219 lines
7.7 KiB
Matlab
219 lines
7.7 KiB
Matlab
import gtsam.*;
|
|
|
|
% Test GTSAM covariances on a graph with betweenFactors
|
|
% Authors: Luca Carlone, David Jensen
|
|
% Date: 2014/4/6
|
|
|
|
clc
|
|
clear all
|
|
close all
|
|
|
|
%% Configuration
|
|
useAspnData = 1; % controls whether or not to use the ASPN data for scenario 2 as the ground truth traj
|
|
|
|
%% Create ground truth trajectory
|
|
trajectoryLength = 49;
|
|
unsmooth_DP = 0.5; % controls smoothness on translation norm
|
|
unsmooth_DR = 0.1; % controls smoothness on rotation norm
|
|
|
|
gtValues = Values;
|
|
gtGraph = NonlinearFactorGraph;
|
|
|
|
if useAspnData == 1
|
|
sigma_ang = 1e-4;
|
|
sigma_cart = 40;
|
|
else
|
|
sigma_ang = 1e-2;
|
|
sigma_cart = 0.1;
|
|
end
|
|
noiseVector = [sigma_ang; sigma_ang; sigma_ang; sigma_cart; sigma_cart; sigma_cart];
|
|
noise = noiseModel.Diagonal.Sigmas(noiseVector);
|
|
|
|
if useAspnData == 1
|
|
% Create a ground truth trajectory using scenario 2 data
|
|
fprintf('\nUsing Scenario 2 ground truth data\n');
|
|
% load scenario 2 ground truth data
|
|
gtScenario2 = load('truth_scen2.mat', 'Lat', 'Lon', 'Alt', 'Roll', 'Pitch', 'Heading');
|
|
|
|
% Add first pose
|
|
currentPoseKey = symbol('x', 0);
|
|
initialPosition = imuSimulator.LatLonHRad_to_ECEF([gtScenario2.Lat(1); gtScenario2.Lon(1); gtScenario2.Alt(1)]);
|
|
initialRotation = [gtScenario2.Roll(1); gtScenario2.Pitch(1); gtScenario2.Heading(1)];
|
|
currentPose = Pose3.Expmap([initialRotation; initialPosition]); % initial pose
|
|
gtValues.insert(currentPoseKey, currentPose);
|
|
gtGraph.add(PriorFactorPose3(currentPoseKey, currentPose, noise));
|
|
prevPose = currentPose;
|
|
|
|
% Limit the trajectory length
|
|
trajectoryLength = min([length(gtScenario2.Lat) trajectoryLength]);
|
|
|
|
for i=2:trajectoryLength
|
|
currentPoseKey = symbol('x', i-1);
|
|
gtECEF = imuSimulator.LatLonHRad_to_ECEF([gtScenario2.Lat(i); gtScenario2.Lon(i); gtScenario2.Alt(i)]);
|
|
gtRotation = [gtScenario2.Roll(i); gtScenario2.Pitch(i); gtScenario2.Heading(i)];
|
|
currentPose = Pose3.Expmap([gtRotation; gtECEF]);
|
|
|
|
% Generate measurements as the current pose measured in the frame of
|
|
% the previous pose
|
|
deltaPose = prevPose.between(currentPose);
|
|
gtDeltaMatrix(i-1,:) = Pose3.Logmap(deltaPose);
|
|
prevPose = currentPose;
|
|
|
|
% Add values
|
|
gtValues.insert(currentPoseKey, currentPose);
|
|
|
|
% Add the factor to the factor graph
|
|
gtGraph.add(BetweenFactorPose3(currentPoseKey-1, currentPoseKey, deltaPose, noise));
|
|
end
|
|
else
|
|
% Create a random trajectory as ground truth
|
|
fprintf('\nCreating a random ground truth trajectory\n');
|
|
% Add first pose
|
|
currentPoseKey = symbol('x', 0);
|
|
currentPose = Pose3; % initial pose
|
|
gtValues.insert(currentPoseKey, currentPose);
|
|
gtGraph.add(PriorFactorPose3(currentPoseKey, currentPose, noise));
|
|
|
|
for i=1:trajectoryLength
|
|
currentPoseKey = symbol('x', i);
|
|
gtDeltaPosition = unsmooth_DP*randn(3,1) + [20;0;0]; % create random vector with mean = [1 0 0] and sigma = 0.5
|
|
gtDeltaRotation = unsmooth_DR*randn(3,1) + [0;0;0]; % create random rotation with mean [0 0 0] and sigma = 0.1 (rad)
|
|
gtDeltaMatrix(i,:) = [gtDeltaRotation; gtDeltaPosition];
|
|
deltaPose = Pose3.Expmap(gtDeltaMatrix(i,:)');
|
|
|
|
% "Deduce" ground truth measurements
|
|
% deltaPose are the gt measurements - save them in some structure
|
|
currentPose = currentPose.compose(deltaPose);
|
|
gtValues.insert(currentPoseKey, currentPose);
|
|
|
|
% Add the factors to the factor graph
|
|
gtGraph.add(BetweenFactorPose3(currentPoseKey-1, currentPoseKey, deltaPose, noise));
|
|
end
|
|
end
|
|
figure(1)
|
|
hold on;
|
|
plot3DTrajectory(gtValues, '-r', [], 1, Marginals(gtGraph, gtValues));
|
|
axis equal
|
|
|
|
numMonteCarloRuns = 10;
|
|
for k=1:numMonteCarloRuns
|
|
fprintf('Monte Carlo Run %d.\n', k');
|
|
% create a new graph
|
|
graph = NonlinearFactorGraph;
|
|
|
|
% noisy prior
|
|
if useAspnData == 1
|
|
currentPoseKey = symbol('x', 0);
|
|
initialPosition = imuSimulator.LatLonHRad_to_ECEF([gtScenario2.Lat(1); gtScenario2.Lon(1); gtScenario2.Alt(1)]);
|
|
initialRotation = [gtScenario2.Roll(1); gtScenario2.Pitch(1); gtScenario2.Heading(1)];
|
|
initialPose = Pose3.Expmap([initialRotation; initialPosition] + (noiseVector .* randn(6,1))); % initial noisy pose
|
|
graph.add(PriorFactorPose3(currentPoseKey, currentPose, noise));
|
|
else
|
|
currentPoseKey = symbol('x', 0);
|
|
noisyDelta = noiseVector .* randn(6,1);
|
|
initialPose = Pose3.Expmap(noisyDelta);
|
|
graph.add(PriorFactorPose3(currentPoseKey, initialPose, noise));
|
|
end
|
|
|
|
for i=1:size(gtDeltaMatrix,1)
|
|
currentPoseKey = symbol('x', i);
|
|
|
|
% for each measurement: add noise and add to graph
|
|
noisyDelta = gtDeltaMatrix(i,:)';% + (noiseVector .* randn(6,1));
|
|
noisyDeltaPose = Pose3.Expmap(noisyDelta);
|
|
|
|
% Add the factors to the factor graph
|
|
graph.add(BetweenFactorPose3(currentPoseKey-1, currentPoseKey, noisyDeltaPose, noise));
|
|
end
|
|
|
|
% 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=1:size(gtDeltaMatrix,1)+1
|
|
% compute estimation errors
|
|
currentPoseKey = symbol('x', i-1);
|
|
gtPosition = gtValues.at(currentPoseKey).translation.vector;
|
|
estPosition = estimate.at(currentPoseKey).translation.vector;
|
|
estR = estimate.at(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) = 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');
|
|
|
|
%%
|
|
figure(1)
|
|
box on
|
|
set(gca,'Fontsize',16)
|
|
title('Ground truth and estimates for each MC runs');
|
|
|
|
%% 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');
|
|
|
|
%% 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
|
|
|