px4-firmware/EKF/matlab/scripts/Inertial Nav EKF/derive_air_data_errors.m

98 lines
2.7 KiB
Matlab

% This script generates c code required to calculate the variance of the
% TAS, AoA and AoS estimates calculated from the vehicle quaternions, NED
% velocity and NED wind velocity. Uncertainty in the quaternions is
% ignored. Variance in vehicle velocity and wind velocity is accounted for.
%% calculate TAS error terms
clear all;
reset(symengine);
syms vn ve vd 'real' % navigation frame NED velocity (m/s)
syms vwn vwe vwd 'real' % navigation frame NED wind velocity (m/s)
syms vn_var ve_var vd_var 'real' % navigation frame NED velocity variances (m/s)^2
syms vwn_var vwe_var vwd_var 'real' % navigation frame NED wind velocity variances (m/s)^2
syms q0 q1 q2 q3 'real' % quaternions defining rotation from navigation NED frame to body XYZ frame
quat = [q0;q1;q2;q3];
% rotation matrix from navigation to body frame
Tnb = transpose(Quat2Tbn(quat));
% crete velocity vectors
ground_velocity_truth = [vn;ve;vd];
wind_velocity_truth = [vwn;vwe;vwd];
% calcuate wind relative velocity
rel_vel_ef = ground_velocity_truth - wind_velocity_truth;
% rotate into body frame
rel_vel_bf = Tnb * rel_vel_ef;
% calculate the true airspeed
TAS = sqrt(rel_vel_bf(1)^2 + rel_vel_bf(2)^2 + rel_vel_bf(3)^2);
% derive the control(disturbance) influence matrix from velocity error to
% TAS error
G_TAS = jacobian(TAS, [ground_velocity_truth;wind_velocity_truth]);
% derive the error matrix
TAS_dist_matrix = diag([vn_var ve_var vd_var vwn_var vwe_var vwd_var]);
Q_TAS = G_TAS*TAS_dist_matrix*transpose(G_TAS);
% save as C code
ccode(Q_TAS,'file','Q_TAS.c');
save temp.mat;
%% calculate AoA error equations
clear all;
reset(symengine);
load temp.mat;
AoA = atan(rel_vel_bf(3) / rel_vel_bf(1));
% derive the control(disturbance) influence matrix from velocity error to
% AoA error
G_AoA = jacobian(AoA, [ground_velocity_truth;wind_velocity_truth]);
% derive the error matrix
AoA_dist_matrix = diag([vn_var ve_var vd_var vwn_var vwe_var vwd_var]);
Q_AoA = G_AoA*AoA_dist_matrix*transpose(G_AoA);
% save as C code
ccode(Q_AoA,'file','Q_AoA.c');
save temp.mat;
%% Calculate AoS error equations
clear all;
reset(symengine);
load temp.mat;
AoS = atan(rel_vel_bf(2) / rel_vel_bf(1));
% derive the control(disturbance) influence matrix from velocity error to
% AoS error
G_AoS = jacobian(AoS, [ground_velocity_truth;wind_velocity_truth]);
% derive the error matrix
AoS_dist_matrix = diag([vn_var ve_var vd_var vwn_var vwe_var vwd_var]);
Q_AoS = G_AoS*AoS_dist_matrix*transpose(G_AoS);
% save as C code
ccode(Q_AoS,'file','Q_AoS.c');
save temp.mat;
%% convert them combined to take advantage of shared terms in the optimiser
clear all;
reset(symengine);
load temp.mat;
% save as C code
ccode([Q_TAS;Q_AoA;Q_AoS],'file','Q_airdata.c');