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Diffstat (limited to 'src/modules/attitude_estimator_ekf/AttitudeEKF.m')
| -rw-r--r-- | src/modules/attitude_estimator_ekf/AttitudeEKF.m | 298 |
1 files changed, 298 insertions, 0 deletions
diff --git a/src/modules/attitude_estimator_ekf/AttitudeEKF.m b/src/modules/attitude_estimator_ekf/AttitudeEKF.m new file mode 100644 index 000000000..fea1a773e --- /dev/null +++ b/src/modules/attitude_estimator_ekf/AttitudeEKF.m @@ -0,0 +1,298 @@ +function [xa_apo,Pa_apo,Rot_matrix,eulerAngles,debugOutput]... + = AttitudeEKF(approx_prediction,use_inertia_matrix,zFlag,dt,z,q_rotSpeed,q_rotAcc,q_acc,q_mag,r_gyro,r_accel,r_mag,J) + + +%LQG Postion Estimator and Controller +% Observer: +% x[n|n] = x[n|n-1] + M(y[n] - Cx[n|n-1] - Du[n]) +% x[n+1|n] = Ax[n|n] + Bu[n] +% +% $Author: Tobias Naegeli $ $Date: 2014 $ $Revision: 3 $ +% +% +% Arguments: +% approx_prediction: if 1 then the exponential map is approximated with a +% first order taylor approximation. has at the moment not a big influence +% (just 1st or 2nd order approximation) we should change it to rodriquez +% approximation. +% use_inertia_matrix: set to true if you have the inertia matrix J for your +% quadrotor +% xa_apo_k: old state vectotr +% zFlag: if sensor measurement is available [gyro, acc, mag] +% dt: dt in s +% z: measurements [gyro, acc, mag] +% q_rotSpeed: process noise gyro +% q_rotAcc: process noise gyro acceleration +% q_acc: process noise acceleration +% q_mag: process noise magnetometer +% r_gyro: measurement noise gyro +% r_accel: measurement noise accel +% r_mag: measurement noise mag +% J: moment of inertia matrix + + +% Output: +% xa_apo: updated state vectotr +% Pa_apo: updated state covariance matrix +% Rot_matrix: rotation matrix +% eulerAngles: euler angles +% debugOutput: not used + + +%% model specific parameters + + + +% compute once the inverse of the Inertia +persistent Ji; +if isempty(Ji) + Ji=single(inv(J)); +end + +%% init +persistent x_apo +if(isempty(x_apo)) + gyro_init=single([0;0;0]); + gyro_acc_init=single([0;0;0]); + acc_init=single([0;0;-9.81]); + mag_init=single([1;0;0]); + x_apo=single([gyro_init;gyro_acc_init;acc_init;mag_init]); + +end + +persistent P_apo +if(isempty(P_apo)) + % P_apo = single(eye(NSTATES) * 1000); + P_apo = single(200*ones(12)); +end + +debugOutput = single(zeros(4,1)); + +%% copy the states +wx= x_apo(1); % x body angular rate +wy= x_apo(2); % y body angular rate +wz= x_apo(3); % z body angular rate + +wax= x_apo(4); % x body angular acceleration +way= x_apo(5); % y body angular acceleration +waz= x_apo(6); % z body angular acceleration + +zex= x_apo(7); % x component gravity vector +zey= x_apo(8); % y component gravity vector +zez= x_apo(9); % z component gravity vector + +mux= x_apo(10); % x component magnetic field vector +muy= x_apo(11); % y component magnetic field vector +muz= x_apo(12); % z component magnetic field vector + + + + +%% prediction section +% compute the apriori state estimate from the previous aposteriori estimate +%body angular accelerations +if (use_inertia_matrix==1) + wak =[wax;way;waz]+Ji*(-cross([wax;way;waz],J*[wax;way;waz]))*dt; +else + wak =[wax;way;waz]; +end + +%body angular rates +wk =[wx; wy; wz] + dt*wak; + +%derivative of the prediction rotation matrix +O=[0,-wz,wy;wz,0,-wx;-wy,wx,0]'; + +%prediction of the earth z vector +if (approx_prediction==1) + %e^(Odt)=I+dt*O+dt^2/2!O^2 + % so we do a first order approximation of the exponential map + zek =(O*dt+single(eye(3)))*[zex;zey;zez]; + +else + zek =(single(eye(3))+O*dt+dt^2/2*O^2)*[zex;zey;zez]; + %zek =expm2(O*dt)*[zex;zey;zez]; not working because use double + %precision +end + + + +%prediction of the magnetic vector +if (approx_prediction==1) + %e^(Odt)=I+dt*O+dt^2/2!O^2 + % so we do a first order approximation of the exponential map + muk =(O*dt+single(eye(3)))*[mux;muy;muz]; +else + muk =(single(eye(3))+O*dt+dt^2/2*O^2)*[mux;muy;muz]; + %muk =expm2(O*dt)*[mux;muy;muz]; not working because use double + %precision +end + +x_apr=[wk;wak;zek;muk]; + +% compute the apriori error covariance estimate from the previous +%aposteriori estimate + +EZ=[0,zez,-zey; + -zez,0,zex; + zey,-zex,0]'; +MA=[0,muz,-muy; + -muz,0,mux; + muy,-mux,0]'; + +E=single(eye(3)); +Z=single(zeros(3)); + +A_lin=[ Z, E, Z, Z + Z, Z, Z, Z + EZ, Z, O, Z + MA, Z, Z, O]; + +A_lin=eye(12)+A_lin*dt; + +%process covariance matrix + +persistent Q +if (isempty(Q)) + Q=diag([ q_rotSpeed,q_rotSpeed,q_rotSpeed,... + q_rotAcc,q_rotAcc,q_rotAcc,... + q_acc,q_acc,q_acc,... + q_mag,q_mag,q_mag]); +end + +P_apr=A_lin*P_apo*A_lin'+Q; + + +%% update +if zFlag(1)==1&&zFlag(2)==1&&zFlag(3)==1 + +% R=[r_gyro,0,0,0,0,0,0,0,0; +% 0,r_gyro,0,0,0,0,0,0,0; +% 0,0,r_gyro,0,0,0,0,0,0; +% 0,0,0,r_accel,0,0,0,0,0; +% 0,0,0,0,r_accel,0,0,0,0; +% 0,0,0,0,0,r_accel,0,0,0; +% 0,0,0,0,0,0,r_mag,0,0; +% 0,0,0,0,0,0,0,r_mag,0; +% 0,0,0,0,0,0,0,0,r_mag]; + R_v=[r_gyro,r_gyro,r_gyro,r_accel,r_accel,r_accel,r_mag,r_mag,r_mag]; + %observation matrix + %[zw;ze;zmk]; + H_k=[ E, Z, Z, Z; + Z, Z, E, Z; + Z, Z, Z, E]; + + y_k=z(1:9)-H_k*x_apr; + + + %S_k=H_k*P_apr*H_k'+R; + S_k=H_k*P_apr*H_k'; + S_k(1:9+1:end) = S_k(1:9+1:end) + R_v; + K_k=(P_apr*H_k'/(S_k)); + + + x_apo=x_apr+K_k*y_k; + P_apo=(eye(12)-K_k*H_k)*P_apr; +else + if zFlag(1)==1&&zFlag(2)==0&&zFlag(3)==0 + + R=[r_gyro,0,0; + 0,r_gyro,0; + 0,0,r_gyro]; + R_v=[r_gyro,r_gyro,r_gyro]; + %observation matrix + + H_k=[ E, Z, Z, Z]; + + y_k=z(1:3)-H_k(1:3,1:12)*x_apr; + + % S_k=H_k(1:3,1:12)*P_apr*H_k(1:3,1:12)'+R(1:3,1:3); + S_k=H_k(1:3,1:12)*P_apr*H_k(1:3,1:12)'; + S_k(1:3+1:end) = S_k(1:3+1:end) + R_v; + K_k=(P_apr*H_k(1:3,1:12)'/(S_k)); + + + x_apo=x_apr+K_k*y_k; + P_apo=(eye(12)-K_k*H_k(1:3,1:12))*P_apr; + else + if zFlag(1)==1&&zFlag(2)==1&&zFlag(3)==0 + +% R=[r_gyro,0,0,0,0,0; +% 0,r_gyro,0,0,0,0; +% 0,0,r_gyro,0,0,0; +% 0,0,0,r_accel,0,0; +% 0,0,0,0,r_accel,0; +% 0,0,0,0,0,r_accel]; + + R_v=[r_gyro,r_gyro,r_gyro,r_accel,r_accel,r_accel]; + %observation matrix + + H_k=[ E, Z, Z, Z; + Z, Z, E, Z]; + + y_k=z(1:6)-H_k(1:6,1:12)*x_apr; + + % S_k=H_k(1:6,1:12)*P_apr*H_k(1:6,1:12)'+R(1:6,1:6); + S_k=H_k(1:6,1:12)*P_apr*H_k(1:6,1:12)'; + S_k(1:6+1:end) = S_k(1:6+1:end) + R_v; + K_k=(P_apr*H_k(1:6,1:12)'/(S_k)); + + + x_apo=x_apr+K_k*y_k; + P_apo=(eye(12)-K_k*H_k(1:6,1:12))*P_apr; + else + if zFlag(1)==1&&zFlag(2)==0&&zFlag(3)==1 +% R=[r_gyro,0,0,0,0,0; +% 0,r_gyro,0,0,0,0; +% 0,0,r_gyro,0,0,0; +% 0,0,0,r_mag,0,0; +% 0,0,0,0,r_mag,0; +% 0,0,0,0,0,r_mag]; + R_v=[r_gyro,r_gyro,r_gyro,r_mag,r_mag,r_mag]; + %observation matrix + + H_k=[ E, Z, Z, Z; + Z, Z, Z, E]; + + y_k=[z(1:3);z(7:9)]-H_k(1:6,1:12)*x_apr; + + %S_k=H_k(1:6,1:12)*P_apr*H_k(1:6,1:12)'+R(1:6,1:6); + S_k=H_k(1:6,1:12)*P_apr*H_k(1:6,1:12)'; + S_k(1:6+1:end) = S_k(1:6+1:end) + R_v; + K_k=(P_apr*H_k(1:6,1:12)'/(S_k)); + + + x_apo=x_apr+K_k*y_k; + P_apo=(eye(12)-K_k*H_k(1:6,1:12))*P_apr; + else + x_apo=x_apr; + P_apo=P_apr; + end + end + end +end + + + +%% euler anglels extraction +z_n_b = -x_apo(7:9)./norm(x_apo(7:9)); +m_n_b = x_apo(10:12)./norm(x_apo(10:12)); + +y_n_b=cross(z_n_b,m_n_b); +y_n_b=y_n_b./norm(y_n_b); + +x_n_b=(cross(y_n_b,z_n_b)); +x_n_b=x_n_b./norm(x_n_b); + + +xa_apo=x_apo; +Pa_apo=P_apo; +% rotation matrix from earth to body system +Rot_matrix=[x_n_b,y_n_b,z_n_b]; + + +phi=atan2(Rot_matrix(2,3),Rot_matrix(3,3)); +theta=-asin(Rot_matrix(1,3)); +psi=atan2(Rot_matrix(1,2),Rot_matrix(1,1)); +eulerAngles=[phi;theta;psi]; + |