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almostCompleteUKF_simpleData.m
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% Position, orientation, velocity, I-C translation, I-C rotation, gravity
% and biases UKF
%clc
close all
writeFiles = 0;
%% UKF parameters
ukf_alpha = .01;
ukf_beta = 2;
%% x: state vector
% Composed by IMU position, rotation quaternion ([w x y z]') and velocity
% in the world frame
% [p_w_i; q_w_i; v_w_i; q_i_c; q_i_c; gravity; bias_accel; bias_gyro] = x(1:26);
%% P: state covariance matrix 24-by-26
% NOTE: P is not 26-by-26 because we consider 3 deg of freedom for the
% rotations
%% u: process inputs
% Composed by measured IMU acceleration and rotational velocity
% u = [accel_i_measured(1:3, i); gyro_i_measured(1:3, i)]
%% n: process noise
%% Q: 12x12 process noise covariance matrix
Qgw = eye(3) * 0.0196^2; % noise gyro bias (more or less as in the data sheet)
Qaw = eye(3) * 0.0001^2; % noise accel bias (more or less as synthesized)
Qacc = eye(3) * 0.1^2;
Qrot = eye(3) * 0.001 * 300 * pi/180; % rad/s
Q = blkdiag(Qacc, Qrot, Qaw, Qgw);
%% z: measurements
% See section 4.3 Measurement Model on page 11
% z is a 2n-by-1 column vector of observed pixel coordinates in the
% form [x1 y1 ... xn yn]' where n is the number of 3D feature points
%% R: measurement noise covariance matrix
% The associated block-daigonal covariance matrix of z
% R = diag(R1 ... Rn) = 0.1^2 * eye(length(z));
%% Starting index
%i = lengthLowPass+1;
%j = lengthLowPass+1;
%nowTime = imuData(i-1,3);
i = 2;
j = 2;
nowTime = imuData(i-1,3);
%% Initial estimate
clear x;
mrpStd = @(deg) tan(deg*pi/720); % mrp error = tan((deg*pi)/(4*180))
iniPos = p_w(:,i) + rand(3,1).*(0.08^2); % initial position in world frame
iniV = v_w(:,i-1) + rand(3,1).*(0.3^2); % initial velocity in world frame
iniQMRPerror = rand(3,1).*(mrpStd(8)^2); % 8 deg of error for initial orientation
norm_mrp_error = sqrt(sum(iniQMRPerror.^2, 1));
dq0 = (1 - norm_mrp_error) ./ (1 + norm_mrp_error);
iniQerror = [ dq0; bsxfun(@times,(1+dq0),iniQMRPerror)];
iniQ = quaternionproduct(iniQerror,q_w_i(:,i)); % initial orientation in world frame
iniQ = iniQ ./ norm(iniQ);
iniP_i_c = p_i_c+.1*randn(3,1);
iniQicMRPerror = rand(3,1).*(mrpStd(5)^2); % 5 deg of error for initial imu-cam orientation
norm_mrp_error = sqrt(sum(iniQicMRPerror.^2, 1));
dq0 = (1 - norm_mrp_error) ./ (1 + norm_mrp_error);
iniQicerror = [ dq0; bsxfun(@times,(1+dq0),iniQicMRPerror)];
iniQ_i_c = quaternionproduct(iniQicerror,q_i_c); % initial orientation in world frame
iniQ_i_c = iniQ_i_c ./ norm(iniQ_i_c);
iniG=-gravity+.1*randn(3,1);
iniBa = bias_accel(:,i) + + 0.1*rand(3,1);
iniBg = bias_gyro(:,i) + + 0.1*rand(3,1);
x = [iniPos; iniQ; iniV; iniP_i_c; iniQ_i_c; iniG; iniBa; iniBg];
Ppos = eye(3).*(.1^2);
Pori = eye(3).*(mrpStd(10)^2);
Pvel = eye(3).*(.5^2);
Ppic=eye(3).*1e-4;
Pqic=eye(3).*(mrpStd(7)^2);
Pgra = diag([1.7 1.7 0.15].^2); % just very small, though ideally it would be zero
Pba = eye(3)*0.001^2;
Pbg = eye(3)*0.02^2;
P=blkdiag(Ppos,Pori,Pvel,Ppic,Pqic,Pgra,Pba,Pbg);
%% Initialize storage matrices and figure
numCamMeasurements = size(observed_pts_c, 2);
numImuMeasurements = length(imuData);
numPoses = numImuMeasurements + numCamMeasurements;
accumPoses = zeros(3,numPoses);
accumQuat = NaN * ones(4,numPoses);
distanceError = zeros(1, numPoses);
orientationError = zeros(1, numPoses);
velocityError = zeros(1, numPoses);
picError=zeros(1,numPoses);
qicError=zeros(1,numPoses);
gravityError = zeros(1, numPoses);
biasAccelError = zeros(1,numPoses);
biasGyroError = zeros(1,numPoses);
process_params = cell(3,1);
obs_params = cell(5,1);
accum_pwc = zeros(3,numPoses);
accum_pwi = zeros(3,numPoses);
accum_pwi_estim = zeros(3,numPoses);
accum_qwc = zeros(4,numPoses);
accum_qwi = zeros(4,numPoses);
accum_qwi_estim = zeros(4,numPoses);
accum_pic_estim = zeros(3,numPoses);
accum_qic_estim = zeros(4,numPoses);
accum_pwc_estim = zeros(3,numPoses);
accum_qwc_estim = zeros(4,numPoses);
h = figure('Name','Position, Orientation and Velocity Estimation', ...
'NumberTitle','off','Position',[10 10 1000 600]);
%% Begin Kalman filter
count = 1;
while (i <= numImuMeasurements && j <= numCamMeasurements )
% Read the timestamp for the next data input
imuTime = imuData(i,3);
camTime = camData(j,3);
% Get previous orientation belief
prev_q = x(4:7);
prev_qic_q=x(14:17);
if (imuTime < camTime)
%% Prediction step
pastTime = nowTime;
nowTime = imuTime;
dt = nowTime - pastTime;
u = [accel_i_measured(:,i); gyro_i_measured(:,i)];
process_params{1} = u;
process_params{2} = dt;
process_params{3} = prev_q;
process_handle = @processModelPQVTRGBB;
% State error vector with q and q_i_c as MRP
x_se = [x(1:3); 0; 0; 0; x(8:13); 0; 0; 0; x(18:26)];
[x_se, Ppred] = predictUKF(x_se, process_handle, process_params, ...
P, Q, ukf_alpha, ukf_beta);
% Convert MRP update vectors to quaternion update
mrp_error = x_se(4:6);
norm_mrp_error = sqrt(sum(mrp_error.^2, 1));
dq0 = (1 - norm_mrp_error) ./ (1 + norm_mrp_error);
q_error = [ dq0;
bsxfun(@times,(1+dq0),mrp_error)];
quat_new = quaternionproduct(q_error, prev_q);
quat_new = quat_new./norm(quat_new);
mrp_qic_error=x_se(13:15);
norm_mrp_qic_error=sqrt(sum(mrp_qic_error.^2,1));
dq_qic0=(1-norm_mrp_qic_error)./(1+norm_mrp_qic_error);
q_qic_error=[dq_qic0; bsxfun(@times,1+dq_qic0,mrp_qic_error)];
quat_qic_new=quaternionproduct(q_qic_error, prev_qic_q);
quat_qic_new=quat_qic_new/norm(quat_qic_new);
x = [x_se(1:3); quat_new; x_se(7:12); quat_qic_new; x_se(16:24)];
P=Ppred;
i = i + 1;
else
%% Correction Step
% Perform correction step
z = noisy_observed_pts_c(:,j);
R = 0.1^2 * eye(length(z));
% State error vector with q and q_i_c as MRP
x_se = [x(1:3); 0; 0; 0; x(8:13); 0; 0; 0; x(18:26)]; % State error vector with q in MRP
obs_params{1} = prev_q;
obs_params{2} = prev_qic_q;
obs_params{3} = pts_w(1:3, :); %landmarks in the world;
obs_params{4} = K;
obs_handle = @measurementModelPQVTRGBB;
[ x_se, P ] = correctUKF( x_se, P, R, z, obs_handle, obs_params, ukf_alpha, ukf_beta );
% Convert MRP update vectors to quaternion update
mrp_error = x_se(4:6);
norm_mrp_error = sqrt(sum(mrp_error.^2, 1));
dq0 = (1 - norm_mrp_error) ./ (1 + norm_mrp_error);
q_error = [ dq0;
bsxfun(@times,(1+dq0),mrp_error)];
quat_new = quaternionproduct(q_error, prev_q);
quat_new = quat_new./norm(quat_new);
mrp_qic_error=x_se(13:15);
norm_mrp_qic_error=sqrt(sum(mrp_qic_error.^2,1));
dq_qic0=(1-norm_mrp_qic_error)./(1+norm_mrp_qic_error);
q_qic_error=[dq_qic0; bsxfun(@times,1+dq_qic0,mrp_qic_error)];
quat_qic_new=quaternionproduct(q_qic_error, prev_qic_q);
quat_qic_new=quat_qic_new/norm(quat_qic_new);
x = [x_se(1:3); quat_new; x_se(7:12); quat_qic_new; x_se(16:24)];
j = j + 1;
end
if (i < numImuMeasurements)
%% Distance error
distanceError(1,count) = norm(x(1:3) - p_w(:,i));
velocityError(1,count) = norm(x(8:10) - v_w(:,i));
orientationError(1,count) = findQuaternionError(x(4:7), q_w_i(:,i));
picError(1,count)=norm(x(11:13)-p_i_c);
qicError(1,count)=findQuaternionError(x(14:17),q_i_c);
gravityError(1,count) = norm(x(18:20) - (-gravity));
biasAccelError(1,count) = norm(x(21:23) - bias_accel(:,i));
biasGyroError(1,count) = norm(x(24:26) - bias_gyro(:,i));
%% Plot
accumPoses(:,count) = x(1:3);
accum_pwi(:,count)=p_w(:,i-1);
accum_pwi_estim(:,count)=x(1:3);
accum_pwc(:,count)=p_w_c(:,i-1);
accum_qwi(:,count)=q_w_i(:,i-1);
accum_qwc(:,count)=q_w_c(:,i-1);
accum_qwi_estim(:,count)=x(4:7);
accum_pic_estim(:,count)=x(11:13);
accum_qic_estim(:,count)=x(14:17);
accum_qwc_estim(:,count)=rotation2quaternion(quaternion2rotation(accum_qwi_estim(:,count))*quaternion2rotation(accum_qic_estim(:,count)));
accum_pwc_estim(:,count)=accum_pwi_estim(:,count)+quaternion2rotation(accum_qwi_estim(:,count))*accum_pic_estim(:,count);
count = count + 1;
if mod(count, 100) == 1
figure(h);
clf
subplot(4,3,[1, 4, 7, 10]);
%plot3(accumPoses(1,1:count-1), accumPoses(2,1:count-1), accumPoses(3,1:count-1),'-');
%hold on;
%plot3(p_w(1,1:i), p_w(2,1:i), p_w(3,1:i), 'g');
% hold on;
% plot3(pts_w(1, :), pts_w(2, :), pts_w(3, :), 'r.');
%axis equal
%axis vis3d
%xlabel('x'); ylabel('y'); zlabel('z');
%grid on;
[accum_pwc_estim,accum_qwc_estim]=prettyPlotSingle(...
accum_pwc,accum_qwc,accum_pwi,...
accum_pwc_estim,accum_qwc_estim,accum_pwi_estim,...
pts_w,pts_center,count-1);
title(sprintf('Motion Estimation (Frame %d)', count));
subplot(4,3,2);
plot(1:count,distanceError(1:count));
maxErr = max(distanceError);
axis([0 numPoses 0 maxErr]);
% xlabel('Time');
%ylabel('Squared Error');
title('Distance Error');
subplot(4,3,3);
plot(1:count,velocityError(1:count));
maxErr = max(velocityError);
axis([0 numPoses 0 maxErr]);
% xlabel('Time');
%ylabel('Squared Error');
title('Velocity Error');
subplot(4,3,5);
plot(1:count,orientationError(1:count));
maxErr = max(orientationError);
axis([0 numPoses 0 maxErr]);
xlabel('Time');
% ylabel('Squared Error');
title('Orientation Error');
subplot(4,3,6);
plot(1:count,gravityError(1:count));
maxErr = max(gravityError);
axis([0 numPoses 0 maxErr]);
xlabel('Time');
%ylabel('Squared Error');
title('Gravity Error');
subplot(4,3,8);
plot(1:count,picError(1:count));
maxErr = max(picError)+.1;
axis([0 numPoses 0 maxErr]);
xlabel('Time');
%ylabel('Squared Error');
title('IMU-Camera Translation Error');
subplot(4,3,9);
plot(1:count,qicError(1:count));
maxErr = max(qicError)+.1;
axis([0 numPoses 0 maxErr]);
xlabel('Time');
% ylabel('Squared Error');
title('IMU-Camera Rotation Error');
subplot(4,3,11);
plot(1:count,biasAccelError(1:count));
maxErr = max(biasAccelError)+.1;
axis([0 numPoses 0 maxErr]);
xlabel('Time');
% ylabel('Squared Error');
title('Accel Bias Error');
subplot(4,3,12);
plot(1:count,biasGyroError(1:count));
maxErr = max(biasGyroError)+.1;
axis([0 numPoses 0 maxErr]);
xlabel('Time');
%ylabel('Squared Error');
title('Gyro Bias Error');
F=getframe(gcf);
if (writeFiles)
imwrite(F.cdata,sprintf('plot/%03d.png',i));
end
%subplot(4,3,[1, 4, 7, 10]);
%F=getframe(gca);
%imwrite(F.cdata,sprintf('motion/%03d.png',i));
%pause
%saveas(gcf,sprintf('plot/%03d.png',i));
subplot(4,3,[1, 4, 7, 10]);
if (writeFiles)
saveas(gca,sprintf('motion/%03d.png',i));
end
%print('-dpng','-r300','-opengl',sprintf('plot/%03d.png',i));
end
end
end