ardupilot/libraries/AP_NavEKF/Models/GimbalEstimatorExample/FuseVelocity.m

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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