307 lines
13 KiB
Matlab
307 lines
13 KiB
Matlab
import gtsam.*;
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% Test GTSAM covariances on a factor graph with:
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% Between Factors
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% IMU factors (type 1 and type 2)
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% GPS prior factors on poses
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% SmartProjectionPoseFactors
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% Authors: Luca Carlone, David Jensen
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% Date: 2014/4/6
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% Check for an extneral configuration, used when running multiple tests
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if ~exist('externallyConfigured', 'var')
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clc
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clear all
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close all
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saveResults = 0;
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%% Configuration
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% General options
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options.useRealData = 1; % controls whether or not to use the real data (if available) as the ground truth traj
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options.includeBetweenFactors = 1; % if true, BetweenFactors will be added between consecutive poses
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options.includeIMUFactors = 0; % if true, IMU factors will be added between consecutive states (biases, poses, velocities)
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options.imuFactorType = 1; % Set to 1 or 2 to use IMU type 1 or type 2 factors (will default to type 1)
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options.imuNonzeroBias = 0; % if true, a nonzero bias is applied to IMU measurements
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options.includeCameraFactors = 1; % if true, SmartProjectionPose3Factors will be used with randomly generated landmarks
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options.numberOfLandmarks = 100; % Total number of visual landmarks (randomly generated in a box around the trajectory)
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options.includeGPSFactors = 0; % if true, GPS factors will be added as priors to poses
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options.gpsStartPose = 100; % Pose number to start including GPS factors at
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options.trajectoryLength = 50;%209; % length of the ground truth trajectory
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options.subsampleStep = 20; % number of poses to skip when using real data (to reduce computation on long trajectories)
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numMonteCarloRuns = 2; % number of Monte Carlo runs to perform
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% Noise values to be adjusted
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sigma_ang = 1e-2; % std. deviation for rotational noise, typical 1e-2
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sigma_cart = 1e-1; % std. deviation for translational noise, typical 1e-1
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sigma_accel = 1e-3; % std. deviation for accelerometer noise, typical 1e-3
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sigma_gyro = 1e-5; % std. deviation for gyroscope noise, typical 1e-5
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sigma_accelBias = 1e-4; % std. deviation for added accelerometer constant bias, typical 1e-3
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sigma_gyroBias = 1e-6; % std. deviation for added gyroscope constant bias, typical 1e-5
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sigma_gps = 1e-4; % std. deviation for noise in GPS position measurements, typical 1e-4
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sigma_camera = 1; % std. deviation for noise in camera measurements (pixels)
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% Set log files
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testName = sprintf('sa-%1.2g-sc-%1.2g-sacc-%1.2g-sg-%1.2g',sigma_ang,sigma_cart,sigma_accel,sigma_gyro)
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folderName = 'results/'
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else
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fprintf('Tests have been externally configured.\n');
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end
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%% Between metadata
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noiseVectorPose = [sigma_ang * ones(3,1); sigma_cart * ones(3,1)];
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noisePose = noiseModel.Diagonal.Sigmas(noiseVectorPose);
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%% Imu metadata
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metadata.imu.epsBias = 1e-10; % was 1e-7
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metadata.imu.g = [0;0;0];
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metadata.imu.omegaCoriolis = [0;0;0];
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metadata.imu.IntegrationSigma = 1e-5;
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metadata.imu.zeroBias = imuBias.ConstantBias(zeros(3,1), zeros(3,1));
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metadata.imu.AccelerometerSigma = sigma_accel;
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metadata.imu.GyroscopeSigma = sigma_gyro;
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metadata.imu.BiasAccelerometerSigma = metadata.imu.epsBias; % noise on expected change in accelerometer bias over time
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metadata.imu.BiasGyroscopeSigma = metadata.imu.epsBias; % noise on expected change in gyroscope bias over time
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% noise on initial accelerometer and gyroscope biases
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if options.imuNonzeroBias == 1
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metadata.imu.BiasAccOmegaInit = [sigma_accelBias * ones(3,1); sigma_gyroBias * ones(3,1)];
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else
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metadata.imu.BiasAccOmegaInit = metadata.imu.epsBias * ones(6,1);
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end
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noiseVel = noiseModel.Isotropic.Sigma(3, 1e-2); % was 0.1
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noiseBiasBetween = noiseModel.Diagonal.Sigmas([metadata.imu.BiasAccelerometerSigma * ones(3,1);...
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metadata.imu.BiasGyroscopeSigma * ones(3,1)]); % between on biases
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noisePriorBias = noiseModel.Diagonal.Sigmas(metadata.imu.BiasAccOmegaInit);
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noiseVectorAccel = metadata.imu.AccelerometerSigma * ones(3,1);
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noiseVectorGyro = metadata.imu.GyroscopeSigma * ones(3,1);
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%% GPS metadata
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noiseVectorGPS = sigma_gps * ones(3,1);
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noiseGPS = noiseModel.Diagonal.Precisions([zeros(3,1); 1/sigma_gps^2 * ones(3,1)]);
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%% Camera metadata
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metadata.camera.calibration = Cal3_S2(500,500,0,640/2,480/2); % Camera calibration
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metadata.camera.xlims = [-100, 650]; % x limits on area for landmark creation
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metadata.camera.ylims = [-100, 700]; % y limits on area for landmark creation
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metadata.camera.zlims = [-10, 30]; % z limits on area for landmark creation
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metadata.camera.CameraSigma = sigma_camera;
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cameraMeasurementNoise = noiseModel.Isotropic.Sigma(2, metadata.camera.CameraSigma);
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noiseVectorCamera = metadata.camera.CameraSigma .* ones(2,1);
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% Create landmarks and smart factors
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if options.includeCameraFactors == 1
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for i = 1:options.numberOfLandmarks
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metadata.camera.gtLandmarkPoints(i) = Point3( ...
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[rand() * (metadata.camera.xlims(2)-metadata.camera.xlims(1)) + metadata.camera.xlims(1); ...
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rand() * (metadata.camera.ylims(2)-metadata.camera.ylims(1)) + metadata.camera.ylims(1);
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rand() * (metadata.camera.zlims(2)-metadata.camera.zlims(1)) + metadata.camera.zlims(1)]);
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end
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end
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%% Create ground truth trajectory and measurements
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[gtValues, gtMeasurements] = imuSimulator.covarianceAnalysisCreateTrajectory(options, metadata);
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%% Create ground truth graph
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% Set up noise models
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gtNoiseModels.noisePose = noisePose;
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gtNoiseModels.noiseVel = noiseVel;
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gtNoiseModels.noiseBiasBetween = noiseBiasBetween;
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gtNoiseModels.noisePriorPose = noisePose;
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gtNoiseModels.noisePriorBias = noisePriorBias;
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gtNoiseModels.noiseGPS = noiseGPS;
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gtNoiseModels.noiseCamera = cameraMeasurementNoise;
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% Set measurement noise to 0, because this is ground truth
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gtMeasurementNoise.poseNoiseVector = zeros(6,1);
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gtMeasurementNoise.imu.accelNoiseVector = zeros(3,1);
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gtMeasurementNoise.imu.gyroNoiseVector = zeros(3,1);
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gtMeasurementNoise.cameraNoiseVector = zeros(2,1);
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gtMeasurementNoise.gpsNoiseVector = zeros(3,1);
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% Set IMU biases to zero
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metadata.imu.accelConstantBiasVector = zeros(3,1);
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metadata.imu.gyroConstantBiasVector = zeros(3,1);
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gtGraph = imuSimulator.covarianceAnalysisCreateFactorGraph( ...
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gtMeasurements, ... % ground truth measurements
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gtValues, ... % ground truth Values
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gtNoiseModels, ... % noise models to use in this graph
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gtMeasurementNoise, ... % noise to apply to measurements
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options, ... % options for the graph (e.g. which factors to include)
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metadata); % misc data necessary for factor creation
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%% Display, printing, and plotting of ground truth
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%gtGraph.print(sprintf('\nGround Truth Factor graph:\n'));
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%gtValues.print(sprintf('\nGround Truth Values:\n '));
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figure(1)
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hold on;
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plot3DPoints(gtValues);
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%plot3DTrajectory(gtValues, '-r', [], 1, Marginals(gtGraph, gtValues));
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plot3DTrajectory(gtValues, '-r');
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axis equal
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% optimize
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optimizer = GaussNewtonOptimizer(gtGraph, gtValues);
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gtEstimate = optimizer.optimize();
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% estimate should match gtValues if graph is correct.
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fprintf('Error in ground truth graph at gtValues: %g \n', gtGraph.error(gtValues) );
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fprintf('Error in ground truth graph at gtEstimate: %g \n', gtGraph.error(gtEstimate) );
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disp('Plotted ground truth')
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%% Monte Carlo Runs
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% Set up noise models
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monteCarloNoiseModels.noisePose = noisePose;
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monteCarloNoiseModels.noiseVel = noiseVel;
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monteCarloNoiseModels.noiseBiasBetween = noiseBiasBetween;
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monteCarloNoiseModels.noisePriorPose = noisePose;
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monteCarloNoiseModels.noisePriorBias = noisePriorBias;
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monteCarloNoiseModels.noiseGPS = noiseGPS;
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monteCarloNoiseModels.noiseCamera = cameraMeasurementNoise;
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% Set measurement noise for monte carlo runs
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monteCarloMeasurementNoise.poseNoiseVector = zeros(6,1); %noiseVectorPose;
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monteCarloMeasurementNoise.imu.accelNoiseVector = noiseVectorAccel;
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monteCarloMeasurementNoise.imu.gyroNoiseVector = noiseVectorGyro;
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monteCarloMeasurementNoise.gpsNoiseVector = noiseVectorGPS;
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monteCarloMeasurementNoise.cameraNoiseVector = noiseVectorCamera;
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for k=1:numMonteCarloRuns
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fprintf('Monte Carlo Run %d...\n', k');
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% Create a random bias for each run
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if options.imuNonzeroBias == 1
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metadata.imu.accelConstantBiasVector = metadata.imu.BiasAccOmegaInit(1:3) .* randn(3,1);
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metadata.imu.gyroConstantBiasVector = metadata.imu.BiasAccOmegaInit(4:6) .* randn(3,1);
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%metadata.imu.accelConstantBiasVector = 1e-2 * ones(3,1);
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%metadata.imu.gyroConstantBiasVector = 1e-3 * ones(3,1);
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else
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metadata.imu.accelConstantBiasVector = zeros(3,1);
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metadata.imu.gyroConstantBiasVector = zeros(3,1);
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end
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% Create a new graph using noisy measurements
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graph = imuSimulator.covarianceAnalysisCreateFactorGraph( ...
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gtMeasurements, ... % ground truth measurements
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gtValues, ... % ground truth Values
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monteCarloNoiseModels, ... % noise models to use in this graph
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monteCarloMeasurementNoise, ... % noise to apply to measurements
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options, ... % options for the graph (e.g. which factors to include)
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metadata); % misc data necessary for factor creation
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%graph.print('graph')
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% optimize
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optimizer = GaussNewtonOptimizer(graph, gtValues);
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estimate = optimizer.optimize();
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figure(1)
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plot3DTrajectory(estimate, '-b');
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marginals = Marginals(graph, estimate);
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% for each pose in the trajectory
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for i=0:options.trajectoryLength
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% compute estimation errors
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currentPoseKey = symbol('x', i);
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gtPosition = gtValues.at(currentPoseKey).translation.vector;
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estPosition = estimate.at(currentPoseKey).translation.vector;
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estR = estimate.at(currentPoseKey).rotation.matrix;
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errPosition = estPosition - gtPosition;
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% compute covariances:
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cov = marginals.marginalCovariance(currentPoseKey);
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covPosition = estR * cov(4:6,4:6) * estR';
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% compute NEES using (estimationError = estimatedValues - gtValues) and estimated covariances
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NEES(k,i+1) = errPosition' * inv(covPosition) * errPosition; % distributed according to a Chi square with n = 3 dof
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end
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figure(2)
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hold on
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plot(NEES(k,:),'-b','LineWidth',1.5)
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end
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%%
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ANEES = mean(NEES);
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plot(ANEES,'-r','LineWidth',2)
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plot(3*ones(size(ANEES,2),1),'k--'); % Expectation(ANEES) = number of dof
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box on
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set(gca,'Fontsize',16)
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title('NEES and ANEES');
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if saveResults
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saveas(gcf,horzcat(folderName,'runs-',testName,'.fig'),'fig');
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saveas(gcf,horzcat(folderName,'runs-',testName,'.png'),'png');
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end
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%%
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figure(1)
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box on
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set(gca,'Fontsize',16)
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title('Ground truth and estimates for each MC runs');
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if saveResults
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saveas(gcf,horzcat(folderName,'gt-',testName,'.fig'),'fig');
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saveas(gcf,horzcat(folderName,'gt-',testName,'.png'),'png');
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end
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%% Let us compute statistics on the overall NEES
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n = 3; % position vector dimension
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N = numMonteCarloRuns; % number of runs
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alpha = 0.01; % confidence level
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% mean_value = n*N; % mean value of the Chi-square distribution
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% (we divide by n * N and for this reason we expect ANEES around 1)
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r1 = chi2inv(alpha, n * N) / (n * N);
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r2 = chi2inv(1-alpha, n * N) / (n * N);
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% output here
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fprintf(1, 'r1 = %g\n', r1);
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fprintf(1, 'r2 = %g\n', r2);
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figure(3)
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hold on
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plot(ANEES/n,'-b','LineWidth',2)
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plot(ones(size(ANEES,2),1),'r-');
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plot(r1*ones(size(ANEES,2),1),'k-.');
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plot(r2*ones(size(ANEES,2),1),'k-.');
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box on
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set(gca,'Fontsize',16)
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title('NEES normalized by dof VS bounds');
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if saveResults
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saveas(gcf,horzcat(folderName,'ANEES-',testName,'.fig'),'fig');
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saveas(gcf,horzcat(folderName,'ANEES-',testName,'.png'),'png');
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logFile = horzcat(folderName,'log-',testName);
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save(logFile)
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end
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%% NEES COMPUTATION (Bar-Shalom 2001, Section 5.4)
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% the nees for a single experiment (i) is defined as
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% NEES_i = xtilda' * inv(P) * xtilda,
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% where xtilda in R^n is the estimation
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% error, and P is the covariance estimated by the approach we want to test
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%
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% Average NEES. Given N Monte Carlo simulations, i=1,...,N, the average
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% NEES is:
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% ANEES = sum(NEES_i)/N
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% The quantity N*ANEES is distributed according to a Chi-square
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% distribution with N*n degrees of freedom.
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%
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% For the single run case, N=1, therefore NEES = ANEES is distributed
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% according to a chi-square distribution with n degrees of freedom (e.g. n=3
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% if we are testing a position estimate)
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% Therefore its mean should be n (difficult to see from a single run)
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% and, with probability alpha, it should hold:
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%
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% NEES in [r1, r2]
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%
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% where r1 and r2 are built from the Chi-square distribution
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