Sanity check sampler, and compare 9*9 covariance on NavState
Frank Dellaert
parent
e52f7ec705
commit
8a31243761
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@ -238,19 +238,40 @@ NavState ScenarioRunner::predict(
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return pim.predict(state_i, estimatedBias);
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}
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Matrix6 ScenarioRunner::estimatePoseCovariance(
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Matrix9 ScenarioRunner::estimateCovariance(
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double T, size_t N, const imuBias::ConstantBias& estimatedBias) const {
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// Get predict prediction from ground truth measurements
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Pose3 prediction = predict(integrate(T)).pose();
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NavState prediction = predict(integrate(T));
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// Sample !
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Matrix samples(9, N);
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Vector9 sum = Vector9::Zero();
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for (size_t i = 0; i < N; i++) {
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NavState sampled = predict(integrate(T, estimatedBias, true));
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samples.col(i) = sampled.localCoordinates(prediction);
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sum += samples.col(i);
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}
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// Compute MC covariance
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Vector9 sampleMean = sum / N;
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Matrix9 Q;
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Q.setZero();
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for (size_t i = 0; i < N; i++) {
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Vector9 xi = samples.col(i);
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xi -= sampleMean;
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Q += xi * xi.transpose();
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}
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return Q / (N - 1);
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}
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Matrix6 ScenarioRunner::estimateNoiseCovariance(size_t N) const {
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Matrix samples(6, N);
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Vector6 sum = Vector6::Zero();
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for (size_t i = 0; i < N; i++) {
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Pose3 sampled = predict(integrate(T, estimatedBias, true)).pose();
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Vector6 xi = sampled.localCoordinates(prediction);
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samples.col(i) = xi;
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sum += xi;
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samples.col(i) << accSampler_.sample() / sqrt_dt_,
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gyroSampler_.sample() / sqrt_dt_;
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sum += samples.col(i);
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}
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// Compute MC covariance
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@ -66,6 +66,9 @@ class PreintegratedMeasurements2 {
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k_(0),
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deltaTij_(0.0) {}
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SharedDiagonal discreteAccelerometerNoiseModel(double dt) const;
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SharedDiagonal discreteGyroscopeNoiseModel(double dt) const;
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/**
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* Add a single IMU measurement to the preintegration.
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* @param measuredAcc Measured acceleration (in body frame)
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@ -97,9 +100,6 @@ class PreintegratedMeasurements2 {
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// We obtain discrete-time noise models by dividing the continuous-time
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// covariances by dt:
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SharedDiagonal discreteAccelerometerNoiseModel(double dt) const;
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SharedDiagonal discreteGyroscopeNoiseModel(double dt) const;
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// initialize posterior with first (corrected) IMU measurement
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SharedBayesNet initPosterior(const Vector3& correctedAcc,
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const Vector3& correctedOmega, double dt) const;
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@ -121,7 +121,7 @@ class ScenarioRunner {
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private:
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const Scenario* scenario_;
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const SharedParams p_;
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const double imuSampleTime_;
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const double imuSampleTime_, sqrt_dt_;
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const imuBias::ConstantBias bias_;
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// Create two samplers for acceleration and omega noise
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@ -134,6 +134,7 @@ class ScenarioRunner {
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: scenario_(scenario),
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p_(p),
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imuSampleTime_(imuSampleTime),
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sqrt_dt_(std::sqrt(imuSampleTime)),
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bias_(bias),
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// NOTE(duy): random seeds that work well:
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gyroSampler_(Diagonal(p->gyroscopeCovariance), 10),
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@ -155,11 +156,11 @@ class ScenarioRunner {
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// versions corrupted by bias and noise
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Vector3 measured_omega_b(double t) const {
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return actual_omega_b(t) + bias_.gyroscope() +
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gyroSampler_.sample() / std::sqrt(imuSampleTime_);
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gyroSampler_.sample() / sqrt_dt_;
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}
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Vector3 measured_specific_force_b(double t) const {
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return actual_specific_force_b(t) + bias_.accelerometer() +
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accSampler_.sample() / std::sqrt(imuSampleTime_);
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accSampler_.sample() / sqrt_dt_;
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}
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const double& imuSampleTime() const { return imuSampleTime_; }
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@ -175,19 +176,13 @@ class ScenarioRunner {
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const imuBias::ConstantBias& estimatedBias =
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imuBias::ConstantBias()) const;
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/// Return pose covariance by re-arranging pim.preintMeasCov() appropriately
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Matrix6 poseCovariance(const PreintegratedMeasurements2& pim) const {
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Matrix9 cov = pim.preintMeasCov();
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Matrix6 poseCov;
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poseCov << cov.block<3, 3>(0, 0), cov.block<3, 3>(0, 3), //
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cov.block<3, 3>(3, 0), cov.block<3, 3>(3, 3);
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return poseCov;
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}
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/// Compute a Monte Carlo estimate of the PIM pose covariance using N samples
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Matrix6 estimatePoseCovariance(double T, size_t N = 1000,
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/// Compute a Monte Carlo estimate of the predict covariance using N samples
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Matrix9 estimateCovariance(double T, size_t N = 1000,
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const imuBias::ConstantBias& estimatedBias =
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imuBias::ConstantBias()) const;
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/// Estimate covariance of sampled noise for sanity-check
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Matrix6 estimateNoiseCovariance(size_t N = 1000) const;
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};
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} // namespace gtsam
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@ -23,7 +23,7 @@ using namespace std;
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using namespace gtsam;
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static const double kDegree = M_PI / 180.0;
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static const double kDeltaT = 1e-2;
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static const double kDt = 1e-2;
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static const double kGyroSigma = 0.02;
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static const double kAccelSigma = 0.1;
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@ -46,14 +46,29 @@ TEST(ScenarioRunner, Spin) {
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const Vector3 W(0, 0, w), V(0, 0, 0);
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const ExpmapScenario scenario(W, V);
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ScenarioRunner runner(&scenario, defaultParams(), kDeltaT);
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const double T = 0.5; // seconds
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auto p = defaultParams();
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ScenarioRunner runner(&scenario, p, kDt);
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const double T = kDt; // seconds
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auto pim = runner.integrate(T);
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EXPECT(assert_equal(scenario.pose(T), runner.predict(pim).pose(), 1e-9));
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Matrix6 estimatedCov = runner.estimatePoseCovariance(T);
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EXPECT(assert_equal(estimatedCov, runner.poseCovariance(pim), 1e-5));
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// Check noise model agreement
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EXPECT(assert_equal(p->accelerometerCovariance / kDt,
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pim.discreteAccelerometerNoiseModel(kDt)->covariance()));
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EXPECT(assert_equal(p->gyroscopeCovariance / kDt,
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pim.discreteGyroscopeNoiseModel(kDt)->covariance()));
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// Check sampled noise is kosher
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Matrix6 expected;
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expected << p->accelerometerCovariance / kDt, Z_3x3, //
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Z_3x3, p->gyroscopeCovariance / kDt;
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Matrix6 actual = runner.estimateNoiseCovariance(10000);
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EXPECT(assert_equal(expected, actual, 1e-2));
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// Check calculated covariance against Monte Carlo estimate
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Matrix9 estimatedCov = runner.estimateCovariance(T);
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EXPECT(assert_equal(estimatedCov, pim.preintMeasCov(), 1e-5));
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}
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/* ************************************************************************* */
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@ -64,26 +79,26 @@ ExpmapScenario scenario(Vector3::Zero(), Vector3(v, 0, 0));
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/* ************************************************************************* */
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TEST(ScenarioRunner, Forward) {
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using namespace forward;
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ScenarioRunner runner(&scenario, defaultParams(), kDeltaT);
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ScenarioRunner runner(&scenario, defaultParams(), kDt);
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const double T = 0.1; // seconds
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auto pim = runner.integrate(T);
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EXPECT(assert_equal(scenario.pose(T), runner.predict(pim).pose(), 1e-9));
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// Matrix6 estimatedCov = runner.estimatePoseCovariance(T);
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// EXPECT(assert_equal(estimatedCov, runner.poseCovariance(pim), 1e-5));
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// Matrix9 estimatedCov = runner.estimateCovariance(T);
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// EXPECT(assert_equal(estimatedCov, pim.preintMeasCov(), 1e-5));
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}
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/* ************************************************************************* */
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TEST(ScenarioRunner, ForwardWithBias) {
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// using namespace forward;
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// ScenarioRunner runner(&scenario, defaultParams(), kDeltaT);
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// ScenarioRunner runner(&scenario, defaultParams(), kDt);
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// const double T = 0.1; // seconds
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//
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// auto pim = runner.integrate(T, kNonZeroBias);
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// Matrix6 estimatedCov = runner.estimatePoseCovariance(T, 1000,
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// Matrix9 estimatedCov = runner.estimateCovariance(T, 1000,
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// kNonZeroBias);
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// EXPECT(assert_equal(estimatedCov, runner.poseCovariance(pim), 0.1));
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// EXPECT(assert_equal(estimatedCov, pim.preintMeasCov(), 0.1));
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}
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/* ************************************************************************* */
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@ -92,14 +107,14 @@ TEST(ScenarioRunner, Circle) {
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const double v = 2, w = 6 * kDegree;
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ExpmapScenario scenario(Vector3(0, 0, w), Vector3(v, 0, 0));
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ScenarioRunner runner(&scenario, defaultParams(), kDeltaT);
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ScenarioRunner runner(&scenario, defaultParams(), kDt);
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const double T = 0.1; // seconds
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auto pim = runner.integrate(T);
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EXPECT(assert_equal(scenario.pose(T), runner.predict(pim).pose(), 0.1));
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// Matrix6 estimatedCov = runner.estimatePoseCovariance(T);
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// EXPECT(assert_equal(estimatedCov, runner.poseCovariance(pim), 1e-5));
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// Matrix9 estimatedCov = runner.estimateCovariance(T);
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// EXPECT(assert_equal(estimatedCov, pim.preintMeasCov(), 1e-5));
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}
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/* ************************************************************************* */
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@ -109,14 +124,14 @@ TEST(ScenarioRunner, Loop) {
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const double v = 2, w = 6 * kDegree;
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ExpmapScenario scenario(Vector3(0, -w, 0), Vector3(v, 0, 0));
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ScenarioRunner runner(&scenario, defaultParams(), kDeltaT);
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ScenarioRunner runner(&scenario, defaultParams(), kDt);
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const double T = 0.1; // seconds
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auto pim = runner.integrate(T);
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EXPECT(assert_equal(scenario.pose(T), runner.predict(pim).pose(), 0.1));
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// Matrix6 estimatedCov = runner.estimatePoseCovariance(T);
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// EXPECT(assert_equal(estimatedCov, runner.poseCovariance(pim), 1e-5));
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// Matrix9 estimatedCov = runner.estimateCovariance(T);
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// EXPECT(assert_equal(estimatedCov, pim.preintMeasCov(), 1e-5));
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}
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/* ************************************************************************* */
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@ -144,8 +159,8 @@ TEST(ScenarioRunner, Accelerating) {
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auto pim = runner.integrate(T);
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EXPECT(assert_equal(scenario.pose(T), runner.predict(pim).pose(), 1e-9));
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// Matrix6 estimatedCov = runner.estimatePoseCovariance(T);
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// EXPECT(assert_equal(estimatedCov, runner.poseCovariance(pim), 0.1));
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// Matrix9 estimatedCov = runner.estimateCovariance(T);
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// EXPECT(assert_equal(estimatedCov, pim.preintMeasCov(), 0.1));
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}
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/* ************************************************************************* */
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@ -157,9 +172,9 @@ TEST(ScenarioRunner, Accelerating) {
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//
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// auto pim = runner.integrate(T,
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// kNonZeroBias);
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// Matrix6 estimatedCov = runner.estimatePoseCovariance(T, 10000,
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// Matrix9 estimatedCov = runner.estimateCovariance(T, 10000,
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// kNonZeroBias);
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// EXPECT(assert_equal(estimatedCov, runner.poseCovariance(pim), 0.1));
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// EXPECT(assert_equal(estimatedCov, pim.preintMeasCov(), 0.1));
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//}
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/* ************************************************************************* */
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@ -175,8 +190,8 @@ TEST(ScenarioRunner, AcceleratingAndRotating) {
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auto pim = runner.integrate(T);
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EXPECT(assert_equal(scenario.pose(T), runner.predict(pim).pose(), 1e-9));
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// Matrix6 estimatedCov = runner.estimatePoseCovariance(T);
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// EXPECT(assert_equal(estimatedCov, runner.poseCovariance(pim), 0.1));
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// Matrix9 estimatedCov = runner.estimateCovariance(T);
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// EXPECT(assert_equal(estimatedCov, pim.preintMeasCov(), 0.1));
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}
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/* ************************************************************************* */
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@ -205,8 +220,8 @@ TEST(ScenarioRunner, Accelerating2) {
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auto pim = runner.integrate(T);
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EXPECT(assert_equal(scenario.pose(T), runner.predict(pim).pose(), 1e-9));
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// Matrix6 estimatedCov = runner.estimatePoseCovariance(T);
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// EXPECT(assert_equal(estimatedCov, runner.poseCovariance(pim), 0.1));
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// Matrix9 estimatedCov = runner.estimateCovariance(T);
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// EXPECT(assert_equal(estimatedCov, pim.preintMeasCov(), 0.1));
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}
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/* ************************************************************************* */
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@ -218,9 +233,9 @@ TEST(ScenarioRunner, Accelerating2) {
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//
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// auto pim = runner.integrate(T,
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// kNonZeroBias);
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// Matrix6 estimatedCov = runner.estimatePoseCovariance(T, 10000,
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// Matrix9 estimatedCov = runner.estimateCovariance(T, 10000,
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// kNonZeroBias);
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// EXPECT(assert_equal(estimatedCov, runner.poseCovariance(pim), 0.1));
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// EXPECT(assert_equal(estimatedCov, pim.preintMeasCov(), 0.1));
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//}
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/* ************************************************************************* */
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@ -236,8 +251,8 @@ TEST(ScenarioRunner, AcceleratingAndRotating2) {
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auto pim = runner.integrate(T);
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EXPECT(assert_equal(scenario.pose(T), runner.predict(pim).pose(), 1e-9));
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// Matrix6 estimatedCov = runner.estimatePoseCovariance(T);
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// EXPECT(assert_equal(estimatedCov, runner.poseCovariance(pim), 0.1));
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// Matrix9 estimatedCov = runner.estimateCovariance(T);
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// EXPECT(assert_equal(estimatedCov, pim.preintMeasCov(), 0.1));
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}
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/* ************************************************************************* */
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@ -267,8 +282,8 @@ TEST(ScenarioRunner, Accelerating3) {
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auto pim = runner.integrate(T);
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EXPECT(assert_equal(scenario.pose(T), runner.predict(pim).pose(), 1e-9));
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// Matrix6 estimatedCov = runner.estimatePoseCovariance(T);
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// EXPECT(assert_equal(estimatedCov, runner.poseCovariance(pim), 0.1));
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// Matrix9 estimatedCov = runner.estimateCovariance(T);
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// EXPECT(assert_equal(estimatedCov, pim.preintMeasCov(), 0.1));
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}
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/* ************************************************************************* */
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@ -280,9 +295,9 @@ TEST(ScenarioRunner, Accelerating3) {
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//
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// auto pim = runner.integrate(T,
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// kNonZeroBias);
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// Matrix6 estimatedCov = runner.estimatePoseCovariance(T, 10000,
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// Matrix9 estimatedCov = runner.estimateCovariance(T, 10000,
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// kNonZeroBias);
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// EXPECT(assert_equal(estimatedCov, runner.poseCovariance(pim), 0.1));
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// EXPECT(assert_equal(estimatedCov, pim.preintMeasCov(), 0.1));
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//}
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/* ************************************************************************* */
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@ -298,8 +313,8 @@ TEST(ScenarioRunner, AcceleratingAndRotating3) {
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auto pim = runner.integrate(T);
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EXPECT(assert_equal(scenario.pose(T), runner.predict(pim).pose(), 1e-9));
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// Matrix6 estimatedCov = runner.estimatePoseCovariance(T);
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// EXPECT(assert_equal(estimatedCov, runner.poseCovariance(pim), 0.1));
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// Matrix9 estimatedCov = runner.estimateCovariance(T);
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// EXPECT(assert_equal(estimatedCov, pim.preintMeasCov(), 0.1));
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}
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/* ************************************************************************* */
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@ -330,8 +345,8 @@ TEST(ScenarioRunner, Accelerating4) {
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auto pim = runner.integrate(T);
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EXPECT(assert_equal(scenario.pose(T), runner.predict(pim).pose(), 1e-9));
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// Matrix6 estimatedCov = runner.estimatePoseCovariance(T);
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// EXPECT(assert_equal(estimatedCov, runner.poseCovariance(pim), 0.1));
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// Matrix9 estimatedCov = runner.estimateCovariance(T);
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// EXPECT(assert_equal(estimatedCov, pim.preintMeasCov(), 0.1));
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}
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/* ************************************************************************* */
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@ -343,9 +358,9 @@ TEST(ScenarioRunner, Accelerating4) {
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//
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// auto pim = runner.integrate(T,
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// kNonZeroBias);
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// Matrix6 estimatedCov = runner.estimatePoseCovariance(T, 10000,
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// Matrix9 estimatedCov = runner.estimateCovariance(T, 10000,
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// kNonZeroBias);
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// EXPECT(assert_equal(estimatedCov, runner.poseCovariance(pim), 0.1));
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// EXPECT(assert_equal(estimatedCov, pim.preintMeasCov(), 0.1));
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//}
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/* ************************************************************************* */
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@ -361,8 +376,8 @@ TEST(ScenarioRunner, AcceleratingAndRotating4) {
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auto pim = runner.integrate(T);
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EXPECT(assert_equal(scenario.pose(T), runner.predict(pim).pose(), 1e-9));
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// Matrix6 estimatedCov = runner.estimatePoseCovariance(T);
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// EXPECT(assert_equal(estimatedCov, runner.poseCovariance(pim), 0.1));
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// Matrix9 estimatedCov = runner.estimateCovariance(T);
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// EXPECT(assert_equal(estimatedCov, pim.preintMeasCov(), 0.1));
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}
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/* ************************************************************************* */
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