]*t102; +A0[11][6] = OP[11][6]; +A0[11][7] = OP[11][7]; +A0[11][8] = OP[11][8]; +A0[11][9] = OP[11][9]; +A0[11][10] = OP[11][10]; +A0[11][11] = OP[11][11]; diff --git a/libraries/AP_NavEKF/Models/GimbalEstimatorExample/calcP.m b/libraries/AP_NavEKF/Models/GimbalEstimatorExample/calcP.m new file mode 100644 index 0000000000..9c534c47c8 --- /dev/null +++ b/libraries/AP_NavEKF/Models/GimbalEstimatorExample/calcP.m @@ -0,0 +1,420 @@ +function PP = calcP(OP_l_1_c_1_r_,OP_l_1_c_2_r_,OP_l_1_c_3_r_,OP_l_1_c_4_r_,OP_l_1_c_5_r_,OP_l_1_c_6_r_,OP_l_1_c_7_r_,OP_l_1_c_8_r_,OP_l_1_c_9_r_,OP_l_2_c_1_r_,OP_l_2_c_2_r_,OP_l_2_c_3_r_,OP_l_2_c_4_r_,OP_l_2_c_5_r_,OP_l_2_c_6_r_,OP_l_2_c_7_r_,OP_l_2_c_8_r_,OP_l_2_c_9_r_,OP_l_3_c_1_r_,OP_l_3_c_2_r_,OP_l_3_c_3_r_,OP_l_3_c_4_r_,OP_l_3_c_5_r_,OP_l_3_c_6_r_,OP_l_3_c_7_r_,OP_l_3_c_8_r_,OP_l_3_c_9_r_,OP_l_4_c_1_r_,OP_l_4_c_2_r_,OP_l_4_c_3_r_,OP_l_4_c_4_r_,OP_l_4_c_5_r_,OP_l_4_c_6_r_,OP_l_4_c_7_r_,OP_l_4_c_8_r_,OP_l_4_c_9_r_,OP_l_5_c_1_r_,OP_l_5_c_2_r_,OP_l_5_c_3_r_,OP_l_5_c_4_r_,OP_l_5_c_5_r_,OP_l_5_c_6_r_,OP_l_5_c_7_r_,OP_l_5_c_8_r_,OP_l_5_c_9_r_,OP_l_6_c_1_r_,OP_l_6_c_2_r_,OP_l_6_c_3_r_,OP_l_6_c_4_r_,OP_l_6_c_5_r_,OP_l_6_c_6_r_,OP_l_6_c_7_r_,OP_l_6_c_8_r_,OP_l_6_c_9_r_,OP_l_7_c_1_r_,OP_l_7_c_2_r_,OP_l_7_c_3_r_,OP_l_7_c_4_r_,OP_l_7_c_5_r_,OP_l_7_c_6_r_,OP_l_7_c_7_r_,OP_l_7_c_8_r_,OP_l_7_c_9_r_,OP_l_8_c_1_r_,OP_l_8_c_2_r_,OP_l_8_c_3_r_,OP_l_8_c_4_r_,OP_l_8_c_5_r_,OP_l_8_c_6_r_,OP_l_8_c_7_r_,OP_l_8_c_8_r_,OP_l_8_c_9_r_,OP_l_9_c_1_r_,OP_l_9_c_2_r_,OP_l_9_c_3_r_,OP_l_9_c_4_r_,OP_l_9_c_5_r_,OP_l_9_c_6_r_,OP_l_9_c_7_r_,OP_l_9_c_8_r_,OP_l_9_c_9_r_,OP_l_10_c_1_r_,OP_l_10_c_2_r_,OP_l_10_c_3_r_,OP_l_10_c_4_r_,OP_l_10_c_5_r_,OP_l_10_c_6_r_,OP_l_10_c_7_r_,OP_l_10_c_8_r_,OP_l_10_c_9_r_,OP_l_1_c_10_r_,OP_l_11_c_1_r_,OP_l_1_c_11_r_,OP_l_11_c_2_r_,OP_l_1_c_12_r_,OP_l_11_c_3_r_,OP_l_11_c_4_r_,OP_l_11_c_5_r_,OP_l_11_c_6_r_,OP_l_11_c_7_r_,OP_l_11_c_8_r_,OP_l_11_c_9_r_,OP_l_12_c_1_r_,OP_l_12_c_2_r_,OP_l_12_c_3_r_,OP_l_12_c_4_r_,OP_l_12_c_5_r_,OP_l_12_c_6_r_,OP_l_12_c_7_r_,OP_l_12_c_8_r_,OP_l_12_c_9_r_,OP_l_2_c_10_r_,OP_l_2_c_11_r_,OP_l_2_c_12_r_,OP_l_3_c_10_r_,OP_l_3_c_11_r_,OP_l_3_c_12_r_,OP_l_4_c_10_r_,OP_l_4_c_11_r_,OP_l_4_c_12_r_,OP_l_5_c_10_r_,OP_l_5_c_11_r_,OP_l_5_c_12_r_,OP_l_6_c_10_r_,OP_l_6_c_11_r_,OP_l_6_c_12_r_,OP_l_7_c_10_r_,OP_l_7_c_11_r_,OP_l_7_c_12_r_,OP_l_8_c_10_r_,OP_l_8_c_11_r_,OP_l_8_c_12_r_,OP_l_9_c_10_r_,OP_l_9_c_11_r_,OP_l_9_c_12_r_,OP_l_10_c_10_r_,OP_l_10_c_11_r_,OP_l_10_c_12_r_,OP_l_11_c_10_r_,OP_l_11_c_11_r_,OP_l_11_c_12_r_,OP_l_12_c_10_r_,OP_l_12_c_11_r_,OP_l_12_c_12_r_,dax,dax_b,day,day_b,daxNoise,daz,daz_b,dayNoise,dazNoise,dvx,dvx_b,dvy,dvy_b,dvxNoise,dvz,dvz_b,dvyNoise,dvzNoise,q0,q1,q2,q3) +%CALCP +% PP = CALCP(OP_L_1_C_1_R_,OP_L_1_C_2_R_,OP_L_1_C_3_R_,OP_L_1_C_4_R_,OP_L_1_C_5_R_,OP_L_1_C_6_R_,OP_L_1_C_7_R_,OP_L_1_C_8_R_,OP_L_1_C_9_R_,OP_L_2_C_1_R_,OP_L_2_C_2_R_,OP_L_2_C_3_R_,OP_L_2_C_4_R_,OP_L_2_C_5_R_,OP_L_2_C_6_R_,OP_L_2_C_7_R_,OP_L_2_C_8_R_,OP_L_2_C_9_R_,OP_L_3_C_1_R_,OP_L_3_C_2_R_,OP_L_3_C_3_R_,OP_L_3_C_4_R_,OP_L_3_C_5_R_,OP_L_3_C_6_R_,OP_L_3_C_7_R_,OP_L_3_C_8_R_,OP_L_3_C_9_R_,OP_L_4_C_1_R_,OP_L_4_C_2_R_,OP_L_4_C_3_R_,OP_L_4_C_4_R_,OP_L_4_C_5_R_,OP_L_4_C_6_R_,OP_L_4_C_7_R_,OP_L_4_C_8_R_,OP_L_4_C_9_R_,OP_L_5_C_1_R_,OP_L_5_C_2_R_,OP_L_5_C_3_R_,OP_L_5_C_4_R_,OP_L_5_C_5_R_,OP_L_5_C_6_R_,OP_L_5_C_7_R_,OP_L_5_C_8_R_,OP_L_5_C_9_R_,OP_L_6_C_1_R_,OP_L_6_C_2_R_,OP_L_6_C_3_R_,OP_L_6_C_4_R_,OP_L_6_C_5_R_,OP_L_6_C_6_R_,OP_L_6_C_7_R_,OP_L_6_C_8_R_,OP_L_6_C_9_R_,OP_L_7_C_1_R_,OP_L_7_C_2_R_,OP_L_7_C_3_R_,OP_L_7_C_4_R_,OP_L_7_C_5_R_,OP_L_7_C_6_R_,OP_L_7_C_7_R_,OP_L_7_C_8_R_,OP_L_7_C_9_R_,OP_L_8_C_1_R_,OP_L_8_C_2_R_,OP_L_8_C_3_R_,OP_L_8_C_4_R_,OP_L_8_C_5_R_,OP_L_8_C_6_R_,OP_L_8_C_7_R_,OP_L_8_C_8_R_,OP_L_8_C_9_R_,OP_L_9_C_1_R_,OP_L_9_C_2_R_,OP_L_9_C_3_R_,OP_L_9_C_4_R_,OP_L_9_C_5_R_,OP_L_9_C_6_R_,OP_L_9_C_7_R_,OP_L_9_C_8_R_,OP_L_9_C_9_R_,OP_L_10_C_1_R_,OP_L_10_C_2_R_,OP_L_10_C_3_R_,OP_L_10_C_4_R_,OP_L_10_C_5_R_,OP_L_10_C_6_R_,OP_L_10_C_7_R_,OP_L_10_C_8_R_,OP_L_10_C_9_R_,OP_L_1_C_10_R_,OP_L_11_C_1_R_,OP_L_1_C_11_R_,OP_L_11_C_2_R_,OP_L_1_C_12_R_,OP_L_11_C_3_R_,OP_L_11_C_4_R_,OP_L_11_C_5_R_,OP_L_11_C_6_R_,OP_L_11_C_7_R_,OP_L_11_C_8_R_,OP_L_11_C_9_R_,OP_L_12_C_1_R_,OP_L_12_C_2_R_,OP_L_12_C_3_R_,OP_L_12_C_4_R_,OP_L_12_C_5_R_,OP_L_12_C_6_R_,OP_L_12_C_7_R_,OP_L_12_C_8_R_,OP_L_12_C_9_R_,OP_L_2_C_10_R_,OP_L_2_C_11_R_,OP_L_2_C_12_R_,OP_L_3_C_10_R_,OP_L_3_C_11_R_,OP_L_3_C_12_R_,OP_L_4_C_10_R_,OP_L_4_C_11_R_,OP_L_4_C_12_R_,OP_L_5_C_10_R_,OP_L_5_C_11_R_,OP_L_5_C_12_R_,OP_L_6_C_10_R_,OP_L_6_C_11_R_,OP_L_6_C_12_R_,OP_L_7_C_10_R_,OP_L_7_C_11_R_,OP_L_7_C_12_R_,OP_L_8_C_10_R_,OP_L_8_C_11_R_,OP_L_8_C_12_R_,OP_L_9_C_10_R_,OP_L_9_C_11_R_,OP_L_9_C_12_R_,OP_L_10_C_10_R_,OP_L_10_C_11_R_,OP_L_10_C_12_R_,OP_L_11_C_10_R_,OP_L_11_C_11_R_,OP_L_11_C_12_R_,OP_L_12_C_10_R_,OP_L_12_C_11_R_,OP_L_12_C_12_R_,DAX,DAX_B,DAY,DAY_B,DAXNOISE,DAZ,DAZ_B,DAYNOISE,DAZNOISE,DVX,DVX_B,DVY,DVY_B,DVXNOISE,DVZ,DVZ_B,DVYNOISE,DVZNOISE,Q0,Q1,Q2,Q3) + +% This function was generated by the Symbolic Math Toolbox version 6.1. +% 15-Feb-2015 15:49:36 + +t2 = dax.*(1.0./2.0); +t3 = dax_b.*(1.0./2.0); +t4 = t2-t3; +t5 = day.*(1.0./2.0); +t6 = day_b.*(1.0./2.0); +t7 = t5-t6; +t8 = daz.*(1.0./2.0); +t9 = daz_b.*(1.0./2.0); +t10 = t8-t9; +t11 = q2.*t4.*(1.0./2.0); +t12 = q1.*t7.*(1.0./2.0); +t13 = q0.*t10.*(1.0./2.0); +t14 = q2.*(1.0./2.0); +t15 = q3.*t4.*(1.0./2.0); +t16 = q1.*t10.*(1.0./2.0); +t17 = q1.*(1.0./2.0); +t18 = q0.*t4.*(1.0./2.0); +t19 = q3.*t7.*(1.0./2.0); +t20 = q0.*(1.0./2.0); +t21 = q2.*t7.*(1.0./2.0); +t22 = q3.*t10.*(1.0./2.0); +t23 = q0.*t7.*(1.0./2.0); +t24 = q3.*(1.0./2.0); +t25 = q1.*t4.*(1.0./2.0); +t26 = q2.*t10.*(1.0./2.0); +t27 = t11+t12+t13-t24; +t28 = t14+t15+t16-t23; +t29 = q2.*t28.*2.0; +t30 = t17+t18+t19-t26; +t31 = q1.*t30.*2.0; +t32 = t20+t21+t22-t25; +t33 = q0.*t32.*2.0; +t40 = q3.*t27.*2.0; +t34 = t29+t31+t33-t40; +t35 = q0.^2; +t36 = q1.^2; +t37 = q2.^2; +t38 = q3.^2; +t39 = t35+t36+t37+t38; +t41 = t11+t12-t13+t24; +t42 = t14-t15+t16+t23; +t43 = q1.*t42.*2.0; +t44 = -t17+t18+t19+t26; +t45 = q2.*t44.*2.0; +t46 = t20-t21+t22+t25; +t47 = q3.*t46.*2.0; +t57 = q0.*t41.*2.0; +t48 = t43+t45+t47-t57; +t49 = -t14+t15+t16+t23; +t50 = q0.*t49.*2.0; +t51 = t11-t12+t13+t24; +t52 = t20+t21-t22+t25; +t53 = q2.*t52.*2.0; +t54 = t17-t18+t19+t26; +t55 = q3.*t54.*2.0; +t58 = q1.*t51.*2.0; +t56 = t50+t53+t55-t58; +t59 = OP_l_1_c_1_r_.*t34; +t60 = OP_l_2_c_1_r_.*t48; +t66 = OP_l_7_c_1_r_.*t39; +t67 = OP_l_3_c_1_r_.*t56; +t61 = t59+t60-t66-t67; +t62 = OP_l_1_c_2_r_.*t34; +t63 = OP_l_2_c_2_r_.*t48; +t64 = OP_l_1_c_3_r_.*t34; +t65 = OP_l_2_c_3_r_.*t48; +t72 = OP_l_7_c_2_r_.*t39; +t73 = OP_l_3_c_2_r_.*t56; +t68 = t62+t63-t72-t73; +t69 = t35+t36-t37-t38; +t86 = OP_l_7_c_3_r_.*t39; +t87 = OP_l_3_c_3_r_.*t56; +t70 = t64+t65-t86-t87; +t71 = dvx-dvx_b; +t74 = q0.*q3.*2.0; +t81 = q1.*q2.*2.0; +t75 = t74-t81; +t76 = q0.*q2.*2.0; +t77 = q1.*q3.*2.0; +t78 = t76+t77; +t79 = dvy-dvy_b; +t80 = dvz-dvz_b; +t82 = OP_l_1_c_11_r_.*t34; +t83 = OP_l_2_c_11_r_.*t48; +t103 = OP_l_7_c_11_r_.*t39; +t104 = OP_l_3_c_11_r_.*t56; +t84 = t82+t83-t103-t104; +t85 = t35-t36+t37-t38; +t88 = t74+t81; +t89 = OP_l_1_c_10_r_.*t34; +t90 = OP_l_2_c_10_r_.*t48; +t100 = OP_l_7_c_10_r_.*t39; +t101 = OP_l_3_c_10_r_.*t56; +t91 = t89+t90-t100-t101; +t92 = q0.*q1.*2.0; +t96 = q2.*q3.*2.0; +t93 = t92-t96; +t94 = OP_l_1_c_12_r_.*t34; +t95 = OP_l_2_c_12_r_.*t48; +t114 = OP_l_7_c_12_r_.*t39; +t115 = OP_l_3_c_12_r_.*t56; +t97 = t94+t95-t114-t115; +t98 = t35-t36-t37+t38; +t99 = t76-t77; +t102 = t92+t96; +t105 = OP_l_1_c_7_r_.*t34; +t106 = OP_l_2_c_7_r_.*t48; +t411 = OP_l_7_c_7_r_.*t39; +t107 = t105+t106-t411-OP_l_3_c_7_r_.*t56; +t108 = OP_l_1_c_8_r_.*t34; +t109 = OP_l_2_c_8_r_.*t48; +t412 = OP_l_7_c_8_r_.*t39; +t110 = t108+t109-t412-OP_l_3_c_8_r_.*t56; +t111 = OP_l_1_c_9_r_.*t34; +t112 = OP_l_2_c_9_r_.*t48; +t413 = OP_l_7_c_9_r_.*t39; +t113 = t111+t112-t413-OP_l_3_c_9_r_.*t56; +t116 = q0.*t27.*2.0; +t117 = q1.*t28.*2.0; +t118 = q3.*t32.*2.0; +t128 = q2.*t30.*2.0; +t119 = t116+t117+t118-t128; +t120 = q0.*t46.*2.0; +t121 = q2.*t42.*2.0; +t122 = q3.*t41.*2.0; +t129 = q1.*t44.*2.0; +t123 = t120+t121+t122-t129; +t124 = q1.*t52.*2.0; +t125 = q2.*t51.*2.0; +t126 = q3.*t49.*2.0; +t130 = q0.*t54.*2.0; +t127 = t124+t125+t126-t130; +t131 = OP_l_8_c_1_r_.*t39; +t132 = OP_l_1_c_1_r_.*t119; +t141 = OP_l_2_c_1_r_.*t123; +t142 = OP_l_3_c_1_r_.*t127; +t133 = t131+t132-t141-t142; +t134 = OP_l_8_c_2_r_.*t39; +t135 = OP_l_1_c_2_r_.*t119; +t147 = OP_l_2_c_2_r_.*t123; +t148 = OP_l_3_c_2_r_.*t127; +t136 = t134+t135-t147-t148; +t137 = OP_l_8_c_3_r_.*t39; +t138 = OP_l_1_c_3_r_.*t119; +t153 = OP_l_2_c_3_r_.*t123; +t154 = OP_l_3_c_3_r_.*t127; +t139 = t137+t138-t153-t154; +t140 = t39.^2; +t143 = q1.*t27.*2.0; +t144 = q2.*t32.*2.0; +t145 = q3.*t30.*2.0; +t204 = q0.*t28.*2.0; +t146 = t143+t144+t145-t204; +t149 = q0.*t44.*2.0; +t150 = q1.*t46.*2.0; +t151 = q2.*t41.*2.0; +t205 = q3.*t42.*2.0; +t152 = t149+t150+t151-t205; +t155 = q0.*t52.*2.0; +t156 = q1.*t54.*2.0; +t157 = q3.*t51.*2.0; +t206 = q2.*t49.*2.0; +t158 = t155+t156+t157-t206; +t159 = t69.*t79; +t160 = t71.*t75; +t161 = t159+t160; +t162 = t69.*t80; +t222 = t71.*t78; +t163 = t162-t222; +t164 = t78.*t79; +t165 = t75.*t80; +t166 = t164+t165; +t167 = OP_l_8_c_11_r_.*t39; +t168 = OP_l_1_c_11_r_.*t119; +t193 = OP_l_2_c_11_r_.*t123; +t194 = OP_l_3_c_11_r_.*t127; +t169 = t167+t168-t193-t194; +t170 = t71.*t85; +t226 = t79.*t88; +t171 = t170-t226; +t172 = t80.*t85; +t173 = t79.*t93; +t174 = t172+t173; +t175 = OP_l_8_c_10_r_.*t39; +t176 = OP_l_1_c_10_r_.*t119; +t191 = OP_l_2_c_10_r_.*t123; +t192 = OP_l_3_c_10_r_.*t127; +t177 = t175+t176-t191-t192; +t178 = OP_l_8_c_12_r_.*t39; +t179 = OP_l_1_c_12_r_.*t119; +t184 = OP_l_2_c_12_r_.*t123; +t185 = OP_l_3_c_12_r_.*t127; +t180 = t178+t179-t184-t185; +t181 = t71.*t93; +t182 = t80.*t88; +t183 = t181+t182; +t186 = t71.*t98; +t187 = t80.*t99; +t188 = t186+t187; +t189 = t79.*t98; +t233 = t80.*t102; +t190 = t189-t233; +t195 = t71.*t102; +t196 = t79.*t99; +t197 = t195+t196; +t198 = OP_l_8_c_7_r_.*t39; +t199 = OP_l_1_c_7_r_.*t119; +t200 = OP_l_8_c_8_r_.*t39; +t201 = OP_l_1_c_8_r_.*t119; +t202 = OP_l_8_c_9_r_.*t39; +t203 = OP_l_1_c_9_r_.*t119; +t207 = OP_l_9_c_1_r_.*t39; +t208 = OP_l_2_c_1_r_.*t152; +t216 = OP_l_1_c_1_r_.*t146; +t217 = OP_l_3_c_1_r_.*t158; +t209 = t207+t208-t216-t217; +t210 = OP_l_9_c_2_r_.*t39; +t211 = OP_l_2_c_2_r_.*t152; +t218 = OP_l_1_c_2_r_.*t146; +t219 = OP_l_3_c_2_r_.*t158; +t212 = t210+t211-t218-t219; +t213 = OP_l_9_c_3_r_.*t39; +t214 = OP_l_2_c_3_r_.*t152; +t220 = OP_l_1_c_3_r_.*t146; +t221 = OP_l_3_c_3_r_.*t158; +t215 = t213+t214-t220-t221; +t223 = OP_l_1_c_11_r_.*t146; +t224 = OP_l_3_c_11_r_.*t158; +t236 = OP_l_9_c_11_r_.*t39; +t237 = OP_l_2_c_11_r_.*t152; +t225 = t223+t224-t236-t237; +t227 = OP_l_1_c_10_r_.*t146; +t228 = OP_l_3_c_10_r_.*t158; +t234 = OP_l_9_c_10_r_.*t39; +t235 = OP_l_2_c_10_r_.*t152; +t229 = t227+t228-t234-t235; +t230 = OP_l_1_c_12_r_.*t146; +t231 = OP_l_3_c_12_r_.*t158; +t244 = OP_l_9_c_12_r_.*t39; +t245 = OP_l_2_c_12_r_.*t152; +t232 = t230+t231-t244-t245; +t238 = OP_l_9_c_7_r_.*t39; +t239 = OP_l_2_c_7_r_.*t152; +t240 = OP_l_9_c_8_r_.*t39; +t241 = OP_l_2_c_8_r_.*t152; +t242 = OP_l_9_c_9_r_.*t39; +t243 = OP_l_2_c_9_r_.*t152; +t246 = OP_l_2_c_1_r_.*t163; +t247 = OP_l_11_c_1_r_.*t75; +t248 = OP_l_1_c_1_r_.*t166; +t258 = OP_l_10_c_1_r_.*t69; +t259 = OP_l_3_c_1_r_.*t161; +t260 = OP_l_12_c_1_r_.*t78; +t249 = OP_l_4_c_1_r_+t246+t247+t248-t258-t259-t260; +t250 = OP_l_2_c_2_r_.*t163; +t251 = OP_l_11_c_2_r_.*t75; +t252 = OP_l_1_c_2_r_.*t166; +t261 = OP_l_10_c_2_r_.*t69; +t262 = OP_l_3_c_2_r_.*t161; +t263 = OP_l_12_c_2_r_.*t78; +t253 = OP_l_4_c_2_r_+t250+t251+t252-t261-t262-t263; +t254 = OP_l_2_c_3_r_.*t163; +t255 = OP_l_11_c_3_r_.*t75; +t256 = OP_l_1_c_3_r_.*t166; +t264 = OP_l_10_c_3_r_.*t69; +t265 = OP_l_3_c_3_r_.*t161; +t266 = OP_l_12_c_3_r_.*t78; +t257 = OP_l_4_c_3_r_+t254+t255+t256-t264-t265-t266; +t267 = OP_l_2_c_10_r_.*t163; +t268 = OP_l_11_c_10_r_.*t75; +t269 = OP_l_1_c_10_r_.*t166; +t279 = OP_l_10_c_10_r_.*t69; +t280 = OP_l_3_c_10_r_.*t161; +t281 = OP_l_12_c_10_r_.*t78; +t270 = OP_l_4_c_10_r_+t267+t268+t269-t279-t280-t281; +t271 = OP_l_2_c_12_r_.*t163; +t272 = OP_l_11_c_12_r_.*t75; +t273 = OP_l_1_c_12_r_.*t166; +t285 = OP_l_10_c_12_r_.*t69; +t286 = OP_l_3_c_12_r_.*t161; +t287 = OP_l_12_c_12_r_.*t78; +t274 = OP_l_4_c_12_r_+t271+t272+t273-t285-t286-t287; +t275 = OP_l_2_c_11_r_.*t163; +t276 = OP_l_11_c_11_r_.*t75; +t277 = OP_l_1_c_11_r_.*t166; +t282 = OP_l_10_c_11_r_.*t69; +t283 = OP_l_3_c_11_r_.*t161; +t284 = OP_l_12_c_11_r_.*t78; +t278 = OP_l_4_c_11_r_+t275+t276+t277-t282-t283-t284; +t288 = OP_l_2_c_7_r_.*t163; +t289 = OP_l_11_c_7_r_.*t75; +t290 = OP_l_1_c_7_r_.*t166; +t291 = OP_l_4_c_7_r_+t288+t289+t290-OP_l_10_c_7_r_.*t69-OP_l_3_c_7_r_.*t161-OP_l_12_c_7_r_.*t78; +t292 = OP_l_2_c_8_r_.*t163; +t293 = OP_l_11_c_8_r_.*t75; +t294 = OP_l_1_c_8_r_.*t166; +t295 = OP_l_4_c_8_r_+t292+t293+t294-OP_l_10_c_8_r_.*t69-OP_l_3_c_8_r_.*t161-OP_l_12_c_8_r_.*t78; +t296 = OP_l_2_c_9_r_.*t163; +t297 = OP_l_11_c_9_r_.*t75; +t298 = OP_l_1_c_9_r_.*t166; +t299 = OP_l_4_c_9_r_+t296+t297+t298-OP_l_10_c_9_r_.*t69-OP_l_3_c_9_r_.*t161-OP_l_12_c_9_r_.*t78; +t300 = OP_l_3_c_1_r_.*t171; +t301 = OP_l_12_c_1_r_.*t93; +t302 = OP_l_2_c_1_r_.*t183; +t312 = OP_l_11_c_1_r_.*t85; +t313 = OP_l_1_c_1_r_.*t174; +t314 = OP_l_10_c_1_r_.*t88; +t303 = OP_l_5_c_1_r_+t300+t301+t302-t312-t313-t314; +t304 = OP_l_3_c_2_r_.*t171; +t305 = OP_l_12_c_2_r_.*t93; +t306 = OP_l_2_c_2_r_.*t183; +t315 = OP_l_11_c_2_r_.*t85; +t316 = OP_l_1_c_2_r_.*t174; +t317 = OP_l_10_c_2_r_.*t88; +t307 = OP_l_5_c_2_r_+t304+t305+t306-t315-t316-t317; +t308 = OP_l_3_c_3_r_.*t171; +t309 = OP_l_12_c_3_r_.*t93; +t310 = OP_l_2_c_3_r_.*t183; +t318 = OP_l_11_c_3_r_.*t85; +t319 = OP_l_1_c_3_r_.*t174; +t320 = OP_l_10_c_3_r_.*t88; +t311 = OP_l_5_c_3_r_+t308+t309+t310-t318-t319-t320; +t321 = dvxNoise.*t69.*t88; +t322 = OP_l_3_c_10_r_.*t171; +t323 = OP_l_12_c_10_r_.*t93; +t324 = OP_l_2_c_10_r_.*t183; +t334 = OP_l_11_c_10_r_.*t85; +t335 = OP_l_1_c_10_r_.*t174; +t336 = OP_l_10_c_10_r_.*t88; +t325 = OP_l_5_c_10_r_+t322+t323+t324-t334-t335-t336; +t326 = OP_l_3_c_12_r_.*t171; +t327 = OP_l_12_c_12_r_.*t93; +t328 = OP_l_2_c_12_r_.*t183; +t340 = OP_l_11_c_12_r_.*t85; +t341 = OP_l_1_c_12_r_.*t174; +t342 = OP_l_10_c_12_r_.*t88; +t329 = OP_l_5_c_12_r_+t326+t327+t328-t340-t341-t342; +t330 = OP_l_3_c_11_r_.*t171; +t331 = OP_l_12_c_11_r_.*t93; +t332 = OP_l_2_c_11_r_.*t183; +t337 = OP_l_11_c_11_r_.*t85; +t338 = OP_l_1_c_11_r_.*t174; +t339 = OP_l_10_c_11_r_.*t88; +t333 = OP_l_5_c_11_r_+t330+t331+t332-t337-t338-t339; +t343 = OP_l_3_c_7_r_.*t171; +t344 = OP_l_12_c_7_r_.*t93; +t345 = OP_l_2_c_7_r_.*t183; +t346 = OP_l_5_c_7_r_+t343+t344+t345-OP_l_1_c_7_r_.*t174-OP_l_10_c_7_r_.*t88-OP_l_11_c_7_r_.*t85; +t347 = OP_l_3_c_8_r_.*t171; +t348 = OP_l_12_c_8_r_.*t93; +t349 = OP_l_2_c_8_r_.*t183; +t350 = OP_l_5_c_8_r_+t347+t348+t349-OP_l_1_c_8_r_.*t174-OP_l_10_c_8_r_.*t88-OP_l_11_c_8_r_.*t85; +t351 = OP_l_3_c_9_r_.*t171; +t352 = OP_l_12_c_9_r_.*t93; +t353 = OP_l_2_c_9_r_.*t183; +t354 = OP_l_5_c_9_r_+t351+t352+t353-OP_l_1_c_9_r_.*t174-OP_l_10_c_9_r_.*t88-OP_l_11_c_9_r_.*t85; +t355 = OP_l_1_c_1_r_.*t190; +t356 = OP_l_10_c_1_r_.*t99; +t357 = OP_l_3_c_1_r_.*t197; +t367 = OP_l_12_c_1_r_.*t98; +t368 = OP_l_2_c_1_r_.*t188; +t369 = OP_l_11_c_1_r_.*t102; +t358 = OP_l_6_c_1_r_+t355+t356+t357-t367-t368-t369; +t359 = OP_l_1_c_2_r_.*t190; +t360 = OP_l_10_c_2_r_.*t99; +t361 = OP_l_3_c_2_r_.*t197; +t370 = OP_l_12_c_2_r_.*t98; +t371 = OP_l_2_c_2_r_.*t188; +t372 = OP_l_11_c_2_r_.*t102; +t362 = OP_l_6_c_2_r_+t359+t360+t361-t370-t371-t372; +t363 = OP_l_1_c_3_r_.*t190; +t364 = OP_l_10_c_3_r_.*t99; +t365 = OP_l_3_c_3_r_.*t197; +t373 = OP_l_12_c_3_r_.*t98; +t374 = OP_l_2_c_3_r_.*t188; +t375 = OP_l_11_c_3_r_.*t102; +t366 = OP_l_6_c_3_r_+t363+t364+t365-t373-t374-t375; +t376 = dvzNoise.*t78.*t98; +t377 = OP_l_1_c_10_r_.*t190; +t378 = OP_l_10_c_10_r_.*t99; +t379 = OP_l_3_c_10_r_.*t197; +t390 = OP_l_12_c_10_r_.*t98; +t391 = OP_l_2_c_10_r_.*t188; +t392 = OP_l_11_c_10_r_.*t102; +t380 = OP_l_6_c_10_r_+t377+t378+t379-t390-t391-t392; +t381 = OP_l_1_c_12_r_.*t190; +t382 = OP_l_10_c_12_r_.*t99; +t383 = OP_l_3_c_12_r_.*t197; +t396 = OP_l_12_c_12_r_.*t98; +t397 = OP_l_2_c_12_r_.*t188; +t398 = OP_l_11_c_12_r_.*t102; +t384 = OP_l_6_c_12_r_+t381+t382+t383-t396-t397-t398; +t385 = OP_l_1_c_11_r_.*t190; +t386 = OP_l_10_c_11_r_.*t99; +t387 = OP_l_3_c_11_r_.*t197; +t393 = OP_l_12_c_11_r_.*t98; +t394 = OP_l_2_c_11_r_.*t188; +t395 = OP_l_11_c_11_r_.*t102; +t388 = OP_l_6_c_11_r_+t385+t386+t387-t393-t394-t395; +t389 = dvyNoise.*t85.*t102; +t399 = OP_l_1_c_7_r_.*t190; +t400 = OP_l_10_c_7_r_.*t99; +t401 = OP_l_3_c_7_r_.*t197; +t402 = OP_l_6_c_7_r_+t399+t400+t401-OP_l_2_c_7_r_.*t188-OP_l_11_c_7_r_.*t102-OP_l_12_c_7_r_.*t98; +t403 = OP_l_1_c_8_r_.*t190; +t404 = OP_l_10_c_8_r_.*t99; +t405 = OP_l_3_c_8_r_.*t197; +t406 = OP_l_6_c_8_r_+t403+t404+t405-OP_l_2_c_8_r_.*t188-OP_l_11_c_8_r_.*t102-OP_l_12_c_8_r_.*t98; +t407 = OP_l_1_c_9_r_.*t190; +t408 = OP_l_10_c_9_r_.*t99; +t409 = OP_l_3_c_9_r_.*t197; +t410 = OP_l_6_c_9_r_+t407+t408+t409-OP_l_2_c_9_r_.*t188-OP_l_11_c_9_r_.*t102-OP_l_12_c_9_r_.*t98; +PP = 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12]); diff --git a/libraries/AP_NavEKF/Models/GimbalEstimatorExample/calcP.txt b/libraries/AP_NavEKF/Models/GimbalEstimatorExample/calcP.txt new file mode 100644 index 0000000000..c6f7a1f9c5 --- /dev/null +++ b/libraries/AP_NavEKF/Models/GimbalEstimatorExample/calcP.txt @@ -0,0 +1,152 @@ +SF = zeros(25,1); +SF(1) = daz/2 - daz_b/2; +SF(2) = day/2 - day_b/2; +SF(3) = dax/2 - dax_b/2; +SF(4) = (q0*SF(2))/2 - q2/2 + (q1*SF(1))/2 + (q3*SF(3))/2; +SF(5) = q3/2 + (q0*SF(1))/2 - (q1*SF(2))/2 + (q2*SF(3))/2; +SF(6) = q0/2 + (q1*SF(3))/2 + (q2*SF(2))/2 - (q3*SF(1))/2; +SF(7) = q1/2 - (q0*SF(3))/2 + (q2*SF(1))/2 + (q3*SF(2))/2; +SF(8) = q3/2 - (q0*SF(1))/2 + (q1*SF(2))/2 + (q2*SF(3))/2; +SF(9) = q2/2 + (q0*SF(2))/2 + (q1*SF(1))/2 - (q3*SF(3))/2; +SF(10) = (q0*SF(3))/2 - q1/2 + (q2*SF(1))/2 + (q3*SF(2))/2; +SF(11) = q0/2 + (q1*SF(3))/2 - (q2*SF(2))/2 + (q3*SF(1))/2; +SF(12) = q0/2 - (q1*SF(3))/2 + (q2*SF(2))/2 + (q3*SF(1))/2; +SF(13) = q1/2 + (q0*SF(3))/2 - (q2*SF(1))/2 + (q3*SF(2))/2; +SF(14) = q2/2 - (q0*SF(2))/2 + (q1*SF(1))/2 + (q3*SF(3))/2; +SF(15) = (q0*SF(1))/2 - q3/2 + (q1*SF(2))/2 + (q2*SF(3))/2; +SF(16) = - q0^2 - q1^2 - q2^2 - q3^2; +SF(17) = q0^2 - q1^2 - q2^2 + q3^2; +SF(18) = q0^2 - q1^2 + q2^2 - q3^2; +SF(19) = q0^2 + q1^2 - q2^2 - q3^2; +SF(20) = 2*q0*q2 - 2*q1*q3; +SF(21) = 2*q0*q1 - 2*q2*q3; +SF(22) = 2*q0*q3 - 2*q1*q2; +SF(23) = 2*q0*q1 + 2*q2*q3; +SF(24) = 2*q0*q3 + 2*q1*q2; +SF(25) = 2*q0*q2 + 2*q1*q3; + + +SG = zeros(5,1); +SG(1) = - q0^2 - q1^2 - q2^2 - q3^2; +SG(2) = q3^2; +SG(3) = q2^2; +SG(4) = q1^2; +SG(5) = q0^2; + + +SQ = zeros(8,1); +SQ(1) = dvyNoise*(2*q0*q1 + 2*q2*q3)*(q0^2 - q1^2 + q2^2 - q3^2) - dvzNoise*(2*q0*q1 - 2*q2*q3)*(q0^2 - q1^2 - q2^2 + q3^2) - dvxNoise*(2*q0*q2 - 2*q1*q3)*(2*q0*q3 + 2*q1*q2); +SQ(2) = dvzNoise*(2*q0*q2 + 2*q1*q3)*(q0^2 - q1^2 - q2^2 + q3^2) - dvxNoise*(2*q0*q2 - 2*q1*q3)*(q0^2 + q1^2 - q2^2 - q3^2) - dvyNoise*(2*q0*q1 + 2*q2*q3)*(2*q0*q3 - 2*q1*q2); +SQ(3) = dvxNoise*(2*q0*q3 + 2*q1*q2)*(q0^2 + q1^2 - q2^2 - q3^2) - dvyNoise*(2*q0*q3 - 2*q1*q2)*(q0^2 - q1^2 + q2^2 - q3^2) - dvzNoise*(2*q0*q1 - 2*q2*q3)*(2*q0*q2 + 2*q1*q3); +SQ(4) = (q0^2 + q1^2 + q2^2 + q3^2)^2; +SQ(5) = q3^2; +SQ(6) = q2^2; +SQ(7) = q1^2; +SQ(8) = q0^2; + + +SPP = zeros(19,1); +SPP(1) = 2*q2*SF(12) - 2*q0*SF(14) + 2*q1*SF(15) + 2*q3*SF(13); +SPP(2) = 2*q0*SF(10) + 2*q2*SF(8) + 2*q1*SF(11) - 2*q3*SF(9); +SPP(3) = 2*q0*SF(15) + 2*q1*SF(14) - 2*q2*SF(13) + 2*q3*SF(12); +SPP(4) = 2*q0*SF(11) - 2*q1*SF(10) + 2*q2*SF(9) + 2*q3*SF(8); +SPP(5) = 2*q0*SF(12) + 2*q1*SF(13) + 2*q2*SF(14) - 2*q3*SF(15); +SPP(6) = 2*q1*SF(9) - 2*q0*SF(8) + 2*q2*SF(10) + 2*q3*SF(11); +SPP(7) = 2*q0*SF(6) - 2*q2*SF(4) + 2*q1*SF(7) + 2*q3*SF(5); +SPP(8) = 2*q1*SF(6) - 2*q0*SF(7) + 2*q2*SF(5) + 2*q3*SF(4); +SPP(9) = 2*q0*SF(4) - 2*q1*SF(5) + 2*q2*SF(6) + 2*q3*SF(7); +SPP(10) = dvy*SF(17) - dvz*SF(23); +SPP(11) = dvx*SF(18) - dvy*SF(24); +SPP(12) = dvx*SF(25) - dvz*SF(19); +SPP(13) = dvx*SF(17) + dvz*SF(20); +SPP(14) = dvx*SF(23) + dvy*SF(20); +SPP(15) = dvy*SF(21) + dvz*SF(18); +SPP(16) = dvx*SF(21) + dvz*SF(24); +SPP(17) = dvy*SF(25) + dvz*SF(22); +SPP(18) = dvx*SF(22) + dvy*SF(19); +SPP(19) = SF(16); + + +nextP = zeros(9,9); +nextP(1,1) = daxNoise*SQ(4) + SPP(5)*(OP_l_1_c_1_r_*SPP(5) + OP_l_2_c_1_r_*SPP(6) - OP_l_3_c_1_r_*SPP(9) + OP_l_7_c_1_r_*SPP(19)) + SPP(6)*(OP_l_1_c_2_r_*SPP(5) + OP_l_2_c_2_r_*SPP(6) - OP_l_3_c_2_r_*SPP(9) + OP_l_7_c_2_r_*SPP(19)) - SPP(9)*(OP_l_1_c_3_r_*SPP(5) + OP_l_2_c_3_r_*SPP(6) - OP_l_3_c_3_r_*SPP(9) + OP_l_7_c_3_r_*SPP(19)) + SPP(19)*(OP_l_1_c_7_r_*SPP(5) + OP_l_2_c_7_r_*SPP(6) - OP_l_3_c_7_r_*SPP(9) + OP_l_7_c_7_r_*SPP(19)); +nextP(1,2) = SPP(4)*(OP_l_1_c_2_r_*SPP(5) + OP_l_2_c_2_r_*SPP(6) - OP_l_3_c_2_r_*SPP(9) + OP_l_7_c_2_r_*SPP(19)) - SPP(3)*(OP_l_1_c_1_r_*SPP(5) + OP_l_2_c_1_r_*SPP(6) - OP_l_3_c_1_r_*SPP(9) + OP_l_7_c_1_r_*SPP(19)) + SPP(8)*(OP_l_1_c_3_r_*SPP(5) + OP_l_2_c_3_r_*SPP(6) - OP_l_3_c_3_r_*SPP(9) + OP_l_7_c_3_r_*SPP(19)) + SPP(19)*(OP_l_1_c_8_r_*SPP(5) + OP_l_2_c_8_r_*SPP(6) - OP_l_3_c_8_r_*SPP(9) + OP_l_7_c_8_r_*SPP(19)); +nextP(1,3) = SPP(1)*(OP_l_1_c_1_r_*SPP(5) + OP_l_2_c_1_r_*SPP(6) - OP_l_3_c_1_r_*SPP(9) + OP_l_7_c_1_r_*SPP(19)) - SPP(2)*(OP_l_1_c_2_r_*SPP(5) + OP_l_2_c_2_r_*SPP(6) - OP_l_3_c_2_r_*SPP(9) + OP_l_7_c_2_r_*SPP(19)) + SPP(7)*(OP_l_1_c_3_r_*SPP(5) + OP_l_2_c_3_r_*SPP(6) - OP_l_3_c_3_r_*SPP(9) + OP_l_7_c_3_r_*SPP(19)) + SPP(19)*(OP_l_1_c_9_r_*SPP(5) + OP_l_2_c_9_r_*SPP(6) - OP_l_3_c_9_r_*SPP(9) + OP_l_7_c_9_r_*SPP(19)); +nextP(1,4) = OP_l_1_c_4_r_*SPP(5) + OP_l_2_c_4_r_*SPP(6) - OP_l_3_c_4_r_*SPP(9) + OP_l_7_c_4_r_*SPP(19) - SPP(12)*(OP_l_1_c_2_r_*SPP(5) + OP_l_2_c_2_r_*SPP(6) - OP_l_3_c_2_r_*SPP(9) + OP_l_7_c_2_r_*SPP(19)) + SPP(17)*(OP_l_1_c_1_r_*SPP(5) + OP_l_2_c_1_r_*SPP(6) - OP_l_3_c_1_r_*SPP(9) + OP_l_7_c_1_r_*SPP(19)) - SPP(18)*(OP_l_1_c_3_r_*SPP(5) + OP_l_2_c_3_r_*SPP(6) - OP_l_3_c_3_r_*SPP(9) + OP_l_7_c_3_r_*SPP(19)); +nextP(1,5) = OP_l_1_c_5_r_*SPP(5) + OP_l_2_c_5_r_*SPP(6) - OP_l_3_c_5_r_*SPP(9) + OP_l_7_c_5_r_*SPP(19) - SPP(15)*(OP_l_1_c_1_r_*SPP(5) + OP_l_2_c_1_r_*SPP(6) - OP_l_3_c_1_r_*SPP(9) + OP_l_7_c_1_r_*SPP(19)) + SPP(11)*(OP_l_1_c_3_r_*SPP(5) + OP_l_2_c_3_r_*SPP(6) - OP_l_3_c_3_r_*SPP(9) + OP_l_7_c_3_r_*SPP(19)) + SPP(16)*(OP_l_1_c_2_r_*SPP(5) + OP_l_2_c_2_r_*SPP(6) - OP_l_3_c_2_r_*SPP(9) + OP_l_7_c_2_r_*SPP(19)); +nextP(1,6) = OP_l_1_c_6_r_*SPP(5) + OP_l_2_c_6_r_*SPP(6) - OP_l_3_c_6_r_*SPP(9) + OP_l_7_c_6_r_*SPP(19) + SPP(10)*(OP_l_1_c_1_r_*SPP(5) + OP_l_2_c_1_r_*SPP(6) - OP_l_3_c_1_r_*SPP(9) + OP_l_7_c_1_r_*SPP(19)) - SPP(13)*(OP_l_1_c_2_r_*SPP(5) + OP_l_2_c_2_r_*SPP(6) - OP_l_3_c_2_r_*SPP(9) + OP_l_7_c_2_r_*SPP(19)) + SPP(14)*(OP_l_1_c_3_r_*SPP(5) + OP_l_2_c_3_r_*SPP(6) - OP_l_3_c_3_r_*SPP(9) + OP_l_7_c_3_r_*SPP(19)); +nextP(1,7) = OP_l_1_c_7_r_*SPP(5) + OP_l_2_c_7_r_*SPP(6) - OP_l_3_c_7_r_*SPP(9) + OP_l_7_c_7_r_*SPP(19); +nextP(1,8) = OP_l_1_c_8_r_*SPP(5) + OP_l_2_c_8_r_*SPP(6) - OP_l_3_c_8_r_*SPP(9) + OP_l_7_c_8_r_*SPP(19); +nextP(1,9) = OP_l_1_c_9_r_*SPP(5) + OP_l_2_c_9_r_*SPP(6) - OP_l_3_c_9_r_*SPP(9) + OP_l_7_c_9_r_*SPP(19); +nextP(2,1) = SPP(5)*(OP_l_2_c_1_r_*SPP(4) - OP_l_1_c_1_r_*SPP(3) + OP_l_3_c_1_r_*SPP(8) + OP_l_8_c_1_r_*SPP(19)) + SPP(6)*(OP_l_2_c_2_r_*SPP(4) - OP_l_1_c_2_r_*SPP(3) + OP_l_3_c_2_r_*SPP(8) + OP_l_8_c_2_r_*SPP(19)) - SPP(9)*(OP_l_2_c_3_r_*SPP(4) - OP_l_1_c_3_r_*SPP(3) + OP_l_3_c_3_r_*SPP(8) + OP_l_8_c_3_r_*SPP(19)) + SPP(19)*(OP_l_2_c_7_r_*SPP(4) - OP_l_1_c_7_r_*SPP(3) + OP_l_3_c_7_r_*SPP(8) + OP_l_8_c_7_r_*SPP(19)); +nextP(2,2) = dayNoise*SQ(4) - SPP(3)*(OP_l_2_c_1_r_*SPP(4) - OP_l_1_c_1_r_*SPP(3) + OP_l_3_c_1_r_*SPP(8) + OP_l_8_c_1_r_*SPP(19)) + SPP(4)*(OP_l_2_c_2_r_*SPP(4) - OP_l_1_c_2_r_*SPP(3) + OP_l_3_c_2_r_*SPP(8) + OP_l_8_c_2_r_*SPP(19)) + SPP(8)*(OP_l_2_c_3_r_*SPP(4) - OP_l_1_c_3_r_*SPP(3) + OP_l_3_c_3_r_*SPP(8) + OP_l_8_c_3_r_*SPP(19)) + SPP(19)*(OP_l_2_c_8_r_*SPP(4) - OP_l_1_c_8_r_*SPP(3) + OP_l_3_c_8_r_*SPP(8) + OP_l_8_c_8_r_*SPP(19)); +nextP(2,3) = SPP(1)*(OP_l_2_c_1_r_*SPP(4) - OP_l_1_c_1_r_*SPP(3) + OP_l_3_c_1_r_*SPP(8) + OP_l_8_c_1_r_*SPP(19)) - SPP(2)*(OP_l_2_c_2_r_*SPP(4) - OP_l_1_c_2_r_*SPP(3) + OP_l_3_c_2_r_*SPP(8) + OP_l_8_c_2_r_*SPP(19)) + SPP(7)*(OP_l_2_c_3_r_*SPP(4) - OP_l_1_c_3_r_*SPP(3) + OP_l_3_c_3_r_*SPP(8) + OP_l_8_c_3_r_*SPP(19)) + SPP(19)*(OP_l_2_c_9_r_*SPP(4) - OP_l_1_c_9_r_*SPP(3) + OP_l_3_c_9_r_*SPP(8) + OP_l_8_c_9_r_*SPP(19)); +nextP(2,4) = OP_l_2_c_4_r_*SPP(4) - OP_l_1_c_4_r_*SPP(3) + OP_l_3_c_4_r_*SPP(8) + OP_l_8_c_4_r_*SPP(19) - SPP(12)*(OP_l_2_c_2_r_*SPP(4) - OP_l_1_c_2_r_*SPP(3) + OP_l_3_c_2_r_*SPP(8) + OP_l_8_c_2_r_*SPP(19)) + SPP(17)*(OP_l_2_c_1_r_*SPP(4) - OP_l_1_c_1_r_*SPP(3) + OP_l_3_c_1_r_*SPP(8) + OP_l_8_c_1_r_*SPP(19)) - SPP(18)*(OP_l_2_c_3_r_*SPP(4) - OP_l_1_c_3_r_*SPP(3) + OP_l_3_c_3_r_*SPP(8) + OP_l_8_c_3_r_*SPP(19)); +nextP(2,5) = OP_l_2_c_5_r_*SPP(4) - OP_l_1_c_5_r_*SPP(3) + OP_l_3_c_5_r_*SPP(8) + OP_l_8_c_5_r_*SPP(19) - SPP(15)*(OP_l_2_c_1_r_*SPP(4) - OP_l_1_c_1_r_*SPP(3) + OP_l_3_c_1_r_*SPP(8) + OP_l_8_c_1_r_*SPP(19)) + SPP(11)*(OP_l_2_c_3_r_*SPP(4) - OP_l_1_c_3_r_*SPP(3) + OP_l_3_c_3_r_*SPP(8) + OP_l_8_c_3_r_*SPP(19)) + SPP(16)*(OP_l_2_c_2_r_*SPP(4) - OP_l_1_c_2_r_*SPP(3) + OP_l_3_c_2_r_*SPP(8) + OP_l_8_c_2_r_*SPP(19)); +nextP(2,6) = OP_l_2_c_6_r_*SPP(4) - OP_l_1_c_6_r_*SPP(3) + OP_l_3_c_6_r_*SPP(8) + OP_l_8_c_6_r_*SPP(19) + SPP(10)*(OP_l_2_c_1_r_*SPP(4) - OP_l_1_c_1_r_*SPP(3) + OP_l_3_c_1_r_*SPP(8) + OP_l_8_c_1_r_*SPP(19)) - SPP(13)*(OP_l_2_c_2_r_*SPP(4) - OP_l_1_c_2_r_*SPP(3) + OP_l_3_c_2_r_*SPP(8) + OP_l_8_c_2_r_*SPP(19)) + SPP(14)*(OP_l_2_c_3_r_*SPP(4) - OP_l_1_c_3_r_*SPP(3) + OP_l_3_c_3_r_*SPP(8) + OP_l_8_c_3_r_*SPP(19)); +nextP(2,7) = OP_l_2_c_7_r_*SPP(4) - OP_l_1_c_7_r_*SPP(3) + OP_l_3_c_7_r_*SPP(8) + OP_l_8_c_7_r_*SPP(19); +nextP(2,8) = OP_l_2_c_8_r_*SPP(4) - OP_l_1_c_8_r_*SPP(3) + OP_l_3_c_8_r_*SPP(8) + OP_l_8_c_8_r_*SPP(19); +nextP(2,9) = OP_l_2_c_9_r_*SPP(4) - OP_l_1_c_9_r_*SPP(3) + OP_l_3_c_9_r_*SPP(8) + OP_l_8_c_9_r_*SPP(19); +nextP(3,1) = SPP(5)*(OP_l_1_c_1_r_*SPP(1) - OP_l_2_c_1_r_*SPP(2) + OP_l_3_c_1_r_*SPP(7) + OP_l_9_c_1_r_*SPP(19)) + SPP(6)*(OP_l_1_c_2_r_*SPP(1) - OP_l_2_c_2_r_*SPP(2) + OP_l_3_c_2_r_*SPP(7) + OP_l_9_c_2_r_*SPP(19)) - SPP(9)*(OP_l_1_c_3_r_*SPP(1) - OP_l_2_c_3_r_*SPP(2) + OP_l_3_c_3_r_*SPP(7) + OP_l_9_c_3_r_*SPP(19)) + SPP(19)*(OP_l_1_c_7_r_*SPP(1) - OP_l_2_c_7_r_*SPP(2) + OP_l_3_c_7_r_*SPP(7) + OP_l_9_c_7_r_*SPP(19)); +nextP(3,2) = SPP(4)*(OP_l_1_c_2_r_*SPP(1) - OP_l_2_c_2_r_*SPP(2) + OP_l_3_c_2_r_*SPP(7) + OP_l_9_c_2_r_*SPP(19)) - SPP(3)*(OP_l_1_c_1_r_*SPP(1) - OP_l_2_c_1_r_*SPP(2) + OP_l_3_c_1_r_*SPP(7) + OP_l_9_c_1_r_*SPP(19)) + SPP(8)*(OP_l_1_c_3_r_*SPP(1) - OP_l_2_c_3_r_*SPP(2) + OP_l_3_c_3_r_*SPP(7) + OP_l_9_c_3_r_*SPP(19)) + SPP(19)*(OP_l_1_c_8_r_*SPP(1) - OP_l_2_c_8_r_*SPP(2) + OP_l_3_c_8_r_*SPP(7) + OP_l_9_c_8_r_*SPP(19)); +nextP(3,3) = dazNoise*SQ(4) + SPP(1)*(OP_l_1_c_1_r_*SPP(1) - OP_l_2_c_1_r_*SPP(2) + OP_l_3_c_1_r_*SPP(7) + OP_l_9_c_1_r_*SPP(19)) - SPP(2)*(OP_l_1_c_2_r_*SPP(1) - OP_l_2_c_2_r_*SPP(2) + OP_l_3_c_2_r_*SPP(7) + OP_l_9_c_2_r_*SPP(19)) + SPP(7)*(OP_l_1_c_3_r_*SPP(1) - OP_l_2_c_3_r_*SPP(2) + OP_l_3_c_3_r_*SPP(7) + OP_l_9_c_3_r_*SPP(19)) + SPP(19)*(OP_l_1_c_9_r_*SPP(1) - OP_l_2_c_9_r_*SPP(2) + OP_l_3_c_9_r_*SPP(7) + OP_l_9_c_9_r_*SPP(19)); +nextP(3,4) = OP_l_1_c_4_r_*SPP(1) - OP_l_2_c_4_r_*SPP(2) + OP_l_3_c_4_r_*SPP(7) + OP_l_9_c_4_r_*SPP(19) - SPP(12)*(OP_l_1_c_2_r_*SPP(1) - OP_l_2_c_2_r_*SPP(2) + OP_l_3_c_2_r_*SPP(7) + OP_l_9_c_2_r_*SPP(19)) + SPP(17)*(OP_l_1_c_1_r_*SPP(1) - OP_l_2_c_1_r_*SPP(2) + OP_l_3_c_1_r_*SPP(7) + OP_l_9_c_1_r_*SPP(19)) - SPP(18)*(OP_l_1_c_3_r_*SPP(1) - OP_l_2_c_3_r_*SPP(2) + OP_l_3_c_3_r_*SPP(7) + OP_l_9_c_3_r_*SPP(19)); +nextP(3,5) = OP_l_1_c_5_r_*SPP(1) - OP_l_2_c_5_r_*SPP(2) + OP_l_3_c_5_r_*SPP(7) + OP_l_9_c_5_r_*SPP(19) - SPP(15)*(OP_l_1_c_1_r_*SPP(1) - OP_l_2_c_1_r_*SPP(2) + OP_l_3_c_1_r_*SPP(7) + OP_l_9_c_1_r_*SPP(19)) + SPP(11)*(OP_l_1_c_3_r_*SPP(1) - OP_l_2_c_3_r_*SPP(2) + OP_l_3_c_3_r_*SPP(7) + OP_l_9_c_3_r_*SPP(19)) + SPP(16)*(OP_l_1_c_2_r_*SPP(1) - OP_l_2_c_2_r_*SPP(2) + OP_l_3_c_2_r_*SPP(7) + OP_l_9_c_2_r_*SPP(19)); +nextP(3,6) = OP_l_1_c_6_r_*SPP(1) - OP_l_2_c_6_r_*SPP(2) + OP_l_3_c_6_r_*SPP(7) + OP_l_9_c_6_r_*SPP(19) + SPP(10)*(OP_l_1_c_1_r_*SPP(1) - OP_l_2_c_1_r_*SPP(2) + OP_l_3_c_1_r_*SPP(7) + OP_l_9_c_1_r_*SPP(19)) - SPP(13)*(OP_l_1_c_2_r_*SPP(1) - OP_l_2_c_2_r_*SPP(2) + OP_l_3_c_2_r_*SPP(7) + OP_l_9_c_2_r_*SPP(19)) + SPP(14)*(OP_l_1_c_3_r_*SPP(1) - OP_l_2_c_3_r_*SPP(2) + OP_l_3_c_3_r_*SPP(7) + OP_l_9_c_3_r_*SPP(19)); +nextP(3,7) = OP_l_1_c_7_r_*SPP(1) - OP_l_2_c_7_r_*SPP(2) + OP_l_3_c_7_r_*SPP(7) + OP_l_9_c_7_r_*SPP(19); +nextP(3,8) = OP_l_1_c_8_r_*SPP(1) - OP_l_2_c_8_r_*SPP(2) + OP_l_3_c_8_r_*SPP(7) + OP_l_9_c_8_r_*SPP(19); +nextP(3,9) = OP_l_1_c_9_r_*SPP(1) - OP_l_2_c_9_r_*SPP(2) + OP_l_3_c_9_r_*SPP(7) + OP_l_9_c_9_r_*SPP(19); +nextP(4,1) = SPP(5)*(OP_l_4_c_1_r_ + OP_l_1_c_1_r_*SPP(17) - OP_l_2_c_1_r_*SPP(12) - OP_l_3_c_1_r_*SPP(18)) + SPP(6)*(OP_l_4_c_2_r_ + OP_l_1_c_2_r_*SPP(17) - OP_l_2_c_2_r_*SPP(12) - OP_l_3_c_2_r_*SPP(18)) - SPP(9)*(OP_l_4_c_3_r_ + OP_l_1_c_3_r_*SPP(17) - OP_l_2_c_3_r_*SPP(12) - OP_l_3_c_3_r_*SPP(18)) + SPP(19)*(OP_l_4_c_7_r_ + OP_l_1_c_7_r_*SPP(17) - OP_l_2_c_7_r_*SPP(12) - OP_l_3_c_7_r_*SPP(18)); +nextP(4,2) = SPP(4)*(OP_l_4_c_2_r_ + OP_l_1_c_2_r_*SPP(17) - OP_l_2_c_2_r_*SPP(12) - OP_l_3_c_2_r_*SPP(18)) - SPP(3)*(OP_l_4_c_1_r_ + OP_l_1_c_1_r_*SPP(17) - OP_l_2_c_1_r_*SPP(12) - OP_l_3_c_1_r_*SPP(18)) + SPP(8)*(OP_l_4_c_3_r_ + OP_l_1_c_3_r_*SPP(17) - OP_l_2_c_3_r_*SPP(12) - OP_l_3_c_3_r_*SPP(18)) + SPP(19)*(OP_l_4_c_8_r_ + OP_l_1_c_8_r_*SPP(17) - OP_l_2_c_8_r_*SPP(12) - OP_l_3_c_8_r_*SPP(18)); +nextP(4,3) = SPP(1)*(OP_l_4_c_1_r_ + OP_l_1_c_1_r_*SPP(17) - OP_l_2_c_1_r_*SPP(12) - OP_l_3_c_1_r_*SPP(18)) - SPP(2)*(OP_l_4_c_2_r_ + OP_l_1_c_2_r_*SPP(17) - OP_l_2_c_2_r_*SPP(12) - OP_l_3_c_2_r_*SPP(18)) + SPP(7)*(OP_l_4_c_3_r_ + OP_l_1_c_3_r_*SPP(17) - OP_l_2_c_3_r_*SPP(12) - OP_l_3_c_3_r_*SPP(18)) + SPP(19)*(OP_l_4_c_9_r_ + OP_l_1_c_9_r_*SPP(17) - OP_l_2_c_9_r_*SPP(12) - OP_l_3_c_9_r_*SPP(18)); +nextP(4,4) = OP_l_4_c_4_r_ + OP_l_1_c_4_r_*SPP(17) - OP_l_2_c_4_r_*SPP(12) - OP_l_3_c_4_r_*SPP(18) + dvyNoise*(2*q0*q3 - 2*q1*q2)^2 + dvzNoise*(2*q0*q2 + 2*q1*q3)^2 - SPP(12)*(OP_l_4_c_2_r_ + OP_l_1_c_2_r_*SPP(17) - OP_l_2_c_2_r_*SPP(12) - OP_l_3_c_2_r_*SPP(18)) + SPP(17)*(OP_l_4_c_1_r_ + OP_l_1_c_1_r_*SPP(17) - OP_l_2_c_1_r_*SPP(12) - OP_l_3_c_1_r_*SPP(18)) - SPP(18)*(OP_l_4_c_3_r_ + OP_l_1_c_3_r_*SPP(17) - OP_l_2_c_3_r_*SPP(12) - OP_l_3_c_3_r_*SPP(18)) + dvxNoise*(SQ(5) + SQ(6) - SQ(7) - SQ(8))^2; +nextP(4,5) = OP_l_4_c_5_r_ + SQ(3) + OP_l_1_c_5_r_*SPP(17) - OP_l_2_c_5_r_*SPP(12) - OP_l_3_c_5_r_*SPP(18) - SPP(15)*(OP_l_4_c_1_r_ + OP_l_1_c_1_r_*SPP(17) - OP_l_2_c_1_r_*SPP(12) - OP_l_3_c_1_r_*SPP(18)) + SPP(11)*(OP_l_4_c_3_r_ + OP_l_1_c_3_r_*SPP(17) - OP_l_2_c_3_r_*SPP(12) - OP_l_3_c_3_r_*SPP(18)) + SPP(16)*(OP_l_4_c_2_r_ + OP_l_1_c_2_r_*SPP(17) - OP_l_2_c_2_r_*SPP(12) - OP_l_3_c_2_r_*SPP(18)); +nextP(4,6) = OP_l_4_c_6_r_ + SQ(2) + OP_l_1_c_6_r_*SPP(17) - OP_l_2_c_6_r_*SPP(12) - OP_l_3_c_6_r_*SPP(18) + SPP(10)*(OP_l_4_c_1_r_ + OP_l_1_c_1_r_*SPP(17) - OP_l_2_c_1_r_*SPP(12) - OP_l_3_c_1_r_*SPP(18)) - SPP(13)*(OP_l_4_c_2_r_ + OP_l_1_c_2_r_*SPP(17) - OP_l_2_c_2_r_*SPP(12) - OP_l_3_c_2_r_*SPP(18)) + SPP(14)*(OP_l_4_c_3_r_ + OP_l_1_c_3_r_*SPP(17) - OP_l_2_c_3_r_*SPP(12) - OP_l_3_c_3_r_*SPP(18)); +nextP(4,7) = OP_l_4_c_7_r_ + OP_l_1_c_7_r_*SPP(17) - OP_l_2_c_7_r_*SPP(12) - OP_l_3_c_7_r_*SPP(18); +nextP(4,8) = OP_l_4_c_8_r_ + OP_l_1_c_8_r_*SPP(17) - OP_l_2_c_8_r_*SPP(12) - OP_l_3_c_8_r_*SPP(18); +nextP(4,9) = OP_l_4_c_9_r_ + OP_l_1_c_9_r_*SPP(17) - OP_l_2_c_9_r_*SPP(12) - OP_l_3_c_9_r_*SPP(18); +nextP(5,1) = SPP(5)*(OP_l_5_c_1_r_ - OP_l_1_c_1_r_*SPP(15) + OP_l_2_c_1_r_*SPP(16) + OP_l_3_c_1_r_*SPP(11)) + SPP(6)*(OP_l_5_c_2_r_ - OP_l_1_c_2_r_*SPP(15) + OP_l_2_c_2_r_*SPP(16) + OP_l_3_c_2_r_*SPP(11)) - SPP(9)*(OP_l_5_c_3_r_ - OP_l_1_c_3_r_*SPP(15) + OP_l_2_c_3_r_*SPP(16) + OP_l_3_c_3_r_*SPP(11)) + SPP(19)*(OP_l_5_c_7_r_ - OP_l_1_c_7_r_*SPP(15) + OP_l_2_c_7_r_*SPP(16) + OP_l_3_c_7_r_*SPP(11)); +nextP(5,2) = SPP(4)*(OP_l_5_c_2_r_ - OP_l_1_c_2_r_*SPP(15) + OP_l_2_c_2_r_*SPP(16) + OP_l_3_c_2_r_*SPP(11)) - SPP(3)*(OP_l_5_c_1_r_ - OP_l_1_c_1_r_*SPP(15) + OP_l_2_c_1_r_*SPP(16) + OP_l_3_c_1_r_*SPP(11)) + SPP(8)*(OP_l_5_c_3_r_ - OP_l_1_c_3_r_*SPP(15) + OP_l_2_c_3_r_*SPP(16) + OP_l_3_c_3_r_*SPP(11)) + SPP(19)*(OP_l_5_c_8_r_ - OP_l_1_c_8_r_*SPP(15) + OP_l_2_c_8_r_*SPP(16) + OP_l_3_c_8_r_*SPP(11)); +nextP(5,3) = SPP(1)*(OP_l_5_c_1_r_ - OP_l_1_c_1_r_*SPP(15) + OP_l_2_c_1_r_*SPP(16) + OP_l_3_c_1_r_*SPP(11)) - SPP(2)*(OP_l_5_c_2_r_ - OP_l_1_c_2_r_*SPP(15) + OP_l_2_c_2_r_*SPP(16) + OP_l_3_c_2_r_*SPP(11)) + SPP(7)*(OP_l_5_c_3_r_ - OP_l_1_c_3_r_*SPP(15) + OP_l_2_c_3_r_*SPP(16) + OP_l_3_c_3_r_*SPP(11)) + SPP(19)*(OP_l_5_c_9_r_ - OP_l_1_c_9_r_*SPP(15) + OP_l_2_c_9_r_*SPP(16) + OP_l_3_c_9_r_*SPP(11)); +nextP(5,4) = OP_l_5_c_4_r_ + SQ(3) - OP_l_1_c_4_r_*SPP(15) + OP_l_2_c_4_r_*SPP(16) + OP_l_3_c_4_r_*SPP(11) - SPP(12)*(OP_l_5_c_2_r_ - OP_l_1_c_2_r_*SPP(15) + OP_l_2_c_2_r_*SPP(16) + OP_l_3_c_2_r_*SPP(11)) + SPP(17)*(OP_l_5_c_1_r_ - OP_l_1_c_1_r_*SPP(15) + OP_l_2_c_1_r_*SPP(16) + OP_l_3_c_1_r_*SPP(11)) - SPP(18)*(OP_l_5_c_3_r_ - OP_l_1_c_3_r_*SPP(15) + OP_l_2_c_3_r_*SPP(16) + OP_l_3_c_3_r_*SPP(11)); +nextP(5,5) = OP_l_5_c_5_r_ - OP_l_1_c_5_r_*SPP(15) + OP_l_2_c_5_r_*SPP(16) + OP_l_3_c_5_r_*SPP(11) + dvxNoise*(2*q0*q3 + 2*q1*q2)^2 + dvzNoise*(2*q0*q1 - 2*q2*q3)^2 - SPP(15)*(OP_l_5_c_1_r_ - OP_l_1_c_1_r_*SPP(15) + OP_l_2_c_1_r_*SPP(16) + OP_l_3_c_1_r_*SPP(11)) + SPP(11)*(OP_l_5_c_3_r_ - OP_l_1_c_3_r_*SPP(15) + OP_l_2_c_3_r_*SPP(16) + OP_l_3_c_3_r_*SPP(11)) + SPP(16)*(OP_l_5_c_2_r_ - OP_l_1_c_2_r_*SPP(15) + OP_l_2_c_2_r_*SPP(16) + OP_l_3_c_2_r_*SPP(11)) + dvyNoise*(SQ(5) - SQ(6) + SQ(7) - SQ(8))^2; +nextP(5,6) = OP_l_5_c_6_r_ + SQ(1) - OP_l_1_c_6_r_*SPP(15) + OP_l_2_c_6_r_*SPP(16) + OP_l_3_c_6_r_*SPP(11) + SPP(10)*(OP_l_5_c_1_r_ - OP_l_1_c_1_r_*SPP(15) + OP_l_2_c_1_r_*SPP(16) + OP_l_3_c_1_r_*SPP(11)) - SPP(13)*(OP_l_5_c_2_r_ - OP_l_1_c_2_r_*SPP(15) + OP_l_2_c_2_r_*SPP(16) + OP_l_3_c_2_r_*SPP(11)) + SPP(14)*(OP_l_5_c_3_r_ - OP_l_1_c_3_r_*SPP(15) + OP_l_2_c_3_r_*SPP(16) + OP_l_3_c_3_r_*SPP(11)); +nextP(5,7) = OP_l_5_c_7_r_ - OP_l_1_c_7_r_*SPP(15) + OP_l_2_c_7_r_*SPP(16) + OP_l_3_c_7_r_*SPP(11); +nextP(5,8) = OP_l_5_c_8_r_ - OP_l_1_c_8_r_*SPP(15) + OP_l_2_c_8_r_*SPP(16) + OP_l_3_c_8_r_*SPP(11); +nextP(5,9) = OP_l_5_c_9_r_ - OP_l_1_c_9_r_*SPP(15) + OP_l_2_c_9_r_*SPP(16) + OP_l_3_c_9_r_*SPP(11); +nextP(6,1) = SPP(5)*(OP_l_6_c_1_r_ + OP_l_1_c_1_r_*SPP(10) - OP_l_2_c_1_r_*SPP(13) + OP_l_3_c_1_r_*SPP(14)) + SPP(6)*(OP_l_6_c_2_r_ + OP_l_1_c_2_r_*SPP(10) - OP_l_2_c_2_r_*SPP(13) + OP_l_3_c_2_r_*SPP(14)) - SPP(9)*(OP_l_6_c_3_r_ + OP_l_1_c_3_r_*SPP(10) - OP_l_2_c_3_r_*SPP(13) + OP_l_3_c_3_r_*SPP(14)) + SPP(19)*(OP_l_6_c_7_r_ + OP_l_1_c_7_r_*SPP(10) - OP_l_2_c_7_r_*SPP(13) + OP_l_3_c_7_r_*SPP(14)); +nextP(6,2) = SPP(4)*(OP_l_6_c_2_r_ + OP_l_1_c_2_r_*SPP(10) - OP_l_2_c_2_r_*SPP(13) + OP_l_3_c_2_r_*SPP(14)) - SPP(3)*(OP_l_6_c_1_r_ + OP_l_1_c_1_r_*SPP(10) - OP_l_2_c_1_r_*SPP(13) + OP_l_3_c_1_r_*SPP(14)) + SPP(8)*(OP_l_6_c_3_r_ + OP_l_1_c_3_r_*SPP(10) - OP_l_2_c_3_r_*SPP(13) + OP_l_3_c_3_r_*SPP(14)) + SPP(19)*(OP_l_6_c_8_r_ + OP_l_1_c_8_r_*SPP(10) - OP_l_2_c_8_r_*SPP(13) + OP_l_3_c_8_r_*SPP(14)); +nextP(6,3) = SPP(1)*(OP_l_6_c_1_r_ + OP_l_1_c_1_r_*SPP(10) - OP_l_2_c_1_r_*SPP(13) + OP_l_3_c_1_r_*SPP(14)) - SPP(2)*(OP_l_6_c_2_r_ + OP_l_1_c_2_r_*SPP(10) - OP_l_2_c_2_r_*SPP(13) + OP_l_3_c_2_r_*SPP(14)) + SPP(7)*(OP_l_6_c_3_r_ + OP_l_1_c_3_r_*SPP(10) - OP_l_2_c_3_r_*SPP(13) + OP_l_3_c_3_r_*SPP(14)) + SPP(19)*(OP_l_6_c_9_r_ + OP_l_1_c_9_r_*SPP(10) - OP_l_2_c_9_r_*SPP(13) + OP_l_3_c_9_r_*SPP(14)); +nextP(6,4) = OP_l_6_c_4_r_ + SQ(2) + OP_l_1_c_4_r_*SPP(10) - OP_l_2_c_4_r_*SPP(13) + OP_l_3_c_4_r_*SPP(14) - SPP(12)*(OP_l_6_c_2_r_ + OP_l_1_c_2_r_*SPP(10) - OP_l_2_c_2_r_*SPP(13) + OP_l_3_c_2_r_*SPP(14)) + SPP(17)*(OP_l_6_c_1_r_ + OP_l_1_c_1_r_*SPP(10) - OP_l_2_c_1_r_*SPP(13) + OP_l_3_c_1_r_*SPP(14)) - SPP(18)*(OP_l_6_c_3_r_ + OP_l_1_c_3_r_*SPP(10) - OP_l_2_c_3_r_*SPP(13) + OP_l_3_c_3_r_*SPP(14)); +nextP(6,5) = OP_l_6_c_5_r_ + SQ(1) + OP_l_1_c_5_r_*SPP(10) - OP_l_2_c_5_r_*SPP(13) + OP_l_3_c_5_r_*SPP(14) - SPP(15)*(OP_l_6_c_1_r_ + OP_l_1_c_1_r_*SPP(10) - OP_l_2_c_1_r_*SPP(13) + OP_l_3_c_1_r_*SPP(14)) + SPP(11)*(OP_l_6_c_3_r_ + OP_l_1_c_3_r_*SPP(10) - OP_l_2_c_3_r_*SPP(13) + OP_l_3_c_3_r_*SPP(14)) + SPP(16)*(OP_l_6_c_2_r_ + OP_l_1_c_2_r_*SPP(10) - OP_l_2_c_2_r_*SPP(13) + OP_l_3_c_2_r_*SPP(14)); +nextP(6,6) = OP_l_6_c_6_r_ + OP_l_1_c_6_r_*SPP(10) - OP_l_2_c_6_r_*SPP(13) + OP_l_3_c_6_r_*SPP(14) + dvxNoise*(2*q0*q2 - 2*q1*q3)^2 + dvyNoise*(2*q0*q1 + 2*q2*q3)^2 + SPP(10)*(OP_l_6_c_1_r_ + OP_l_1_c_1_r_*SPP(10) - OP_l_2_c_1_r_*SPP(13) + OP_l_3_c_1_r_*SPP(14)) - SPP(13)*(OP_l_6_c_2_r_ + OP_l_1_c_2_r_*SPP(10) - OP_l_2_c_2_r_*SPP(13) + OP_l_3_c_2_r_*SPP(14)) + SPP(14)*(OP_l_6_c_3_r_ + OP_l_1_c_3_r_*SPP(10) - OP_l_2_c_3_r_*SPP(13) + OP_l_3_c_3_r_*SPP(14)) + dvzNoise*(SQ(5) - SQ(6) - SQ(7) + SQ(8))^2; +nextP(6,7) = OP_l_6_c_7_r_ + OP_l_1_c_7_r_*SPP(10) - OP_l_2_c_7_r_*SPP(13) + OP_l_3_c_7_r_*SPP(14); +nextP(6,8) = OP_l_6_c_8_r_ + OP_l_1_c_8_r_*SPP(10) - OP_l_2_c_8_r_*SPP(13) + OP_l_3_c_8_r_*SPP(14); +nextP(6,9) = OP_l_6_c_9_r_ + OP_l_1_c_9_r_*SPP(10) - OP_l_2_c_9_r_*SPP(13) + OP_l_3_c_9_r_*SPP(14); +nextP(7,1) = OP_l_7_c_1_r_*SPP(5) + OP_l_7_c_2_r_*SPP(6) - OP_l_7_c_3_r_*SPP(9) + OP_l_7_c_7_r_*SPP(19); +nextP(7,2) = OP_l_7_c_2_r_*SPP(4) - OP_l_7_c_1_r_*SPP(3) + OP_l_7_c_3_r_*SPP(8) + OP_l_7_c_8_r_*SPP(19); +nextP(7,3) = OP_l_7_c_1_r_*SPP(1) - OP_l_7_c_2_r_*SPP(2) + OP_l_7_c_3_r_*SPP(7) + OP_l_7_c_9_r_*SPP(19); +nextP(7,4) = OP_l_7_c_4_r_ - OP_l_7_c_2_r_*SPP(12) + OP_l_7_c_1_r_*SPP(17) - OP_l_7_c_3_r_*SPP(18); +nextP(7,5) = OP_l_7_c_5_r_ + OP_l_7_c_3_r_*SPP(11) - OP_l_7_c_1_r_*SPP(15) + OP_l_7_c_2_r_*SPP(16); +nextP(7,6) = OP_l_7_c_6_r_ + OP_l_7_c_1_r_*SPP(10) - OP_l_7_c_2_r_*SPP(13) + OP_l_7_c_3_r_*SPP(14); +nextP(7,7) = OP_l_7_c_7_r_; +nextP(7,8) = OP_l_7_c_8_r_; +nextP(7,9) = OP_l_7_c_9_r_; +nextP(8,1) = OP_l_8_c_1_r_*SPP(5) + OP_l_8_c_2_r_*SPP(6) - OP_l_8_c_3_r_*SPP(9) + OP_l_8_c_7_r_*SPP(19); +nextP(8,2) = OP_l_8_c_2_r_*SPP(4) - OP_l_8_c_1_r_*SPP(3) + OP_l_8_c_3_r_*SPP(8) + OP_l_8_c_8_r_*SPP(19); +nextP(8,3) = OP_l_8_c_1_r_*SPP(1) - OP_l_8_c_2_r_*SPP(2) + OP_l_8_c_3_r_*SPP(7) + OP_l_8_c_9_r_*SPP(19); +nextP(8,4) = OP_l_8_c_4_r_ - OP_l_8_c_2_r_*SPP(12) + OP_l_8_c_1_r_*SPP(17) - OP_l_8_c_3_r_*SPP(18); +nextP(8,5) = OP_l_8_c_5_r_ + OP_l_8_c_3_r_*SPP(11) - OP_l_8_c_1_r_*SPP(15) + OP_l_8_c_2_r_*SPP(16); +nextP(8,6) = OP_l_8_c_6_r_ + OP_l_8_c_1_r_*SPP(10) - OP_l_8_c_2_r_*SPP(13) + OP_l_8_c_3_r_*SPP(14); +nextP(8,7) = OP_l_8_c_7_r_; +nextP(8,8) = OP_l_8_c_8_r_; +nextP(8,9) = OP_l_8_c_9_r_; +nextP(9,1) = OP_l_9_c_1_r_*SPP(5) + OP_l_9_c_2_r_*SPP(6) - OP_l_9_c_3_r_*SPP(9) + OP_l_9_c_7_r_*SPP(19); +nextP(9,2) = OP_l_9_c_2_r_*SPP(4) - OP_l_9_c_1_r_*SPP(3) + OP_l_9_c_3_r_*SPP(8) + OP_l_9_c_8_r_*SPP(19); +nextP(9,3) = OP_l_9_c_1_r_*SPP(1) - OP_l_9_c_2_r_*SPP(2) + OP_l_9_c_3_r_*SPP(7) + OP_l_9_c_9_r_*SPP(19); +nextP(9,4) = OP_l_9_c_4_r_ - OP_l_9_c_2_r_*SPP(12) + OP_l_9_c_1_r_*SPP(17) - OP_l_9_c_3_r_*SPP(18); +nextP(9,5) = OP_l_9_c_5_r_ + OP_l_9_c_3_r_*SPP(11) - OP_l_9_c_1_r_*SPP(15) + OP_l_9_c_2_r_*SPP(16); +nextP(9,6) = OP_l_9_c_6_r_ + OP_l_9_c_1_r_*SPP(10) - OP_l_9_c_2_r_*SPP(13) + OP_l_9_c_3_r_*SPP(14); +nextP(9,7) = OP_l_9_c_7_r_; +nextP(9,8) = OP_l_9_c_8_r_; +nextP(9,9) = OP_l_9_c_9_r_; + diff --git a/libraries/AP_NavEKF/Models/GimbalEstimatorExample/calcQ.c b/libraries/AP_NavEKF/Models/GimbalEstimatorExample/calcQ.c new file mode 100644 index 0000000000..7db892b5c7 --- /dev/null +++ b/libraries/AP_NavEKF/Models/GimbalEstimatorExample/calcQ.c @@ -0,0 +1,38 @@ + t3 = q0*q0; + t4 = q1*q1; + t5 = q2*q2; + t6 = q3*q3; + t2 = t3+t4+t5+t6; + t7 = t2*t2; + t11 = q0*q3*2.0; + t12 = q1*q2*2.0; + t8 = t11-t12; + t13 = q0*q2*2.0; + t14 = q1*q3*2.0; + t9 = t13+t14; + t10 = t3+t4-t5-t6; + t15 = q0*q1*2.0; + t16 = t11+t12; + t17 = dvxNoise*t10*t16; + t18 = t3-t4+t5-t6; + t19 = q2*q3*2.0; + t20 = t15-t19; + t21 = t15+t19; + t22 = t3-t4-t5+t6; + t23 = t13-t14; + t24 = dvzNoise*t9*t22; + t25 = t24-dvxNoise*t10*t23-dvyNoise*t8*t21; + t26 = dvyNoise*t18*t21; + t27 = t26-dvxNoise*t16*t23-dvzNoise*t20*t22; + A0[0][0] = daxNoise*t7; + A0[1][1] = dayNoise*t7; + A0[2][2] = dazNoise*t7; + A0[3][3] = dvxNoise*(t10*t10)+dvyNoise*(t8*t8)+dvzNoise*(t9*t9); + A0[3][4] = t17-dvzNoise*t9*(t15-q2*q3*2.0)-dvyNoise*t8*t18; + A0[3][5] = t25; + A0[4][3] = t17-dvyNoise*t8*t18-dvzNoise*t9*t20; + A0[4][4] = dvxNoise*(t16*t16)+dvyNoise*(t18*t18)+dvzNoise*(t20*t20); + A0[4][5] = t27; + A0[5][3] = t25; + A0[5][4] = t27; + A0[5][5] = dvxNoise*(t23*t23)+dvyNoise*(t21*t21)+dvzNoise*(t22*t22); diff --git a/libraries/AP_NavEKF/Models/GimbalEstimatorExample/calcQ.cpp b/libraries/AP_NavEKF/Models/GimbalEstimatorExample/calcQ.cpp new file mode 100644 index 0000000000..4b4b7eed85 --- /dev/null +++ b/libraries/AP_NavEKF/Models/GimbalEstimatorExample/calcQ.cpp @@ -0,0 +1,38 @@ +float t3 = q0*q0; +float t4 = q1*q1; +float t5 = q2*q2; +float t6 = q3*q3; +float t2 = t3+t4+t5+t6; +float t7 = t2*t2; +float t11 = q0*q3*2.0f; +float t12 = q1*q2*2.0f; +float t8 = t11-t12; +float t13 = q0*q2*2.0f; +float t14 = q1*q3*2.0f; +float t9 = t13+t14; +float t10 = t3+t4-t5-t6; +float t15 = q0*q1*2.0f; +float t16 = t11+t12; +float t17 = dvxNoise*t10*t16; +float t18 = t3-t4+t5-t6; +float t19 = q2*q3*2.0f; +float t20 = t15-t19; +float t21 = t15+t19; +float t22 = t3-t4-t5+t6; +float t23 = t13-t14; +float t24 = dvzNoise*t9*t22; +float t25 = t24-dvxNoise*t10*t23-dvyNoise*t8*t21; +float t26 = dvyNoise*t18*t21; +float t27 = t26-dvxNoise*t16*t23-dvzNoise*t20*t22; +A0[0][0] = daxNoise*t7; +A0[1][1] = dayNoise*t7; +A0[2][2] = dazNoise*t7; +A0[3][3] = dvxNoise*(t10*t10)+dvyNoise*(t8*t8)+dvzNoise*(t9*t9); +A0[3][4] = t17-dvzNoise*t9*(t15-q2*q3*2.0f)-dvyNoise*t8*t18; +A0[3][5] = t25; +A0[4][3] = t17-dvyNoise*t8*t18-dvzNoise*t9*t20; +A0[4][4] = dvxNoise*(t16*t16)+dvyNoise*(t18*t18)+dvzNoise*(t20*t20); +A0[4][5] = t27; +A0[5][3] = t25; +A0[5][4] = t27; +A0[5][5] = dvxNoise*(t23*t23)+dvyNoise*(t21*t21)+dvzNoise*(t22*t22); diff --git a/libraries/AP_NavEKF/Models/GimbalEstimatorExample/calcQ.m b/libraries/AP_NavEKF/Models/GimbalEstimatorExample/calcQ.m new file mode 100644 index 0000000000..54404e8041 --- /dev/null +++ b/libraries/AP_NavEKF/Models/GimbalEstimatorExample/calcQ.m @@ -0,0 +1,34 @@ +function Q = calcQ(daxNoise,dayNoise,dazNoise,dvxNoise,dvyNoise,dvzNoise,q0,q1,q2,q3) +%CALCQ +% Q = CALCQ(DAXNOISE,DAYNOISE,DAZNOISE,DVXNOISE,DVYNOISE,DVZNOISE,Q0,Q1,Q2,Q3) + +% This function was generated by the Symbolic Math Toolbox version 6.1. +% 15-Feb-2015 15:45:50 + +t3 = q0.^2; +t4 = q1.^2; +t5 = q2.^2; +t6 = q3.^2; +t2 = t3+t4+t5+t6; +t7 = t2.^2; +t11 = q0.*q3.*2.0; +t12 = q1.*q2.*2.0; +t8 = t11-t12; +t13 = q0.*q2.*2.0; +t14 = q1.*q3.*2.0; +t9 = t13+t14; +t10 = t3+t4-t5-t6; +t15 = q0.*q1.*2.0; +t16 = t11+t12; +t17 = dvxNoise.*t10.*t16; +t18 = t3-t4+t5-t6; +t19 = q2.*q3.*2.0; +t20 = t15-t19; +t21 = t15+t19; +t22 = t3-t4-t5+t6; +t23 = t13-t14; +t24 = dvzNoise.*t9.*t22; +t25 = t24-dvxNoise.*t10.*t23-dvyNoise.*t8.*t21; +t26 = dvyNoise.*t18.*t21; +t27 = t26-dvxNoise.*t16.*t23-dvzNoise.*t20.*t22; +Q = reshape([daxNoise.*t7,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,dayNoise.*t7,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,dazNoise.*t7,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,dvxNoise.*t10.^2+dvyNoise.*t8.^2+dvzNoise.*t9.^2,t17-dvyNoise.*t8.*t18-dvzNoise.*t9.*t20,t25,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,t17-dvzNoise.*t9.*(t15-q2.*q3.*2.0)-dvyNoise.*t8.*t18,dvxNoise.*t16.^2+dvyNoise.*t18.^2+dvzNoise.*t20.^2,t27,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,t25,t27,dvxNoise.*t23.^2+dvyNoise.*t21.^2+dvzNoise.*t22.^2,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0],[12, 12]); diff --git a/libraries/AP_NavEKF/Models/GimbalEstimatorExample/calcSF.c b/libraries/AP_NavEKF/Models/GimbalEstimatorExample/calcSF.c new file mode 100644 index 0000000000..9a7960c83b --- /dev/null +++ b/libraries/AP_NavEKF/Models/GimbalEstimatorExample/calcSF.c @@ -0,0 +1,51 @@ + t2 = SF(1.0); + t3 = SF(2.0); + t4 = SF(3.0); + t5 = q3*(1.0/2.0); + t6 = q0*t2*(1.0/2.0); + t7 = q2*t4*(1.0/2.0); + t8 = q0*t3*(1.0/2.0); + t9 = q1*t2*(1.0/2.0); + t10 = q3*t4*(1.0/2.0); + t11 = q1*(1.0/2.0); + t12 = q2*t2*(1.0/2.0); + t13 = q3*t3*(1.0/2.0); + t14 = q0*(1.0/2.0); + t15 = q1*t4*(1.0/2.0); + t16 = q2*t3*(1.0/2.0); + t17 = q3*t2*(1.0/2.0); + t18 = q0*t4*(1.0/2.0); + t19 = q2*(1.0/2.0); + t20 = q1*t3*(1.0/2.0); + t21 = q0*q0; + t22 = q1*q1; + t23 = q2*q2; + t24 = q3*q3; + t25 = q0*q1*2.0; + t26 = q0*q3*2.0; + t27 = q0*q2*2.0; + A0[0][0] = daz*(1.0/2.0)-daz_b*(1.0/2.0); + A0[1][0] = day*(1.0/2.0)-day_b*(1.0/2.0); + A0[2][0] = dax*(1.0/2.0)-dax_b*(1.0/2.0); + A0[3][0] = q2*(-1.0/2.0)+t8+t9+t10; + A0[4][0] = t5+t6+t7-q1*t3*(1.0/2.0); + A0[5][0] = t14+t15+t16-q3*t2*(1.0/2.0); + A0[6][0] = t11+t12+t13-q0*t4*(1.0/2.0); + A0[7][0] = t5-t6+t7+t20; + A0[8][0] = t8+t9-t10+t19; + A0[9][0] = -t11+t12+t13+t18; + A0[10][0] = t14+t15-t16+t17; + A0[11][0] = t14-t15+t16+t17; + A0[12][0] = t11-t12+t13+t18; + A0[13][0] = -t8+t9+t10+t19; + A0[14][0] = -t5+t6+t7+t20; + A0[15][0] = -t21-t22-t23-t24; + A0[16][0] = t21-t22-t23+t24; + A0[17][0] = t21-t22+t23-t24; + A0[18][0] = t21+t22-t23-t24; + A0[19][0] = t27-q1*q3*2.0; + A0[20][0] = t25-q2*q3*2.0; + A0[21][0] = t26-q1*q2*2.0; + A0[22][0] = t25+q2*q3*2.0; + A0[23][0] = t26+q1*q2*2.0; + A0[24][0] = t27+q1*q3*2.0; diff --git a/libraries/AP_NavEKF/Models/GimbalEstimatorExample/calcSP.c b/libraries/AP_NavEKF/Models/GimbalEstimatorExample/calcSP.c new file mode 100644 index 0000000000..29e135ac25 --- /dev/null +++ b/libraries/AP_NavEKF/Models/GimbalEstimatorExample/calcSP.c @@ -0,0 +1,40 @@ + t2 = SF(1.5E1); + t3 = SF(1.4E1); + t4 = SF(1.3E1); + t5 = SF(1.2E1); + t6 = SF(1.1E1); + t7 = SF(1.0E1); + t8 = SF(9.0); + t9 = SF(8.0); + t10 = SF(7.0); + t11 = SF(6.0); + t12 = SF(5.0); + t13 = SF(4.0); + t14 = SF(1.7E1); + t15 = SF(2.3E1); + t16 = SF(2.0E1); + t17 = SF(1.8E1); + t18 = SF(2.1E1); + t19 = SF(2.4E1); + t20 = SF(2.5E1); + t21 = SF(2.2E1); + t22 = SF(1.9E1); + A0[0][0] = q0*t3*-2.0+q1*t2*2.0+q2*t5*2.0+q3*t4*2.0; + A0[1][0] = q0*t7*2.0+q1*t6*2.0+q2*t9*2.0-q3*t8*2.0; + A0[2][0] = q0*t2*2.0+q1*t3*2.0-q2*t4*2.0+q3*t5*2.0; + A0[3][0] = q0*t6*2.0-q1*t7*2.0+q2*t8*2.0+q3*t9*2.0; + A0[4][0] = q0*t5*2.0+q1*t4*2.0+q2*t3*2.0-q3*t2*2.0; + A0[5][0] = q0*t9*-2.0+q1*t8*2.0+q2*t7*2.0+q3*t6*2.0; + A0[6][0] = q0*t11*2.0+q1*t10*2.0-q2*t13*2.0+q3*t12*2.0; + A0[7][0] = q0*t10*-2.0+q1*t11*2.0+q2*t12*2.0+q3*t13*2.0; + A0[8][0] = q0*t13*2.0-q1*t12*2.0+q2*t11*2.0+q3*t10*2.0; + A0[9][0] = dvy*t14-dvz*t15; + A0[10][0] = dvx*t17-dvy*t19; + A0[11][0] = dvx*t20-dvz*t22; + A0[12][0] = dvx*t14+dvz*t16; + A0[13][0] = dvx*t15+dvy*t16; + A0[14][0] = dvy*t18+dvz*t17; + A0[15][0] = dvx*t18+dvz*t19; + A0[16][0] = dvy*t20+dvz*t21; + A0[17][0] = dvx*t21+dvy*t22; + A0[18][0] = SF(1.6E1); diff --git a/libraries/AP_NavEKF/Models/GimbalEstimatorExample/calcTmn.c b/libraries/AP_NavEKF/Models/GimbalEstimatorExample/calcTmn.c new file mode 100644 index 0000000000..2f24ba7da7 --- /dev/null +++ b/libraries/AP_NavEKF/Models/GimbalEstimatorExample/calcTmn.c @@ -0,0 +1,46 @@ + t2 = cos(gPsi); + t3 = sin(gTheta); + t4 = cos(gTheta); + t5 = sin(gPhi); + t6 = sin(gPsi); + t7 = q0*q0; + t8 = q1*q1; + t9 = q2*q2; + t10 = q3*q3; + t11 = t7+t8-t9-t10; + t12 = q0*q2*2.0; + t13 = q1*q3*2.0; + t14 = t12+t13; + t15 = cos(gPhi); + t16 = q0*q3*2.0; + t18 = q1*q2*2.0; + t17 = t16-t18; + t19 = t2*t3; + t20 = t4*t5*t6; + t21 = t19+t20; + t22 = t2*t4; + t34 = t3*t5*t6; + t23 = t22-t34; + t24 = t4*t6; + t25 = t2*t3*t5; + t26 = t24+t25; + t27 = t16+t18; + t28 = t3*t6; + t35 = t2*t4*t5; + t29 = t28-t35; + t30 = q0*q1*2.0; + t33 = q2*q3*2.0; + t31 = t30-t33; + t32 = t7-t8+t9-t10; + t36 = t7-t8-t9+t10; + t37 = t12-t13; + t38 = t30+t33; + A0[0][0] = t11*t23+t14*t21+t6*t15*t17; + A0[0][1] = t11*t26+t14*t29-t2*t15*t17; + A0[0][2] = -t5*t17-t3*t11*t15+t4*t14*t15; + A0[1][0] = t23*t27-t21*t31-t6*t15*t32; + A0[1][1] = t26*t27-t29*t31+t2*t15*t32; + A0[1][2] = t5*t32-t3*t15*t27-t4*t15*t31; + A0[2][0] = t21*t36-t23*t37-t6*t15*t38; + A0[2][1] = -t26*t37+t29*t36+t2*t15*t38; + A0[2][2] = t5*t38+t3*t15*t37+t4*t15*t36; diff --git a/libraries/AP_NavEKF/Models/GimbalEstimatorExample/calcTmn.m b/libraries/AP_NavEKF/Models/GimbalEstimatorExample/calcTmn.m new file mode 100644 index 0000000000..219c228789 --- /dev/null +++ b/libraries/AP_NavEKF/Models/GimbalEstimatorExample/calcTmn.m @@ -0,0 +1,45 @@ +function Tmn = calcTmn(gPhi,gPsi,gTheta,q0,q1,q2,q3) +%CALCTMN +% TMN = CALCTMN(GPHI,GPSI,GTHETA,Q0,Q1,Q2,Q3) + +% This function was generated by the Symbolic Math Toolbox version 6.1. +% 15-Feb-2015 16:02:10 + +t2 = cos(gPsi); +t3 = sin(gTheta); +t4 = cos(gTheta); +t5 = sin(gPhi); +t6 = sin(gPsi); +t7 = q0.^2; +t8 = q1.^2; +t9 = q2.^2; +t10 = q3.^2; +t11 = t7+t8-t9-t10; +t12 = q0.*q2.*2.0; +t13 = q1.*q3.*2.0; +t14 = t12+t13; +t15 = cos(gPhi); +t16 = q0.*q3.*2.0; +t18 = q1.*q2.*2.0; +t17 = t16-t18; +t19 = t2.*t3; +t20 = t4.*t5.*t6; +t21 = t19+t20; +t22 = t2.*t4; +t34 = t3.*t5.*t6; +t23 = t22-t34; +t24 = t4.*t6; +t25 = t2.*t3.*t5; +t26 = t24+t25; +t27 = t16+t18; +t28 = t3.*t6; +t35 = t2.*t4.*t5; +t29 = t28-t35; +t30 = q0.*q1.*2.0; +t33 = q2.*q3.*2.0; +t31 = t30-t33; +t32 = t7-t8+t9-t10; +t36 = t7-t8-t9+t10; +t37 = t12-t13; +t38 = t30+t33; +Tmn = reshape([t11.*t23+t14.*t21+t6.*t15.*t17,t23.*t27-t21.*t31-t6.*t15.*t32,t21.*t36-t23.*t37-t6.*t15.*t38,t11.*t26+t14.*t29-t2.*t15.*t17,t26.*t27-t29.*t31+t2.*t15.*t32,-t26.*t37+t29.*t36+t2.*t15.*t38,-t5.*t17-t3.*t11.*t15+t4.*t14.*t15,t5.*t32-t3.*t15.*t27-t4.*t15.*t31,t5.*t38+t3.*t15.*t37+t4.*t15.*t36],[3, 3]); diff --git a/libraries/AP_NavEKF/Models/GimbalEstimatorExample/calcTms.c b/libraries/AP_NavEKF/Models/GimbalEstimatorExample/calcTms.c new file mode 100644 index 0000000000..16c1e5a17c --- /dev/null +++ b/libraries/AP_NavEKF/Models/GimbalEstimatorExample/calcTms.c @@ -0,0 +1 @@ + t0 = _symans_32_297; diff --git a/libraries/AP_NavEKF/Models/GimbalEstimatorExample/calcTms.m b/libraries/AP_NavEKF/Models/GimbalEstimatorExample/calcTms.m new file mode 100644 index 0000000000..b642a444e8 --- /dev/null +++ b/libraries/AP_NavEKF/Models/GimbalEstimatorExample/calcTms.m @@ -0,0 +1,14 @@ +function Tms = calcTms(gPhi,gPsi,gTheta) +%CALCTMS +% TMS = CALCTMS(GPHI,GPSI,GTHETA) + +% This function was generated by the Symbolic Math Toolbox version 6.1. +% 15-Feb-2015 16:02:09 + +t2 = cos(gTheta); +t3 = sin(gPsi); +t4 = cos(gPsi); +t5 = sin(gPhi); +t6 = sin(gTheta); +t7 = cos(gPhi); +Tms = reshape([t2.*t4-t3.*t5.*t6,-t3.*t7,t4.*t6+t2.*t3.*t5,t2.*t3+t4.*t5.*t6,t4.*t7,t3.*t6-t2.*t4.*t5,-t6.*t7,t5,t2.*t7],[3, 3]); diff --git a/libraries/AP_NavEKF/Models/QuaternionMathExample/FuseMagnetometer.m b/libraries/AP_NavEKF/Models/QuaternionMathExample/FuseMagnetometer.m new file mode 100644 index 0000000000..69bae206a3 --- /dev/null +++ b/libraries/AP_NavEKF/Models/QuaternionMathExample/FuseMagnetometer.m @@ -0,0 +1,56 @@ +function [... + states, ... % state vector after fusion of measurements + P, ... % state covariance matrix after fusion of corrections + innovation, ... % Declination innovation - rad + varInnov] ... % + = FuseMagnetometer( ... + states, ... % predicted states + P, ... % predicted covariance + magData, ... % body frame magnetic flux measurements + measDec, ... % magnetic field declination - azimuth angle measured from true north (rad) + Tbn) % Estimated coordinate transformation matrix from body to NED frame + +q0 = states(1); +q1 = states(2); +q2 = states(3); +q3 = states(4); + +magX = magData(1); +magY = magData(2); +magZ = magData(3); + +R_MAG = 0.05^2; + +H = calcH_MAG(magX,magY,magZ,q0,q1,q2,q3); +varInnov = (H*P*transpose(H) + R_MAG); +Kfusion = (P*transpose(H))/varInnov; + +% Calculate the predicted magnetic declination +magMeasNED = Tbn*[magX;magY;magZ]; +predDec = atan2(magMeasNED(2),magMeasNED(1)); + +% Calculate the measurement innovation +innovation = predDec - measDec; + +% correct the state vector +states = states - Kfusion * innovation; + +% re-normalise the quaternion +quatMag = sqrt(states(1)^2 + states(2)^2 + states(3)^2 + states(4)^2); +states(1:4) = states(1:4) / quatMag; + +% correct the covariance P = P - K*H*P +P = P - Kfusion*H*P; + +% Force symmetry on the covariance matrix to prevent ill-conditioning +% of the matrix which would cause the filter to blow-up +P = 0.5*(P + transpose(P)); + +% ensure diagonals are positive +for i=1:10 + if P(i,i) < 0 + P(i,i) = 0; + end +end + +end \ No newline at end of file diff --git a/libraries/AP_NavEKF/Models/QuaternionMathExample/FuseVelocity.m b/libraries/AP_NavEKF/Models/QuaternionMathExample/FuseVelocity.m new file mode 100644 index 0000000000..23a4868f5f --- /dev/null +++ b/libraries/AP_NavEKF/Models/QuaternionMathExample/FuseVelocity.m @@ -0,0 +1,51 @@ +function [... + states, ... % state vector after fusion of measurements + P, ... % state covariance matrix after fusion of corrections + innovation,... % NED velocity innovations (m/s) + varInnov] ... % NED velocity innovation variance ((m/s)^2) + = FuseVelocity( ... + states, ... % predicted states from the INS + P, ... % predicted covariance + measVel) % NED velocity measurements (m/s) + +R_OBS = 0.5^2; +innovation = zeros(1,3); +varInnov = zeros(1,3); +% Fuse measurements sequentially +for obsIndex = 1:3 + stateIndex = 4 + obsIndex; + % Calculate the velocity measurement innovation + innovation(obsIndex) = states(stateIndex) - measVel(obsIndex); + + % Calculate the Kalman Gain + H = zeros(1,10); + H(1,stateIndex) = 1; + varInnov(obsIndex) = (H*P*transpose(H) + R_OBS); + K = (P*transpose(H))/varInnov(obsIndex); + + % Calculate state corrections + xk = K * innovation(obsIndex); + + % Apply the state corrections + states = states - xk; + + % re-normalise the quaternion + quatMag = sqrt(states(1)^2 + states(2)^2 + states(3)^2 + states(4)^2); + states(1:4) = states(1:4) / quatMag; + + % Update the covariance + P = P - K*H*P; + + % Force symmetry on the covariance matrix to prevent ill-conditioning + P = 0.5*(P + transpose(P)); + + % ensure diagonals are positive + for i=1:10 + if P(i,i) < 0 + P(i,i) = 0; + end + end + +end + +end \ No newline at end of file diff --git a/libraries/AP_NavEKF/Models/QuaternionMathExample/GenerateEquations.m b/libraries/AP_NavEKF/Models/QuaternionMathExample/GenerateEquations.m new file mode 100644 index 0000000000..bd4ec97906 --- /dev/null +++ b/libraries/AP_NavEKF/Models/QuaternionMathExample/GenerateEquations.m @@ -0,0 +1,113 @@ +% IMPORTANT - This script requires the Matlab symbolic toolbox + +% Author: Paul Riseborough +% Last Modified: 16 Feb 2014 + +% Derivation of a navigation EKF using a local NED earth Tangent Frame for +% the initial alignment and gyro bias estimation from a moving platform +% Uses quaternions for attitude propagation + +% State vector: +% quaternions +% Velocity - North, East, Down (m/s) +% Delta Angle bias - X,Y,Z (rad) + +% Observations: +% NED velocity - N,E,D (m/s) +% body fixed magnetic field vector - X,Y,Z + +% Time varying parameters: +% XYZ delta angle measurements in body axes - rad +% XYZ delta velocity measurements in body axes - m/sec +% magnetic declination +clear all; + +%% define symbolic variables and constants +syms dax day daz real % IMU delta angle measurements in body axes - rad +syms dvx dvy dvz real % IMU delta velocity measurements in body axes - m/sec +syms q0 q1 q2 q3 real % quaternions defining attitude of body axes relative to local NED +syms vn ve vd real % NED velocity - m/sec +syms dax_b day_b daz_b real % delta angle bias - rad +syms dvx_b dvy_b dvz_b real % delta velocity bias - m/sec +syms dt real % IMU time step - sec +syms gravity real % gravity - m/sec^2 +syms daxNoise dayNoise dazNoise dvxNoise dvyNoise dvzNoise real; % IMU delta angle and delta velocity measurement noise +syms vwn vwe real; % NE wind velocity - m/sec +syms magX magY magZ real; % XYZ body fixed magnetic field measurements - milligauss +syms magN magE magD real; % NED earth fixed magnetic field components - milligauss +syms R_VN R_VE R_VD real % variances for NED velocity measurements - (m/sec)^2 +syms R_MAG real % variance for magnetic flux measurements - milligauss^2 + +%% define the process equations + +% define the measured Delta angle and delta velocity vectors +dAngMeas = [dax; day; daz]; +dVelMeas = [dvx; dvy; dvz]; + +% define the delta angle bias errors +dAngBias = [dax_b; day_b; daz_b]; + +% define the quaternion rotation vector for the state estimate +quat = [q0;q1;q2;q3]; + +% derive the truth body to nav direction cosine matrix +Tbn = Quat2Tbn(quat); + +% define the truth delta angle +% ignore coning acompensation as these effects are negligible in terms of +% covariance growth for our application and grade of sensor +dAngTruth = dAngMeas - dAngBias; + +% Define the truth delta velocity +dVelTruth = dVelMeas; + +% define the attitude update equations +% use a first order expansion of rotation to calculate the quaternion increment +% acceptable for propagation of covariances +deltaQuat = [1; + 0.5*dAngTruth(1); + 0.5*dAngTruth(2); + 0.5*dAngTruth(3); + ]; +quatNew = QuatMult(quat,deltaQuat); + +% define the velocity update equations +% ignore coriolis terms for linearisation purposes +vNew = [vn;ve;vd] + [0;0;gravity]*dt + Tbn*dVelTruth; + +% define the IMU bias error update equations +dabNew = [dax_b; day_b; daz_b]; + +% Define the state vector & number of states +stateVector = [quat;vn;ve;vd;dAngBias]; +nStates=numel(stateVector); + +%% derive the covariance prediction equation +% This reduces the number of floating point operations by a factor of 6 or +% more compared to using the standard matrix operations in code + +% Define the control (disturbance) vector. Use the measured delta angles +% and velocities (not truth) to simplify the derivation +distVector = [dAngMeas;dVelMeas]; + +% derive the control(disturbance) influence matrix +G = jacobian([quatNew;vNew;dabNew], distVector); +f = matlabFunction(G,'file','calcG.m'); + +% derive the state error matrix +imuNoise = diag([daxNoise dayNoise dazNoise dvxNoise dvyNoise dvzNoise]); +Q = G*imuNoise*transpose(G); +f = matlabFunction(Q,'file','calcQ.m'); + +% derive the state transition matrix +F = jacobian([quatNew;vNew;dabNew], stateVector); +f = matlabFunction(F,'file','calcF.m'); + +%% derive equations for fusion of magnetic deviation measurement +% rotate body measured field into earth axes +magMeasNED = Tbn*[magX;magY;magZ]; +% the predicted measurement is the angle wrt true north of the horizontal +% component of the measured field +angMeas = tan(magMeasNED(2)/magMeasNED(1)); +H_MAG = jacobian(angMeas,stateVector); % measurement Jacobian +f = matlabFunction(H_MAG,'file','calcH_MAG.m'); diff --git a/libraries/AP_NavEKF/Models/QuaternionMathExample/PlotData.m b/libraries/AP_NavEKF/Models/QuaternionMathExample/PlotData.m new file mode 100644 index 0000000000..df700b9b65 --- /dev/null +++ b/libraries/AP_NavEKF/Models/QuaternionMathExample/PlotData.m @@ -0,0 +1,21 @@ +%% plot gyro bias estimates +figure; +plot(statesLog(1,:)*0.001,statesLog(9:11,:)/dt*180/pi); +grid on; +ylabel('Gyro Bias Estimate (deg/sec)'); +xlabel('time (sec)'); + +%% plot Euler angle estimates +figure; +eulLog(4,:) = eulLog(4,:) + pi; +plot(eulLog(1,:)*0.001,eulLog(2:4,:)*180/pi); +grid on; +ylabel('Euler Angle Estimates (deg)'); +xlabel('time (sec)'); + +%% plot velocity innovations +figure; +plot(statesLog(1,:)*0.001,statesLog(6:8,:)); +grid on; +ylabel('EKF velocity Innovations (m/s)'); +xlabel('time (sec)'); \ No newline at end of file diff --git a/libraries/AP_NavEKF/Models/QuaternionMathExample/PredictCovariance.m b/libraries/AP_NavEKF/Models/QuaternionMathExample/PredictCovariance.m new file mode 100644 index 0000000000..54b0aa8a7d --- /dev/null +++ b/libraries/AP_NavEKF/Models/QuaternionMathExample/PredictCovariance.m @@ -0,0 +1,60 @@ +function P = PredictCovariance(deltaAngle, ... + deltaVelocity, ... + quat, ... + states,... + P, ... % Previous state covariance matrix + dt) ... % IMU and prediction time step + +% Set the filter state process noise (IMU errors are already built into the +% equations). It includes the process noise required for evolution of the +% IMU bias errors + +dAngBiasSigma = dt*1E-6; +processNoise = [0*ones(1,7), dAngBiasSigma*[1 1 1]]; + +% Specify the estimated errors on the delta angles and delta velocities +daxNoise = (dt*25.0/60*pi/180)^2; +dayNoise = (dt*25.0/60*pi/180)^2; +dazNoise = (dt*25.0/60*pi/180)^2; +dvxNoise = (dt*0.5)^2; +dvyNoise = (dt*0.5)^2; +dvzNoise = (dt*0.5)^2; + +dvx = deltaVelocity(1); +dvy = deltaVelocity(2); +dvz = deltaVelocity(3); +dax = deltaAngle(1); +day = deltaAngle(2); +daz = deltaAngle(3); + +q0 = quat(1); +q1 = quat(2); +q2 = quat(3); +q3 = quat(4); + +dax_b = states(8); +day_b = states(9); +daz_b = states(10); + +% Predicted covariance +F = calcF(dax,dax_b,day,day_b,daz,daz_b,dvx,dvy,dvz,q0,q1,q2,q3); +Q = calcQ(daxNoise,dayNoise,dazNoise,dvxNoise,dvyNoise,dvzNoise,q0,q1,q2,q3); +P = F*P*transpose(F) + Q; + +% Add the general process noise +for i = 1:10 + P(i,i) = P(i,i) + processNoise(i)^2; +end + +% Force symmetry on the covariance matrix to prevent ill-conditioning +% of the matrix which would cause the filter to blow-up +P = 0.5*(P + transpose(P)); + +% ensure diagonals are positive +for i=1:9 + if P(i,i) < 0 + P(i,i) = 0; + end +end + +end \ No newline at end of file diff --git a/libraries/AP_NavEKF/Models/QuaternionMathExample/PredictStates.m b/libraries/AP_NavEKF/Models/QuaternionMathExample/PredictStates.m new file mode 100644 index 0000000000..8b694405e2 --- /dev/null +++ b/libraries/AP_NavEKF/Models/QuaternionMathExample/PredictStates.m @@ -0,0 +1,84 @@ +function [nextQuat, nextStates, Tbn, correctedDelAng, correctedDelVel] = PredictStates( ... + quat, ... % previous quaternion states 4x1 + states, ... % previous states (3x1 rotation error, 3x1 velocity, 3x1 gyro bias) + angRate, ... % IMU rate gyro measurements, 3x1 (rad/sec) + accel, ... % IMU accelerometer measurements 3x1 (m/s/s) + dt) % time since last IMU measurement (sec) + +% Define parameters used for previous angular rates and acceleration shwich +% are used for trapezoidal integration +persistent prevAngRate; +if isempty(prevAngRate) + prevAngRate = angRate; +end +persistent prevAccel; +if isempty(prevAccel) + prevAccel = accel; +end +% define persistent variables for previous delta angle and velocity which +% are required for sculling and coning error corrections +persistent prevDelAng; +if isempty(prevDelAng) + prevDelAng = single([0;0;0]); +end +persistent prevDelVel; +if isempty(prevDelVel) + prevDelVel = single([0;0;0]); +end + +% Convert IMU data to delta angles and velocities using trapezoidal +% integration +dAng = 0.5*(angRate + prevAngRate)*dt; +dVel = 0.5*(accel + prevAccel )*dt; +prevAngRate = angRate; +prevAccel = accel; + +% Remove sensor bias errors +dAng = dAng - states(7:9); + +% Apply rotational and skulling corrections +correctedDelVel= dVel + ... + 0.5*cross(prevDelAng + dAng , prevDelVel + dVel) + 1/6*cross(prevDelAng + dAng , cross(prevDelAng + dAng , prevDelVel + dVel)) + ... % rotational correction + 1/12*(cross(prevDelAng , dVel) + cross(prevDelVel , dAng)); % sculling correction + +% Apply corrections for coning errors +correctedDelAng = dAng - 1/12*cross(prevDelAng , dAng); + +% Save current measurements +prevDelAng = dAng; +prevDelVel = dVel; + +% Initialise the updated state vector +nextQuat = quat; +nextStates = states; + +% Convert the rotation vector to its equivalent quaternion +rotationMag = sqrt(correctedDelAng(1)^2 + correctedDelAng(2)^2 + correctedDelAng(3)^2); +if rotationMag<1e-12 + deltaQuat = single([1;0;0;0]); +else + deltaQuat = [cos(0.5*rotationMag); correctedDelAng/rotationMag*sin(0.5*rotationMag)]; +end + +% Update the quaternions by rotating from the previous attitude through +% the delta angle rotation quaternion +qUpdated = [quat(1)*deltaQuat(1)-transpose(quat(2:4))*deltaQuat(2:4); quat(1)*deltaQuat(2:4) + deltaQuat(1)*quat(2:4) + cross(quat(2:4),deltaQuat(2:4))]; + +% Normalise the quaternions and update the quaternion states +quatMag = sqrt(qUpdated(1)^2 + qUpdated(2)^2 + qUpdated(3)^2 + qUpdated(4)^2); +if (quatMag < 1e-16) + nextQuat(1:4) = qUpdated; +else + nextQuat(1:4) = qUpdated / quatMag; +end + +% Calculate the body to nav cosine matrix +Tbn = Quat2Tbn(nextQuat); + +% transform body delta velocities to delta velocities in the nav frame +delVelNav = Tbn * correctedDelVel + [0;0;9.807]*dt; + +% Sum delta velocities to get velocity +nextStates(4:6) = states(4:6) + delVelNav(1:3); + +end \ No newline at end of file diff --git a/libraries/AP_NavEKF/Models/QuaternionMathExample/RunRealData.m b/libraries/AP_NavEKF/Models/QuaternionMathExample/RunRealData.m new file mode 100644 index 0000000000..8ab4969d16 --- /dev/null +++ b/libraries/AP_NavEKF/Models/QuaternionMathExample/RunRealData.m @@ -0,0 +1,71 @@ +%% Set initial conditions +clear all; +load('fltTest.mat'); +startDelayTime = 100; % number of seconds to delay filter start (used to simulate in-flight restart) +dt = 1/50; +startTime = 0.001*(IMU(1,2)); +stopTime = 0.001*(IMU(length(IMU),2)); +indexLimit = length(IMU); +magIndexlimit = length(MAG); +statesLog = zeros(11,indexLimit); +eulLog = zeros(4,indexLimit); +velInnovLog = zeros(4,indexLimit); +angErrLog = velInnovLog; +decInnovLog = zeros(2,magIndexlimit); +velInnovVarLog = velInnovLog; +decInnovVarLog = decInnovLog; +% initialise the filter to level +quat = [1;0;0;0]; +states = zeros(10,1); +Tbn = Quat2Tbn(quat); +% Set the expected declination +measDec = 0.18; +% define the state covariances with the exception of the quaternion covariances +Sigma_velNED = 0.5; % 1 sigma uncertainty in horizontal velocity components +Sigma_dAngBias = 5*pi/180*dt; % 1 Sigma uncertainty in delta angle bias +Sigma_quatErr = 1; % 1 Sigma uncertainty in angular misalignment (rad) +covariance = single(diag([Sigma_quatErr*[1;1;1;1];Sigma_velNED*[1;1;1];Sigma_dAngBias*[1;1;1]].^2)); +%% Main Loop +magIndex = 1; +time = 0; +tiltError = 0; +headingAligned = 0; +angErrVec = [0;0;0]; +startIndex = max(11,ceil(startDelayTime/dt)); +for index = startIndex:indexLimit + time=time+dt + startIndex*dt; + % read IMU measurements and correct rates using estimated bias + angRate = IMU(index,3:5)' - states(7:9)./dt; + accel = IMU(index,6:8)'; + % predict states + [quat, states, Tbn, delAng, delVel] = PredictStates(quat,states,angRate,accel,dt); + statesLog(1,index) = time; + statesLog(2:11,index) = states; + eulLog(1,index) = time; + eulLog(2:4,index) = QuatToEul(quat); + % predict covariance matrix + covariance = PredictCovariance(delAng,delVel,quat,states,covariance,dt); + % read magnetometer measurements + while ((MAG(magIndex,1) < IMU(index,1)) && (magIndex < magIndexlimit)) + magIndex = magIndex + 1; + % fuse magnetometer measurements if new data available and when tilt has settled + if ((MAG(magIndex,1) >= IMU(index,1)) && ((angErrVec(1)^2 + angErrVec(2)^2) < 0.05^2) && (index > 50)) + magBody = 0.001*MAG(magIndex,3:5)'; + [states,covariance,decInnov,decInnovVar] = FuseMagnetometer(states,covariance,magBody,measDec,Tbn); + decInnovLog(1,magIndex) = time; + decInnovLog(2,magIndex) = decInnov; + decInnovVarLog(1,magIndex) = time; + decInnovVarLog(2,magIndex) = decInnovVar; + end + end + % fuse velocity measurements - use synthetic measurements + measVel = [0;0;0]; + [states,covariance,velInnov,velInnovVar] = FuseVelocity(states,covariance,measVel); + velInnovLog(1,index) = time; + velInnovLog(2:4,index) = velInnov; + velInnovVarLog(1,index) = time; + velInnovVarLog(2:4,index) = velInnovVar; +end + +%% Generate Plots +PlotData; \ No newline at end of file diff --git a/libraries/AP_NavEKF/Models/QuaternionMathExample/calcF.m b/libraries/AP_NavEKF/Models/QuaternionMathExample/calcF.m new file mode 100644 index 0000000000..c1b67e8b1b --- /dev/null +++ b/libraries/AP_NavEKF/Models/QuaternionMathExample/calcF.m @@ -0,0 +1,36 @@ +function F = calcF(dax,dax_b,day,day_b,daz,daz_b,dvx,dvy,dvz,q0,q1,q2,q3) +%CALCF +% F = CALCF(DAX,DAX_B,DAY,DAY_B,DAZ,DAZ_B,DVX,DVY,DVZ,Q0,Q1,Q2,Q3) + +% This function was generated by the Symbolic Math Toolbox version 5.8. +% 14-Jan-2015 11:09:08 + +t2 = dax_b.*(1.0./2.0); +t3 = daz_b.*(1.0./2.0); +t4 = day_b.*(1.0./2.0); +t8 = day.*(1.0./2.0); +t5 = t4-t8; +t6 = q3.*(1.0./2.0); +t7 = q2.*(1.0./2.0); +t9 = daz.*(1.0./2.0); +t10 = dax.*(1.0./2.0); +t11 = -t2+t10; +t12 = q1.*(1.0./2.0); +t13 = -t3+t9; +t14 = -t4+t8; +t15 = dvz.*q1.*2.0; +t16 = dvy.*q1.*2.0; +t17 = dvz.*q0.*2.0; +t18 = dvx.*q1.*2.0; +t19 = dvy.*q2.*2.0; +t20 = dvz.*q3.*2.0; +t21 = t18+t19+t20; +t22 = dvx.*q0.*2.0; +t23 = dvz.*q2.*2.0; +t29 = dvy.*q3.*2.0; +t24 = t22+t23-t29; +t25 = dvx.*q2.*2.0; +t26 = dvx.*q3.*2.0; +t27 = dvy.*q0.*2.0; +t28 = -t15+t26+t27; +F = reshape([1.0,t11,t14,t13,t24,t28,t16+t17-t25,0.0,0.0,0.0,dax.*(-1.0./2.0)+t2,1.0,t3-t9,t14,t21,-t16-t17+t25,t28,0.0,0.0,0.0,t5,t13,1.0,t2-t10,t16+t17-dvx.*q2.*2.0,t21,-t22-t23+t29,0.0,0.0,0.0,daz.*(-1.0./2.0)+t3,t5,t11,1.0,t15-dvx.*q3.*2.0-dvy.*q0.*2.0,t24,t21,0.0,0.0,0.0,0.0,0.0,0.0,0.0,1.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,1.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,1.0,0.0,0.0,0.0,t12,q0.*(-1.0./2.0),-t6,t7,0.0,0.0,0.0,1.0,0.0,0.0,t7,t6,q0.*(-1.0./2.0),-t12,0.0,0.0,0.0,0.0,1.0,0.0,t6,-t7,t12,q0.*(-1.0./2.0),0.0,0.0,0.0,0.0,0.0,1.0],[10, 10]); diff --git a/libraries/AP_NavEKF/Models/QuaternionMathExample/calcG.m b/libraries/AP_NavEKF/Models/QuaternionMathExample/calcG.m new file mode 100644 index 0000000000..0cce31bc9c --- /dev/null +++ b/libraries/AP_NavEKF/Models/QuaternionMathExample/calcG.m @@ -0,0 +1,18 @@ +function G = calcG(q0,q1,q2,q3) +%CALCG +% G = CALCG(Q0,Q1,Q2,Q3) + +% This function was generated by the Symbolic Math Toolbox version 5.8. +% 14-Jan-2015 11:09:06 + +t2 = q0.*(1.0./2.0); +t3 = q2.*(1.0./2.0); +t4 = q1.*q2.*2.0; +t5 = q0.^2; +t6 = q1.^2; +t7 = q2.^2; +t8 = q3.^2; +t9 = q0.*q2.*2.0; +t10 = q1.*q3.*2.0; +t11 = q2.*q3.*2.0; +G = reshape([q1.*(-1.0./2.0),t2,q3.*(1.0./2.0),-t3,0.0,0.0,0.0,0.0,0.0,0.0,q2.*(-1.0./2.0),q3.*(-1.0./2.0),t2,q1.*(1.0./2.0),0.0,0.0,0.0,0.0,0.0,0.0,q3.*(-1.0./2.0),t3,q1.*(-1.0./2.0),t2,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,t5+t6-t7-t8,t4+q0.*q3.*2.0,-t9+t10,0.0,0.0,0.0,0.0,0.0,0.0,0.0,t4-q0.*q3.*2.0,t5-t6+t7-t8,t11+q0.*q1.*2.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,t9+t10,t11-q0.*q1.*2.0,t5-t6-t7+t8,0.0,0.0,0.0],[10, 6]); diff --git a/libraries/AP_NavEKF/Models/QuaternionMathExample/calcH_MAG.m b/libraries/AP_NavEKF/Models/QuaternionMathExample/calcH_MAG.m new file mode 100644 index 0000000000..367f8657cc --- /dev/null +++ b/libraries/AP_NavEKF/Models/QuaternionMathExample/calcH_MAG.m @@ -0,0 +1,52 @@ +function H_MAG = calcH_MAG(magX,magY,magZ,q0,q1,q2,q3) +%CALCH_MAG +% H_MAG = CALCH_MAG(MAGX,MAGY,MAGZ,Q0,Q1,Q2,Q3) + +% This function was generated by the Symbolic Math Toolbox version 5.8. +% 14-Jan-2015 11:09:09 + +t2 = q0.^2; +t3 = q1.^2; +t4 = q2.^2; +t5 = q3.^2; +t6 = q0.*q3.*2.0; +t8 = t2+t3-t4-t5; +t9 = magX.*t8; +t10 = q1.*q2.*2.0; +t11 = q0.*q2.*2.0; +t12 = q1.*q3.*2.0; +t13 = t11+t12; +t14 = magZ.*t13; +t17 = t2-t3+t4-t5; +t18 = magY.*t17; +t19 = t6+t10; +t20 = magX.*t19; +t21 = q0.*q1.*2.0; +t22 = q2.*q3.*2.0; +t23 = t21-t22; +t24 = magZ.*t23; +t25 = t18+t20-t24; +t7 = tan(t25./(t9+t14-magY.*(t6-q1.*q2.*2.0))); +t15 = t6-t10; +t26 = magY.*t15; +t16 = t9+t14-t26; +t27 = 1.0./t16; +t30 = t25.*t27; +t28 = tan(t30); +t29 = 1.0./t16.^2; +t31 = t28.^2; +t32 = t31+1.0; +t33 = magX.*q1.*2.0; +t34 = magY.*q2.*2.0; +t35 = magZ.*q3.*2.0; +t36 = t33+t34+t35; +t37 = magY.*q1.*2.0; +t38 = magZ.*q0.*2.0; +t39 = t37+t38-magX.*q2.*2.0; +t40 = magX.*q0.*2.0; +t41 = magZ.*q2.*2.0; +t42 = t40+t41-magY.*q3.*2.0; +t43 = magY.*q0.*2.0; +t44 = magX.*q3.*2.0; +t45 = t43+t44-magZ.*q1.*2.0; +H_MAG = [(t7.^2+1.0).*(t27.*t45-t25.*t29.*t42),-t32.*(t27.*t39+t25.*t29.*t36),t32.*(t27.*t36-t25.*t29.*t39),t32.*(t27.*t42+t25.*t29.*t45),0.0,0.0,0.0,0.0,0.0,0.0]; diff --git a/libraries/AP_NavEKF/Models/QuaternionMathExample/calcQ.m b/libraries/AP_NavEKF/Models/QuaternionMathExample/calcQ.m new file mode 100644 index 0000000000..a3c34c95ae --- /dev/null +++ b/libraries/AP_NavEKF/Models/QuaternionMathExample/calcQ.m @@ -0,0 +1,45 @@ +function Q = calcQ(daxNoise,dayNoise,dazNoise,dvxNoise,dvyNoise,dvzNoise,q0,q1,q2,q3) +%CALCQ +% Q = CALCQ(DAXNOISE,DAYNOISE,DAZNOISE,DVXNOISE,DVYNOISE,DVZNOISE,Q0,Q1,Q2,Q3) + +% This function was generated by the Symbolic Math Toolbox version 5.8. +% 14-Jan-2015 11:09:07 + +t2 = dayNoise.*q2.*q3.*(1.0./4.0); +t3 = t2-daxNoise.*q0.*q1.*(1.0./4.0)-dazNoise.*q2.*q3.*(1.0./4.0); +t4 = q3.^2; +t5 = q2.^2; +t6 = dazNoise.*q1.*q3.*(1.0./4.0); +t7 = t6-daxNoise.*q1.*q3.*(1.0./4.0)-dayNoise.*q0.*q2.*(1.0./4.0); +t8 = daxNoise.*q0.*q3.*(1.0./4.0); +t9 = t8-dayNoise.*q0.*q3.*(1.0./4.0)-dazNoise.*q1.*q2.*(1.0./4.0); +t10 = q0.^2; +t11 = q1.^2; +t12 = daxNoise.*q1.*q2.*(1.0./4.0); +t13 = t12-dayNoise.*q1.*q2.*(1.0./4.0)-dazNoise.*q0.*q3.*(1.0./4.0); +t14 = dazNoise.*q0.*q2.*(1.0./4.0); +t15 = t14-daxNoise.*q0.*q2.*(1.0./4.0)-dayNoise.*q1.*q3.*(1.0./4.0); +t16 = dayNoise.*q0.*q1.*(1.0./4.0); +t17 = t16-daxNoise.*q2.*q3.*(1.0./4.0)-dazNoise.*q0.*q1.*(1.0./4.0); +t21 = q0.*q3.*2.0; +t22 = q1.*q2.*2.0; +t18 = t21-t22; +t23 = q0.*q2.*2.0; +t24 = q1.*q3.*2.0; +t19 = t23+t24; +t20 = t4+t5-t10-t11; +t25 = q0.*q1.*2.0; +t26 = t21+t22; +t32 = t4-t5-t10+t11; +t27 = dvyNoise.*t18.*t32; +t28 = q2.*q3.*2.0; +t29 = t25-t28; +t30 = t4-t5-t10+t11; +t31 = t25+t28; +t33 = t4-t5+t10-t11; +t34 = t23-t24; +t35 = dvxNoise.*t34.*(t4+t5-t10-t11); +t36 = dvzNoise.*t19.*t33; +t37 = t35+t36-dvyNoise.*t18.*t31; +t38 = -dvxNoise.*t26.*t34-dvyNoise.*t31.*t32-dvzNoise.*t29.*t33; +Q = reshape([daxNoise.*t11.*(1.0./4.0)+dayNoise.*t5.*(1.0./4.0)+dazNoise.*t4.*(1.0./4.0),t3,t7,t13,0.0,0.0,0.0,0.0,0.0,0.0,t3,daxNoise.*t10.*(1.0./4.0)+dayNoise.*t4.*(1.0./4.0)+dazNoise.*t5.*(1.0./4.0),t9,t15,0.0,0.0,0.0,0.0,0.0,0.0,t7,t9,daxNoise.*t4.*(1.0./4.0)+dayNoise.*t10.*(1.0./4.0)+dazNoise.*t11.*(1.0./4.0),t17,0.0,0.0,0.0,0.0,0.0,0.0,t13,t15,t17,daxNoise.*t5.*(1.0./4.0)+dayNoise.*t11.*(1.0./4.0)+dazNoise.*t10.*(1.0./4.0),0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,dvxNoise.*t20.^2+dvyNoise.*t18.^2+dvzNoise.*t19.^2,t27-dvxNoise.*t20.*t26-dvzNoise.*t19.*t29,t37,0.0,0.0,0.0,0.0,0.0,0.0,0.0,t27-dvzNoise.*t19.*(t25-q2.*q3.*2.0)-dvxNoise.*t20.*t26,dvxNoise.*t26.^2+dvyNoise.*t30.^2+dvzNoise.*t29.^2,t38,0.0,0.0,0.0,0.0,0.0,0.0,0.0,t37,t38,dvxNoise.*t34.^2+dvyNoise.*t31.^2+dvzNoise.*t33.^2,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0],[10, 10]); diff --git a/libraries/AP_NavEKF/Models/ReadMe.txt b/libraries/AP_NavEKF/Models/ReadMe.txt new file mode 100644 index 0000000000..a39ab05268 --- /dev/null +++ b/libraries/AP_NavEKF/Models/ReadMe.txt @@ -0,0 +1,7 @@ +Matlab derivations and simulations relating to development of the small EKF containing the following material: + +testData: bench and flight test data used by the various estimator test harnesses +QuaternionMathExample: Small EKF using the same quaternion attitude representation as the main EKF and with a in-flight alignment test using real data. The inability to perform and in-flight alignment demonstrated by this example shows why we have change to a different attitude representation for the samll EKF. +AttErrVecExample: Small EKF using a new error vector representation for the vehicle attitude and subjected to in-flight alignment tests using both simulated and real data. The robust alignment achieved shows why this new math has been selected for use in the small EKF. +GimbalEstimatorExample: A simulation of 3 axis stabilised gimbal estimator showing application of the small EKF combined with a high rate predictor running on the gimbal that is corrected using the EKF attitude estimates. +Common: Common Matlab functions \ No newline at end of file diff --git a/libraries/AP_NavEKF/Models/testData/fltTest.mat b/libraries/AP_NavEKF/Models/testData/fltTest.mat new file mode 100644 index 0000000000000000000000000000000000000000..aa93fbbbeff034e4eca1090daa01111ccad4db29 GIT binary patch literal 1359364 zcma%hc~nzZ^ln>Q(V|dm6)0e8ooYc4LYM+XYn3WfEe;@)7)XjBhyfx)60HL&F;r0@ zfe;k|kqCq^2ZDkmA{h`QBur7GKp=w%B#;<*2m9VzzqQ^!kEIK4_C0rhXYcRZ`cDf87Q>dH&?d@&|6`%%6X~?8q;))xR!p3*Du7XZ{XC%gMV%S$2?X^lbgA z6$abCbrv^xUwrxHFVbyL`#yVGhG8SQv5funJHzs?XP`ynXw+%m_Kh#Xk2t08{&epC ztG6eXzg0x^6MvmFIb;p_E@bCVGt9ek^u-rXdF#%7#5qp?W%$_H54lOspRio@GGW&) 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