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showOrientationMergeFiltered2.m
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showOrientationMergeFiltered2.m
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clear all; home;
%% Load the data
%dataSetFolder = fullfile(fileparts(which(mfilename)), '..' , '..', 'data', 'set-2', 'roll-and-tilt-at-45-90');
dataSetFolder = fullfile(fileparts(which(mfilename)), '..' , '..', 'data', 'set-2', 'unmoved-with-x-pointing-forward');
%dataSetFolder = fullfile(fileparts(which(mfilename)), '..' , '..', 'data', 'set-2', 'rotate-ccw-around-x-pointing-forward');
%dataSetFolder = fullfile(fileparts(which(mfilename)), '..' , '..', 'data', 'set-2', 'rotate-ccw-around-y-pointing-left');
%dataSetFolder = fullfile(fileparts(which(mfilename)), '..' , '..', 'data', 'set-2', 'rotate-ccw-around-x-pointing-up');
%dataSetFolder = fullfile(fileparts(which(mfilename)), '..' , '..', 'data', 'set-2', 'rotate-ccw-around-z-pointing-up');
[accelerometer, gyroscope, compass, ~] = loadData(dataSetFolder, true);
% resample the time series
[acceleration, gyroscope, compass] = lerpTimeSeries(accelerometer, gyroscope, compass);
% extract time vector
time = acceleration.Time;
N = acceleration.Length;
%% Prepare the Kalman filter
% State variables:
% phi, psi, theta
% omega{phi, psi, theta}
% alpha{phi, psi, theta}
% state matrix
x = [0 0 0, 0 0 0, 0 0 0, 0 0 0]';
% state covariance matrix
vg(1) = 2; % 100*compass.UserData.variance(1);
vg(2) = 2; % 100*compass.UserData.variance(2);
vg(3) = 2; % 100*compass.UserData.variance(3);
P = [
1.9 0 0, 0 0 0, 0 0 0 0 0 0;
0 1.9 0, 0 0 0, 0 0 0 0 0 0;
0 0 1.9, 0 0 0, 0 0 0 0 0 0;
0 0 0, vg(1) 0 0, 0 0 0 0 0 0;
0 0 0, 0 vg(2) 0, 0 0 0 0 0 0;
0 0 0, 0 0 vg(3), 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 1 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 1 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 1];
% measurement noise matrix
R = [
5 0 0, 1 0 0, 0 0 0;
0 5 0, 0 1 0, 0 0 0;
0 0 5, 0 0 1, 0 0 0;
1 0 0, 2 0 0, 0 0 0;
0 1 0, 0 2 0, 0 0 0;
0 0 1, 0 0 2, 0 0 0;
0 0 0, 0 0 0, 0.3 0 0;
0 0 0, 0 0 0, 0 0.3 0;
0 0 0, 0 0 0, 0 0 0.3];
% Lambda coefficient for artificial increase of covariance
lambda = 0.97;
%% Get roll, pitch and yaw
hwb = waitbar(0, 'Calculating states ...');
ypr = zeros(N, 3);
ypr2 = zeros(N, 3);
ypr_kf = zeros(N, 3);
ypr_gyro = zeros(N, 3);
omega_kf = zeros(N, 3);
omega_ddcm = zeros(N, 3);
oldDCM = zeros(3);
maxx = -Inf;
maxP = -Inf;
maxA = -Inf;
maxz = -Inf;
maxH = -Inf;
maxR = -Inf;
minx = +Inf;
minP = +Inf;
minA = +Inf;
minz = +Inf;
minH = +Inf;
minR = +Inf;
for i=1:N
% fetch RPY from accelerometer and magnetometer
a = acceleration.Data(i, :);
m = compass.Data(i, :);
[yaw, pitch, roll, DCM, coordinateSystem, ~] = yawPitchRoll(a, m);
ypr(i,:) = [yaw, pitch, roll];
% correct inverted DCM
DCM = DCM';
% fetch RPY from integrated gyro
ypr_gyro(i, :) = [yaw, pitch, roll];
ypr_gyro_current = [0 0 0];
if i > 1
ypr_gyro_current = [gyroscope.Data(i, 3) -gyroscope.Data(i, 2) -gyroscope.Data(i, 1)];
dt = gyroscope.Time(i) - gyroscope.Time(i-1);
ypr_gyro_now = ypr_gyro(i-1, :) + ypr_gyro_current * dt;
ypr_gyro(i, :) = ypr_gyro_now;
end
% calculate the difference of the rotation and hence the
% angular velocity
difference = DCM*oldDCM';
om_pitchY = -asind(difference(1, 3));
om_rollX = atan2d(difference(2, 3), difference(3, 3));
om_yawZ = atan2d(difference(1, 2), difference(1, 1));
omega_ddcm(i, :) = [om_rollX, om_pitchY, om_yawZ];
% integrate the angular velocity
old_ypr2 = [yaw pitch roll]; % ypr(i, :);
if i > 1
old_ypr2 = ypr2(i-1, :);
end
ypr2_now = old_ypr2 + [om_yawZ, om_pitchY, om_rollX];
ypr2(i, :) = ypr2_now;
% save current DCM for next iteration
diffDCM = difference;
oldDCM = DCM;
% Prepare Kalman Filter
T = 0.1;
if i > 1
T = round(T*1E5)/1E5;
T = gyroscope.Time(i) - gyroscope.Time(i-1);
end
% state matrix
A = [
1 0 0, T 0 0, 0.5*T^2 0 0 0 0 0;
0 1 0, 0 T 0, 0 0.5*T^2 0 0 0 0;
0 0 1, 0 0 T, 0 0 0.5*T^2 0 0 0;
0 0 0, 1 0 0, T 0 0 -T 0 0;
0 0 0, 0 1 0, 0 T 0, 0 -T 0;
0 0 0, 0 0 1, 0 0 T, 0 0 -T;
0 0 0, 0 0 0, 1 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 1, 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 1 0;
0 0 0, 0 0 0, 0 0 0, 0 0 1];
% Kalman Filter: Initial Prediction
if i == 1
x(1:3) = [yaw pitch roll];
x(4:6) = [ypr_gyro_current(1) ypr_gyro_current(2) ypr_gyro_current(3)];
[x, P] = kf_predict(x, A, P, lambda);
end
% measurement transformation matrix
H = [
1 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 1, 0 0 0, 0 0 0, 0 0 0;
1 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 1, 0 0 0, 0 0 0, 0 0 0;
0 0 0, 1 0 0, 0 0 0, 1 0 0;
0 0 0, 0 1 0, 0 0 0, 0 1 0;
0 0 0, 0 0 1, 0 0 0, 0 0 1];
% Measurement vector
z = [
ypr2(i, 1) ypr2(i, 2) ypr2(i, 3), ...
ypr_gyro(i, 1) ypr_gyro(i, 2) ypr_gyro(i, 3), ... %om_yawZ, om_pitchY, om_rollX, ...
ypr_gyro_current(1) ypr_gyro_current(2) ypr_gyro_current(3)]';
maxx = max(max(x), maxx);
maxA = max(max(max(A)), maxA);
maxP = max(max(max(P)), maxP);
maxz = max(max(z), maxz);
if maxP > 1000
disp('whoa');
end
minx = min(min(x), minx);
minA = min(min(min(A)), minA);
minP = min(min(min(P)), minP);
minz = min(min(z), minz);
% Kalman Filter: Measurement Update
[x, P] = kf_update(x, z, P, H, R);
maxx = max(max(x), maxx);
maxP = max(max(max(P)), maxP);
maxH = max(max(max(H)), maxH);
maxR = max(max(max(R)), maxR);
minx = min(min(x), minx);
minP = min(min(min(P)), minP);
minH = min(min(min(H)), minH);
minR = min(min(min(R)), minR);
% Cancel out covariances known to not exist
%P = P .* P_mask;
ypr_kf(i, :) = x(1:3); % merge based on variance
omega_kf(i, :) = [x(6), x(5), x(4)];
% Kalman Filter: Predict
[x, P] = kf_predict(x, A, P, lambda);
waitbar(i/N, hwb);
end
close(hwb);
% clamp angles to -180..180
ypr2 = clampangle(ypr2);
ypr_gyro = clampangle(ypr_gyro);
ypr_kf = clampangle(ypr_kf);
% Stats
fprintf('\nSimple statistics\n');
fprintf('x range: %f .. %f\n', minx, maxx);
fprintf('z range: %f .. %f\n', minz, maxz);
fprintf('A range: %f .. %f\n', minA, maxA);
fprintf('P range: %f .. %f\n', minP, maxP);
fprintf('H range: %f .. %f\n', minH, maxH);
fprintf('R range: %f .. %f\n', minR, maxR);
%{
x range: -209.968656 .. 214.802285
z range: -179.832503 .. 179.699638
A range: 0.000000 .. 1.000000
P range: -2.217640 .. 3.373620
H range: 0.000000 .. 1.000000
R range: 0.000000 .. 189.996904
x range: -283.402185 .. 721.907373
z range: -125.421459 .. 732.398431
A range: 0.000000 .. 1.000000
P range: -91.204589 .. 129.724623
H range: 0.000000 .. 1.000000
R range: 0.000000 .. 10.087000
%}
%% Plot data
figureHandle = figure('Name', 'Raw and derived inertial sensor data', ...
'NumberTitle', 'off', ...
'Color', [0.027 0.211 0.259] ...
);
% define base colors
lineColor(1, :) = [1 0.25 0]; % x axis
lineColor(2, :) = [0.5 1 0]; % y axis
lineColor(3, :) = [0 0.5 1]; % z axis
lineColor(4, :) = [1 1 0]; % x axis
lineColor(5, :) = [1 0 1]; % y axis
lineColor(6, :) = [1.0 0.75 0.25]; % z axis
meanColor = [1 1 1];
axesColor = [0.473 0.473 0.473];
plotBackground = [0.15 0.15 0.15];
titleColor = [1 1 1];
%% Roll
axisRpy(1) = subplot(3, 3, 1, ...
'Parent', figureHandle, ...
'XGrid', 'on', ...
'XColor', axesColor, ...
'YGrid', 'on', ...
'YColor', axesColor, ...
'Color', plotBackground ...
);
t = time;
roll = ypr(:, 3);
line(t, roll, ...
'Parent', axisRpy(1), ...
'LineStyle', 'none', ...
'Marker', '.', ...
'MarkerSize', 2, ...
'Color', lineColor(4, :) ...
);
roll = ypr2(:, 3);
line(t, roll, ...
'Parent', axisRpy(1), ...
'LineStyle', 'none', ...
'Marker', '.', ...
'MarkerSize', 2, ...
'Color', [1 1 1] ...
);
xlim([0 t(end)]);
ylim([-180 180]);
title('Roll', ...
'Color', titleColor ...
);
ylabel('angle [\circ]');
xlabel('t [s]');
legendHandle = legend('DCM raw', 'DCM int');
set(legendHandle, 'TextColor', [1 1 1]);
%% Pitch
axisRpy(2) = subplot(3, 3, 4, ...
'Parent', figureHandle, ...
'XGrid', 'on', ...
'XColor', axesColor, ...
'YGrid', 'on', ...
'YColor', axesColor, ...
'Color', plotBackground ...
);
t = time;
pitch = ypr(:, 2);
line(t, pitch, ...
'Parent', axisRpy(2), ...
'LineStyle', 'none', ...
'Marker', '.', ...
'MarkerSize', 2, ...
'Color', lineColor(5, :) ...
);
pitch = ypr2(:, 2);
line(t, pitch, ...
'Parent', axisRpy(2), ...
'LineStyle', 'none', ...
'Marker', '.', ...
'MarkerSize', 2, ...
'Color', [1 1 1] ...
);
xlim([0 t(end)]);
ylim([-180 180]);
title('Pitch (elevation)', ...
'Color', titleColor ...
);
ylabel('angle [\circ]');
xlabel('t [s]');
legendHandle = legend('DCM raw', 'DCM int');
set(legendHandle, 'TextColor', [1 1 1]);
%% Yaw
axisRpy(3) = subplot(3, 3, 7, ...
'Parent', figureHandle, ...
'XGrid', 'on', ...
'XColor', axesColor, ...
'YGrid', 'on', ...
'YColor', axesColor, ...
'Color', plotBackground ...
);
t = time;
yaw = ypr(:, 1);
line(t, yaw, ...
'Parent', axisRpy(3), ...
'LineStyle', 'none', ...
'Marker', '.', ...
'MarkerSize', 2, ...
'Color', lineColor(6, :) ...
);
yaw = ypr2(:, 1);
line(t, yaw, ...
'Parent', axisRpy(3), ...
'LineStyle', 'none', ...
'Marker', '.', ...
'MarkerSize', 2, ...
'Color', [1 1 1] ...
);
xlim([0 t(end)]);
ylim([-180 180]);
title('Yaw (azimuth, heading)', ...
'Color', titleColor ...
);
ylabel('angle [\circ]');
xlabel('t [s]');
legendHandle = legend('DCM raw', 'DCM int');
set(legendHandle, 'TextColor', [1 1 1]);
%% Roll
axisRpy(4) = subplot(3, 3, 2, ...
'Parent', figureHandle, ...
'XGrid', 'on', ...
'XColor', axesColor, ...
'YGrid', 'on', ...
'YColor', axesColor, ...
'Color', plotBackground ...
);
t = time;
roll = ypr_gyro(:, 3);
line(t, roll, ...
'Parent', axisRpy(4), ...
'LineStyle', 'none', ...
'Marker', '.', ...
'MarkerSize', 2, ...
'Color', lineColor(4, :) ...
);
hold on;
roll = ypr_kf(:, 3);
line(t, roll, ...
'Parent', axisRpy(4), ...
'LineStyle', 'none', ...
'Marker', '.', ...
'MarkerSize', 2, ...
'Color', [1 1 1] ...
);
xlim([0 t(end)]);
ylim([-180 180]);
title('Roll', ...
'Color', titleColor ...
);
ylabel('angle [\circ]');
xlabel('t [s]');
legendHandle = legend('gyro int', 'kf');
set(legendHandle, 'TextColor', [1 1 1]);
%% Pitch
axisRpy(5) = subplot(3, 3, 5, ...
'Parent', figureHandle, ...
'XGrid', 'on', ...
'XColor', axesColor, ...
'YGrid', 'on', ...
'YColor', axesColor, ...
'Color', plotBackground ...
);
t = time;
pitch = ypr_gyro(:, 2);
line(t, pitch, ...
'Parent', axisRpy(5), ...
'LineStyle', 'none', ...
'Marker', '.', ...
'MarkerSize', 2, ...
'Color', lineColor(5, :) ...
);
hold on;
pitch = ypr_kf(:, 2);
line(t, pitch, ...
'Parent', axisRpy(5), ...
'LineStyle', 'none', ...
'Marker', '.', ...
'MarkerSize', 2, ...
'Color', [1 1 1] ...
);
xlim([0 t(end)]);
ylim([-180 180]);
title('Pitch (elevation)', ...
'Color', titleColor ...
);
ylabel('angle [\circ]');
xlabel('t [s]');
legendHandle = legend('gyro int', 'kf');
set(legendHandle, 'TextColor', [1 1 1]);
%% Yaw
axisRpy(6) = subplot(3, 3, 8, ...
'Parent', figureHandle, ...
'XGrid', 'on', ...
'XColor', axesColor, ...
'YGrid', 'on', ...
'YColor', axesColor, ...
'Color', plotBackground ...
);
t = time;
yaw = ypr_gyro(:, 1);
line(t, yaw, ...
'Parent', axisRpy(6), ...
'LineStyle', 'none', ...
'Marker', '.', ...
'MarkerSize', 2, ...
'Color', lineColor(6, :) ...
);
hold on;
yaw = ypr_kf(:, 1);
line(t, yaw, ...
'Parent', axisRpy(6), ...
'LineStyle', 'none', ...
'Marker', '.', ...
'MarkerSize', 2, ...
'Color', [1 1 1] ...
);
xlim([0 t(end)]);
ylim([-180 180]);
title('Yaw (azimuth, heading)', ...
'Color', titleColor ...
);
ylabel('angle [\circ]');
xlabel('t [s]');
legendHandle = legend('gyro int', 'kf');
set(legendHandle, 'TextColor', [1 1 1]);
%% Roll
axisRpy(7) = subplot(3, 3, 3, ...
'Parent', figureHandle, ...
'XGrid', 'on', ...
'XColor', axesColor, ...
'YGrid', 'on', ...
'YColor', axesColor, ...
'Color', plotBackground ...
);
t = time;
roll = -gyroscope.Data(:,1);
line(t, roll, ...
'Parent', axisRpy(7), ...
'LineStyle', 'none', ...
'Marker', '.', ...
'MarkerSize', 2, ...
'Color', lineColor(4, :) ...
);
hold on;
roll = omega_kf(:,1);
line(t, roll, ...
'Parent', axisRpy(7), ...
'LineStyle', 'none', ...
'Marker', '.', ...
'MarkerSize', 2, ...
'Color', [1 1 1] ...
);
xlim([0 t(end)]);
ylim([-180 180]);
title('Roll', ...
'Color', titleColor ...
);
ylabel('angle [\circ]');
xlabel('t [s]');
legendHandle = legend('gyro', 'gyro_{kf}');
set(legendHandle, 'TextColor', [1 1 1]);
%% Pitch
axisRpy(8) = subplot(3, 3, 6, ...
'Parent', figureHandle, ...
'XGrid', 'on', ...
'XColor', axesColor, ...
'YGrid', 'on', ...
'YColor', axesColor, ...
'Color', plotBackground ...
);
t = time;
pitch = -gyroscope.Data(:,2);
line(t, pitch, ...
'Parent', axisRpy(8), ...
'LineStyle', 'none', ...
'Marker', '.', ...
'MarkerSize', 2, ...
'Color', lineColor(5, :) ...
);
hold on;
pitch = omega_kf(:,2);
line(t, pitch, ...
'Parent', axisRpy(8), ...
'LineStyle', 'none', ...
'Marker', '.', ...
'MarkerSize', 2, ...
'Color', [1 1 1] ...
);
xlim([0 t(end)]);
ylim([-180 180]);
title('Pitch (elevation)', ...
'Color', titleColor ...
);
ylabel('angle [\circ]');
xlabel('t [s]');
legendHandle = legend('gyro', 'gyro_{kf}');
set(legendHandle, 'TextColor', [1 1 1]);
%% Yaw
axisRpy(9) = subplot(3, 3, 9, ...
'Parent', figureHandle, ...
'XGrid', 'on', ...
'XColor', axesColor, ...
'YGrid', 'on', ...
'YColor', axesColor, ...
'Color', plotBackground ...
);
t = time;
yaw = gyroscope.Data(:,3);
line(t, yaw, ...
'Parent', axisRpy(9), ...
'LineStyle', 'none', ...
'Marker', '.', ...
'MarkerSize', 2, ...
'Color', lineColor(6, :) ...
);
hold on;
yaw = omega_kf(:,3);
line(t, yaw, ...
'Parent', axisRpy(9), ...
'LineStyle', 'none', ...
'Marker', '.', ...
'MarkerSize', 2, ...
'Color', [1 1 1] ...
);
xlim([0 t(end)]);
ylim([-180 180]);
title('Yaw (azimuth, heading)', ...
'Color', titleColor ...
);
ylabel('angle [\circ]');
xlabel('t [s]');
legendHandle = legend('gyro', 'gyro_{kf}');
set(legendHandle, 'TextColor', [1 1 1]);
%% Plot refining
% link the axes
linkaxes(axisRpy, 'xy');