326 lines
13 KiB
Matlab
326 lines
13 KiB
Matlab
import gtsam.*;
|
|
|
|
% Test GTSAM covariances on a factor graph with:
|
|
% Between Factors
|
|
% IMU factors (type 1 and type 2)
|
|
% GPS prior factors on poses
|
|
% SmartProjectionPoseFactors
|
|
% Authors: Luca Carlone, David Jensen
|
|
% Date: 2014/4/6
|
|
|
|
|
|
% Check for an extneral configuration, used when running multiple tests
|
|
if ~exist('externallyConfigured', 'var')
|
|
clc
|
|
clear all
|
|
close all
|
|
|
|
saveResults = 0;
|
|
|
|
%% Configuration
|
|
% General options
|
|
options.useRealData = 1; % controls whether or not to use the real data (if available) as the ground truth traj
|
|
options.includeBetweenFactors = 0; % if true, BetweenFactors will be added between consecutive poses
|
|
|
|
options.includeIMUFactors = 1; % if true, IMU factors will be added between consecutive states (biases, poses, velocities)
|
|
options.imuFactorType = 1; % Set to 1 or 2 to use IMU type 1 or type 2 factors (will default to type 1)
|
|
options.imuNonzeroBias = 0; % if true, a nonzero bias is applied to IMU measurements
|
|
|
|
options.includeCameraFactors = 1; % if true, SmartProjectionPose3Factors will be used with randomly generated landmarks
|
|
options.numberOfLandmarks = 1000; % Total number of visual landmarks (randomly generated in a box around the trajectory)
|
|
|
|
options.includeGPSFactors = 0; % if true, GPS factors will be added as priors to poses
|
|
options.gpsStartPose = 100; % Pose number to start including GPS factors at
|
|
|
|
options.trajectoryLength = 100;%209; % length of the ground truth trajectory
|
|
options.subsampleStep = 20; % number of poses to skip when using real data (to reduce computation on long trajectories)
|
|
|
|
numMonteCarloRuns = 2; % number of Monte Carlo runs to perform
|
|
|
|
% Noise values to be adjusted
|
|
sigma_ang = 1e-2; % std. deviation for rotational noise, typical 1e-2
|
|
sigma_cart = 1e-1; % std. deviation for translational noise, typical 1e-1
|
|
sigma_accel = 1e-3; % std. deviation for accelerometer noise, typical 1e-3
|
|
sigma_gyro = 1e-5; % std. deviation for gyroscope noise, typical 1e-5
|
|
sigma_accelBias = 1e-4; % std. deviation for added accelerometer constant bias, typical 1e-3
|
|
sigma_gyroBias = 1e-6; % std. deviation for added gyroscope constant bias, typical 1e-5
|
|
sigma_gps = 1e-4; % std. deviation for noise in GPS position measurements, typical 1e-4
|
|
sigma_camera = 1; % std. deviation for noise in camera measurements (pixels)
|
|
|
|
% Set log files
|
|
testName = sprintf('sa-%1.2g-sc-%1.2g-sacc-%1.2g-sg-%1.2g',sigma_ang,sigma_cart,sigma_accel,sigma_gyro)
|
|
folderName = 'results/'
|
|
else
|
|
fprintf('Tests have been externally configured.\n');
|
|
end
|
|
|
|
%% Between metadata
|
|
noiseVectorPose = [sigma_ang * ones(3,1); sigma_cart * ones(3,1)];
|
|
noisePose = noiseModel.Diagonal.Sigmas(noiseVectorPose);
|
|
|
|
%% Imu metadata
|
|
metadata.imu.epsBias = 1e-10; % was 1e-7
|
|
metadata.imu.g = [0;0;0];
|
|
metadata.imu.omegaCoriolis = [0;0;0];
|
|
metadata.imu.IntegrationSigma = 1e-5;
|
|
metadata.imu.zeroBias = imuBias.ConstantBias(zeros(3,1), zeros(3,1));
|
|
metadata.imu.AccelerometerSigma = sigma_accel;
|
|
metadata.imu.GyroscopeSigma = sigma_gyro;
|
|
metadata.imu.BiasAccelerometerSigma = metadata.imu.epsBias; % noise on expected change in accelerometer bias over time
|
|
metadata.imu.BiasGyroscopeSigma = metadata.imu.epsBias; % noise on expected change in gyroscope bias over time
|
|
% noise on initial accelerometer and gyroscope biases
|
|
if options.imuNonzeroBias == 1
|
|
metadata.imu.BiasAccOmegaInit = [sigma_accelBias * ones(3,1); sigma_gyroBias * ones(3,1)];
|
|
else
|
|
metadata.imu.BiasAccOmegaInit = metadata.imu.epsBias * ones(6,1);
|
|
end
|
|
|
|
noiseVel = noiseModel.Isotropic.Sigma(3, 1e-2); % was 0.1
|
|
noiseBiasBetween = noiseModel.Diagonal.Sigmas([metadata.imu.BiasAccelerometerSigma * ones(3,1);...
|
|
metadata.imu.BiasGyroscopeSigma * ones(3,1)]); % between on biases
|
|
noisePriorBias = noiseModel.Diagonal.Sigmas(metadata.imu.BiasAccOmegaInit);
|
|
|
|
noiseVectorAccel = metadata.imu.AccelerometerSigma * ones(3,1);
|
|
noiseVectorGyro = metadata.imu.GyroscopeSigma * ones(3,1);
|
|
|
|
%% GPS metadata
|
|
noiseVectorGPS = sigma_gps * ones(3,1);
|
|
noiseGPS = noiseModel.Diagonal.Precisions([zeros(3,1); 1/sigma_gps^2 * ones(3,1)]);
|
|
|
|
%% Camera metadata
|
|
metadata.camera.calibration = Cal3_S2(500,500,0,1920/2,1200/2); % Camera calibration
|
|
metadata.camera.xlims = [-100, 650]; % x limits on area for landmark creation
|
|
metadata.camera.ylims = [-100, 700]; % y limits on area for landmark creation
|
|
metadata.camera.zlims = [-30, 30]; % z limits on area for landmark creation
|
|
metadata.camera.visualRange = 100; % maximum distance from the camera that a landmark can be seen (meters)
|
|
metadata.camera.bodyPoseCamera = Pose3; % pose of camera in body
|
|
metadata.camera.CameraSigma = sigma_camera;
|
|
cameraMeasurementNoise = noiseModel.Isotropic.Sigma(2, metadata.camera.CameraSigma);
|
|
noiseVectorCamera = metadata.camera.CameraSigma .* ones(2,1);
|
|
|
|
% Create landmarks and smart factors
|
|
if options.includeCameraFactors == 1
|
|
for i = 1:options.numberOfLandmarks
|
|
metadata.camera.gtLandmarkPoints(i) = Point3( ...
|
|
[rand() * (metadata.camera.xlims(2)-metadata.camera.xlims(1)) + metadata.camera.xlims(1); ...
|
|
rand() * (metadata.camera.ylims(2)-metadata.camera.ylims(1)) + metadata.camera.ylims(1); ...
|
|
rand() * (metadata.camera.zlims(2)-metadata.camera.zlims(1)) + metadata.camera.zlims(1)]);
|
|
end
|
|
end
|
|
|
|
|
|
%% Create ground truth trajectory and measurements
|
|
[gtValues, gtMeasurements] = imuSimulator.covarianceAnalysisCreateTrajectory(options, metadata);
|
|
|
|
%% Create ground truth graph
|
|
% Set up noise models
|
|
gtNoiseModels.noisePose = noisePose;
|
|
gtNoiseModels.noiseVel = noiseVel;
|
|
gtNoiseModels.noiseBiasBetween = noiseBiasBetween;
|
|
gtNoiseModels.noisePriorPose = noisePose;
|
|
gtNoiseModels.noisePriorBias = noisePriorBias;
|
|
gtNoiseModels.noiseGPS = noiseGPS;
|
|
gtNoiseModels.noiseCamera = cameraMeasurementNoise;
|
|
|
|
% Set measurement noise to 0, because this is ground truth
|
|
gtMeasurementNoise.poseNoiseVector = zeros(6,1);
|
|
gtMeasurementNoise.imu.accelNoiseVector = zeros(3,1);
|
|
gtMeasurementNoise.imu.gyroNoiseVector = zeros(3,1);
|
|
gtMeasurementNoise.cameraNoiseVector = zeros(2,1);
|
|
gtMeasurementNoise.gpsNoiseVector = zeros(3,1);
|
|
|
|
% Set IMU biases to zero
|
|
metadata.imu.accelConstantBiasVector = zeros(3,1);
|
|
metadata.imu.gyroConstantBiasVector = zeros(3,1);
|
|
|
|
[gtGraph, projectionFactorSeenBy] = imuSimulator.covarianceAnalysisCreateFactorGraph( ...
|
|
gtMeasurements, ... % ground truth measurements
|
|
gtValues, ... % ground truth Values
|
|
gtNoiseModels, ... % noise models to use in this graph
|
|
gtMeasurementNoise, ... % noise to apply to measurements
|
|
options, ... % options for the graph (e.g. which factors to include)
|
|
metadata); % misc data necessary for factor creation
|
|
|
|
%% Display, printing, and plotting of ground truth
|
|
%gtGraph.print(sprintf('\nGround Truth Factor graph:\n'));
|
|
%gtValues.print(sprintf('\nGround Truth Values:\n '));
|
|
|
|
figure(1)
|
|
hold on;
|
|
|
|
if options.includeCameraFactors
|
|
b = [-1000 2000 -2000 2000 -30 30];
|
|
for i = 1:size(metadata.camera.gtLandmarkPoints,2)
|
|
p = metadata.camera.gtLandmarkPoints(i);
|
|
if(p(1) > b(1) && p(1) < b(2) && p(2) > b(3) && p(2) < b(4) && p(3) > b(5) && p(3) < b(6))
|
|
plot3(p(1), p(2), p(3), 'k+');
|
|
end
|
|
end
|
|
pointsToPlot = metadata.camera.gtLandmarkPoints(find(projectionFactorSeenBy > 0));
|
|
for i = 1:length(pointsToPlot)
|
|
p = pointsToPlot(i);
|
|
plot3(p(1), p(2), p(3), 'gs', 'MarkerSize', 10);
|
|
end
|
|
end
|
|
plot3DPoints(gtValues);
|
|
%plot3DTrajectory(gtValues, '-r', [], 1, Marginals(gtGraph, gtValues));
|
|
plot3DTrajectory(gtValues, '-r');
|
|
|
|
axis equal
|
|
|
|
% optimize
|
|
optimizer = GaussNewtonOptimizer(gtGraph, gtValues);
|
|
gtEstimate = optimizer.optimize();
|
|
plot3DTrajectory(gtEstimate, '-k');
|
|
% estimate should match gtValues if graph is correct.
|
|
fprintf('Error in ground truth graph at gtValues: %g \n', gtGraph.error(gtValues) );
|
|
fprintf('Error in ground truth graph at gtEstimate: %g \n', gtGraph.error(gtEstimate) );
|
|
|
|
disp('Plotted ground truth')
|
|
|
|
%% Monte Carlo Runs
|
|
|
|
% Set up noise models
|
|
monteCarloNoiseModels.noisePose = noisePose;
|
|
monteCarloNoiseModels.noiseVel = noiseVel;
|
|
monteCarloNoiseModels.noiseBiasBetween = noiseBiasBetween;
|
|
monteCarloNoiseModels.noisePriorPose = noisePose;
|
|
monteCarloNoiseModels.noisePriorBias = noisePriorBias;
|
|
monteCarloNoiseModels.noiseGPS = noiseGPS;
|
|
monteCarloNoiseModels.noiseCamera = cameraMeasurementNoise;
|
|
|
|
% Set measurement noise for monte carlo runs
|
|
monteCarloMeasurementNoise.poseNoiseVector = zeros(6,1); %noiseVectorPose;
|
|
monteCarloMeasurementNoise.imu.accelNoiseVector = noiseVectorAccel;
|
|
monteCarloMeasurementNoise.imu.gyroNoiseVector = noiseVectorGyro;
|
|
monteCarloMeasurementNoise.gpsNoiseVector = noiseVectorGPS;
|
|
monteCarloMeasurementNoise.cameraNoiseVector = noiseVectorCamera;
|
|
|
|
for k=1:numMonteCarloRuns
|
|
fprintf('Monte Carlo Run %d...\n', k');
|
|
|
|
% Create a random bias for each run
|
|
if options.imuNonzeroBias == 1
|
|
metadata.imu.accelConstantBiasVector = metadata.imu.BiasAccOmegaInit(1:3) .* randn(3,1);
|
|
metadata.imu.gyroConstantBiasVector = metadata.imu.BiasAccOmegaInit(4:6) .* randn(3,1);
|
|
%metadata.imu.accelConstantBiasVector = 1e-2 * ones(3,1);
|
|
%metadata.imu.gyroConstantBiasVector = 1e-3 * ones(3,1);
|
|
else
|
|
metadata.imu.accelConstantBiasVector = zeros(3,1);
|
|
metadata.imu.gyroConstantBiasVector = zeros(3,1);
|
|
end
|
|
|
|
% Create a new graph using noisy measurements
|
|
[graph, projectionFactorSeenBy] = imuSimulator.covarianceAnalysisCreateFactorGraph( ...
|
|
gtMeasurements, ... % ground truth measurements
|
|
gtValues, ... % ground truth Values
|
|
monteCarloNoiseModels, ... % noise models to use in this graph
|
|
monteCarloMeasurementNoise, ... % noise to apply to measurements
|
|
options, ... % options for the graph (e.g. which factors to include)
|
|
metadata); % misc data necessary for factor creation
|
|
|
|
%graph.print('graph')
|
|
|
|
% optimize
|
|
optimizer = GaussNewtonOptimizer(graph, gtValues);
|
|
estimate = optimizer.optimize();
|
|
figure(1)
|
|
plot3DTrajectory(estimate, '-b');
|
|
|
|
marginals = Marginals(graph, estimate);
|
|
|
|
% for each pose in the trajectory
|
|
for i=0:options.trajectoryLength
|
|
% compute estimation errors
|
|
currentPoseKey = symbol('x', i);
|
|
gtPosition = gtValues.atPose3(currentPoseKey).translation;
|
|
estPosition = estimate.atPose3(currentPoseKey).translation;
|
|
estR = estimate.atPose3(currentPoseKey).rotation.matrix;
|
|
errPosition = estPosition - gtPosition;
|
|
|
|
% compute covariances:
|
|
cov = marginals.marginalCovariance(currentPoseKey);
|
|
covPosition = estR * cov(4:6,4:6) * estR';
|
|
% compute NEES using (estimationError = estimatedValues - gtValues) and estimated covariances
|
|
NEES(k,i+1) = errPosition' * inv(covPosition) * errPosition; % distributed according to a Chi square with n = 3 dof
|
|
end
|
|
|
|
figure(2)
|
|
hold on
|
|
plot(NEES(k,:),'-b','LineWidth',1.5)
|
|
end
|
|
%%
|
|
ANEES = mean(NEES);
|
|
plot(ANEES,'-r','LineWidth',2)
|
|
plot(3*ones(size(ANEES,2),1),'k--'); % Expectation(ANEES) = number of dof
|
|
box on
|
|
set(gca,'Fontsize',16)
|
|
title('NEES and ANEES');
|
|
if saveResults
|
|
saveas(gcf,horzcat(folderName,'runs-',testName,'.fig'),'fig');
|
|
saveas(gcf,horzcat(folderName,'runs-',testName,'.png'),'png');
|
|
end
|
|
|
|
%%
|
|
figure(1)
|
|
box on
|
|
set(gca,'Fontsize',16)
|
|
title('Ground truth and estimates for each MC runs');
|
|
if saveResults
|
|
saveas(gcf,horzcat(folderName,'gt-',testName,'.fig'),'fig');
|
|
saveas(gcf,horzcat(folderName,'gt-',testName,'.png'),'png');
|
|
end
|
|
|
|
%% Let us compute statistics on the overall NEES
|
|
n = 3; % position vector dimension
|
|
N = numMonteCarloRuns; % number of runs
|
|
alpha = 0.01; % confidence level
|
|
|
|
% mean_value = n*N; % mean value of the Chi-square distribution
|
|
% (we divide by n * N and for this reason we expect ANEES around 1)
|
|
r1 = chi2inv(alpha, n * N) / (n * N);
|
|
r2 = chi2inv(1-alpha, n * N) / (n * N);
|
|
|
|
% output here
|
|
fprintf(1, 'r1 = %g\n', r1);
|
|
fprintf(1, 'r2 = %g\n', r2);
|
|
|
|
figure(3)
|
|
hold on
|
|
plot(ANEES/n,'-b','LineWidth',2)
|
|
plot(ones(size(ANEES,2),1),'r-');
|
|
plot(r1*ones(size(ANEES,2),1),'k-.');
|
|
plot(r2*ones(size(ANEES,2),1),'k-.');
|
|
box on
|
|
set(gca,'Fontsize',16)
|
|
title('NEES normalized by dof VS bounds');
|
|
if saveResults
|
|
saveas(gcf,horzcat(folderName,'ANEES-',testName,'.fig'),'fig');
|
|
saveas(gcf,horzcat(folderName,'ANEES-',testName,'.png'),'png');
|
|
logFile = horzcat(folderName,'log-',testName);
|
|
save(logFile)
|
|
end
|
|
|
|
%% NEES COMPUTATION (Bar-Shalom 2001, Section 5.4)
|
|
% the nees for a single experiment (i) is defined as
|
|
% NEES_i = xtilda' * inv(P) * xtilda,
|
|
% where xtilda in R^n is the estimation
|
|
% error, and P is the covariance estimated by the approach we want to test
|
|
%
|
|
% Average NEES. Given N Monte Carlo simulations, i=1,...,N, the average
|
|
% NEES is:
|
|
% ANEES = sum(NEES_i)/N
|
|
% The quantity N*ANEES is distributed according to a Chi-square
|
|
% distribution with N*n degrees of freedom.
|
|
%
|
|
% For the single run case, N=1, therefore NEES = ANEES is distributed
|
|
% according to a chi-square distribution with n degrees of freedom (e.g. n=3
|
|
% if we are testing a position estimate)
|
|
% Therefore its mean should be n (difficult to see from a single run)
|
|
% and, with probability alpha, it should hold:
|
|
%
|
|
% NEES in [r1, r2]
|
|
%
|
|
% where r1 and r2 are built from the Chi-square distribution
|
|
|