From 28d0393abd7cd94dd690b4a9b95805add462917a Mon Sep 17 00:00:00 2001 From: Varun Agrawal Date: Sun, 19 Sep 2021 10:51:24 -0400 Subject: [PATCH 01/24] add test for checking covariances between ImuFactor and CombinedImuFactor --- .../tests/testCombinedImuFactor.cpp | 443 ++++++++++-------- 1 file changed, 254 insertions(+), 189 deletions(-) diff --git a/gtsam/navigation/tests/testCombinedImuFactor.cpp b/gtsam/navigation/tests/testCombinedImuFactor.cpp index dc9ae288ae..f7acfa79e5 100644 --- a/gtsam/navigation/tests/testCombinedImuFactor.cpp +++ b/gtsam/navigation/tests/testCombinedImuFactor.cpp @@ -18,16 +18,16 @@ * @author Stephen Williams */ -#include +#include +#include +#include +#include +#include #include #include -#include +#include +#include #include -#include -#include -#include - -#include #include @@ -44,207 +44,272 @@ static boost::shared_ptr Params() { } } -/* ************************************************************************* */ -TEST( CombinedImuFactor, PreintegratedMeasurements ) { - // Linearization point - Bias bias(Vector3(0, 0, 0), Vector3(0, 0, 0)); ///< Current estimate of acceleration and angular rate biases - - // Measurements - Vector3 measuredAcc(0.1, 0.0, 0.0); - Vector3 measuredOmega(M_PI / 100.0, 0.0, 0.0); - double deltaT = 0.5; - double tol = 1e-6; - - auto p = testing::Params(); - - // Actual preintegrated values - PreintegratedImuMeasurements expected1(p, bias); - expected1.integrateMeasurement(measuredAcc, measuredOmega, deltaT); - - PreintegratedCombinedMeasurements actual1(p, bias); - - actual1.integrateMeasurement(measuredAcc, measuredOmega, deltaT); - - EXPECT(assert_equal(Vector(expected1.deltaPij()), actual1.deltaPij(), tol)); - EXPECT(assert_equal(Vector(expected1.deltaVij()), actual1.deltaVij(), tol)); - EXPECT(assert_equal(expected1.deltaRij(), actual1.deltaRij(), tol)); - DOUBLES_EQUAL(expected1.deltaTij(), actual1.deltaTij(), tol); -} - -/* ************************************************************************* */ -TEST( CombinedImuFactor, ErrorWithBiases ) { - Bias bias(Vector3(0.2, 0, 0), Vector3(0, 0, 0.3)); // Biases (acc, rot) - Bias bias2(Vector3(0.2, 0.2, 0), Vector3(1, 0, 0.3)); // Biases (acc, rot) - Pose3 x1(Rot3::Expmap(Vector3(0, 0, M_PI / 4.0)), Point3(5.0, 1.0, -50.0)); - Vector3 v1(0.5, 0.0, 0.0); - Pose3 x2(Rot3::Expmap(Vector3(0, 0, M_PI / 4.0 + M_PI / 10.0)), - Point3(5.5, 1.0, -50.0)); - Vector3 v2(0.5, 0.0, 0.0); - - auto p = testing::Params(); - p->omegaCoriolis = Vector3(0,0.1,0.1); - PreintegratedImuMeasurements pim( - p, Bias(Vector3(0.2, 0.0, 0.0), Vector3(0.0, 0.0, 0.0))); - - // Measurements - Vector3 measuredOmega; - measuredOmega << 0, 0, M_PI / 10.0 + 0.3; - Vector3 measuredAcc = - x1.rotation().unrotate(-p->n_gravity) + Vector3(0.2, 0.0, 0.0); - double deltaT = 1.0; - double tol = 1e-6; - - pim.integrateMeasurement(measuredAcc, measuredOmega, deltaT); - - PreintegratedCombinedMeasurements combined_pim(p, - Bias(Vector3(0.2, 0.0, 0.0), Vector3(0.0, 0.0, 0.0))); - - combined_pim.integrateMeasurement(measuredAcc, measuredOmega, deltaT); - - // Create factor - ImuFactor imuFactor(X(1), V(1), X(2), V(2), B(1), pim); - - noiseModel::Gaussian::shared_ptr Combinedmodel = - noiseModel::Gaussian::Covariance(combined_pim.preintMeasCov()); - CombinedImuFactor combinedfactor(X(1), V(1), X(2), V(2), B(1), B(2), - combined_pim); - - Vector errorExpected = imuFactor.evaluateError(x1, v1, x2, v2, bias); - Vector errorActual = combinedfactor.evaluateError(x1, v1, x2, v2, bias, - bias2); - EXPECT(assert_equal(errorExpected, errorActual.head(9), tol)); - - // Expected Jacobians - Matrix H1e, H2e, H3e, H4e, H5e; - (void) imuFactor.evaluateError(x1, v1, x2, v2, bias, H1e, H2e, H3e, H4e, H5e); - - // Actual Jacobians - Matrix H1a, H2a, H3a, H4a, H5a, H6a; - (void) combinedfactor.evaluateError(x1, v1, x2, v2, bias, bias2, H1a, H2a, - H3a, H4a, H5a, H6a); - - EXPECT(assert_equal(H1e, H1a.topRows(9))); - EXPECT(assert_equal(H2e, H2a.topRows(9))); - EXPECT(assert_equal(H3e, H3a.topRows(9))); - EXPECT(assert_equal(H4e, H4a.topRows(9))); - EXPECT(assert_equal(H5e, H5a.topRows(9))); -} - -/* ************************************************************************* */ -#ifdef GTSAM_TANGENT_PREINTEGRATION -TEST(CombinedImuFactor, FirstOrderPreIntegratedMeasurements) { - auto p = testing::Params(); - testing::SomeMeasurements measurements; - - auto preintegrated = [=](const Vector3& a, const Vector3& w) { - PreintegratedImuMeasurements pim(p, Bias(a, w)); - testing::integrateMeasurements(measurements, &pim); - return pim.preintegrated(); - }; - - // Actual pre-integrated values - PreintegratedCombinedMeasurements pim(p); - testing::integrateMeasurements(measurements, &pim); - - EXPECT(assert_equal(numericalDerivative21(preintegrated, Z_3x1, Z_3x1), - pim.preintegrated_H_biasAcc())); - EXPECT(assert_equal(numericalDerivative22(preintegrated, Z_3x1, Z_3x1), - pim.preintegrated_H_biasOmega(), 1e-3)); -} -#endif - -/* ************************************************************************* */ -TEST(CombinedImuFactor, PredictPositionAndVelocity) { - const Bias bias(Vector3(0, 0.1, 0), Vector3(0, 0.1, 0)); // Biases (acc, rot) - - auto p = testing::Params(); +// /* ************************************************************************* */ +// TEST(CombinedImuFactor, PreintegratedMeasurements ) { +// // Linearization point +// Bias bias(Vector3(0, 0, 0), Vector3(0, 0, 0)); ///< Current estimate of acceleration and angular rate biases + +// // Measurements +// Vector3 measuredAcc(0.1, 0.0, 0.0); +// Vector3 measuredOmega(M_PI / 100.0, 0.0, 0.0); +// double deltaT = 0.5; +// double tol = 1e-6; + +// auto p = testing::Params(); + +// // Actual preintegrated values +// PreintegratedImuMeasurements expected1(p, bias); +// expected1.integrateMeasurement(measuredAcc, measuredOmega, deltaT); + +// PreintegratedCombinedMeasurements actual1(p, bias); + +// actual1.integrateMeasurement(measuredAcc, measuredOmega, deltaT); + +// EXPECT(assert_equal(Vector(expected1.deltaPij()), actual1.deltaPij(), tol)); +// EXPECT(assert_equal(Vector(expected1.deltaVij()), actual1.deltaVij(), tol)); +// EXPECT(assert_equal(expected1.deltaRij(), actual1.deltaRij(), tol)); +// DOUBLES_EQUAL(expected1.deltaTij(), actual1.deltaTij(), tol); +// } + +// /* ************************************************************************* */ +// TEST(CombinedImuFactor, Accelerating) { +// const double a = 0.2, v = 50; + +// // Set up body pointing towards y axis, and start at 10,20,0 with velocity going in X +// // The body itself has Z axis pointing down +// const Rot3 nRb(Point3(0, 1, 0), Point3(1, 0, 0), Point3(0, 0, -1)); +// const Point3 initial_position(10, 20, 0); +// const Vector3 initial_velocity(v, 0, 0); + +// const AcceleratingScenario scenario(nRb, initial_position, initial_velocity, +// Vector3(a, 0, 0)); + +// const double T = 3.0; // seconds +// CombinedScenarioRunner runner(scenario, testing::Params(), T / 10); + +// PreintegratedCombinedMeasurements pim = runner.integrate(T); +// EXPECT(assert_equal(scenario.pose(T), runner.predict(pim).pose(), 1e-9)); + +// auto estimatedCov = runner.estimateCovariance(T, 100); +// Eigen::Matrix expected = pim.preintMeasCov(); +// // EXPECT(assert_equal(estimatedCov, expected, 0.1)); +// } + +// /* ************************************************************************* */ +// TEST(CombinedImuFactor, ErrorWithBiases ) { +// Bias bias(Vector3(0.2, 0, 0), Vector3(0, 0, 0.3)); // Biases (acc, rot) +// Bias bias2(Vector3(0.2, 0.2, 0), Vector3(1, 0, 0.3)); // Biases (acc, rot) +// Pose3 x1(Rot3::Expmap(Vector3(0, 0, M_PI / 4.0)), Point3(5.0, 1.0, -50.0)); +// Vector3 v1(0.5, 0.0, 0.0); +// Pose3 x2(Rot3::Expmap(Vector3(0, 0, M_PI / 4.0 + M_PI / 10.0)), +// Point3(5.5, 1.0, -50.0)); +// Vector3 v2(0.5, 0.0, 0.0); + +// auto p = testing::Params(); +// p->omegaCoriolis = Vector3(0,0.1,0.1); +// PreintegratedImuMeasurements pim( +// p, Bias(Vector3(0.2, 0.0, 0.0), Vector3(0.0, 0.0, 0.0))); + +// // Measurements +// Vector3 measuredOmega; +// measuredOmega << 0, 0, M_PI / 10.0 + 0.3; +// Vector3 measuredAcc = +// x1.rotation().unrotate(-p->n_gravity) + Vector3(0.2, 0.0, 0.0); +// double deltaT = 1.0; +// double tol = 1e-6; + +// pim.integrateMeasurement(measuredAcc, measuredOmega, deltaT); + +// PreintegratedCombinedMeasurements combined_pim(p, +// Bias(Vector3(0.2, 0.0, 0.0), Vector3(0.0, 0.0, 0.0))); + +// combined_pim.integrateMeasurement(measuredAcc, measuredOmega, deltaT); + +// // Create factor +// ImuFactor imuFactor(X(1), V(1), X(2), V(2), B(1), pim); + +// noiseModel::Gaussian::shared_ptr Combinedmodel = +// noiseModel::Gaussian::Covariance(combined_pim.preintMeasCov()); +// CombinedImuFactor combinedfactor(X(1), V(1), X(2), V(2), B(1), B(2), +// combined_pim); + +// Vector errorExpected = imuFactor.evaluateError(x1, v1, x2, v2, bias); +// Vector errorActual = combinedfactor.evaluateError(x1, v1, x2, v2, bias, +// bias2); +// EXPECT(assert_equal(errorExpected, errorActual.head(9), tol)); + +// // Expected Jacobians +// Matrix H1e, H2e, H3e, H4e, H5e; +// (void) imuFactor.evaluateError(x1, v1, x2, v2, bias, H1e, H2e, H3e, H4e, H5e); + +// // Actual Jacobians +// Matrix H1a, H2a, H3a, H4a, H5a, H6a; +// (void) combinedfactor.evaluateError(x1, v1, x2, v2, bias, bias2, H1a, H2a, +// H3a, H4a, H5a, H6a); + +// EXPECT(assert_equal(H1e, H1a.topRows(9))); +// EXPECT(assert_equal(H2e, H2a.topRows(9))); +// EXPECT(assert_equal(H3e, H3a.topRows(9))); +// EXPECT(assert_equal(H4e, H4a.topRows(9))); +// EXPECT(assert_equal(H5e, H5a.topRows(9))); +// } + +// /* ************************************************************************* */ +// #ifdef GTSAM_TANGENT_PREINTEGRATION +// TEST(CombinedImuFactor, FirstOrderPreIntegratedMeasurements) { +// auto p = testing::Params(); +// testing::SomeMeasurements measurements; + +// auto preintegrated = [=](const Vector3& a, const Vector3& w) { +// PreintegratedImuMeasurements pim(p, Bias(a, w)); +// testing::integrateMeasurements(measurements, &pim); +// return pim.preintegrated(); +// }; + +// // Actual pre-integrated values +// PreintegratedCombinedMeasurements pim(p); +// testing::integrateMeasurements(measurements, &pim); + +// EXPECT(assert_equal(numericalDerivative21(preintegrated, Z_3x1, Z_3x1), +// pim.preintegrated_H_biasAcc())); +// EXPECT(assert_equal(numericalDerivative22(preintegrated, Z_3x1, Z_3x1), +// pim.preintegrated_H_biasOmega(), 1e-3)); +// } +// #endif + +// /* ************************************************************************* */ +// TEST(CombinedImuFactor, PredictPositionAndVelocity) { +// const Bias bias(Vector3(0, 0.1, 0), Vector3(0, 0.1, 0)); // Biases (acc, rot) + +// auto p = testing::Params(); + +// // Measurements +// const Vector3 measuredOmega(0, 0.1, 0); // M_PI/10.0+0.3; +// const Vector3 measuredAcc(0, 1.1, -kGravity); +// const double deltaT = 0.01; + +// PreintegratedCombinedMeasurements pim(p, bias); + +// for (int i = 0; i < 100; ++i) +// pim.integrateMeasurement(measuredAcc, measuredOmega, deltaT); + +// // Create factor +// const noiseModel::Gaussian::shared_ptr combinedmodel = +// noiseModel::Gaussian::Covariance(pim.preintMeasCov()); +// const CombinedImuFactor Combinedfactor(X(1), V(1), X(2), V(2), B(1), B(2), pim); + +// // Predict +// const NavState actual = pim.predict(NavState(), bias); +// const Pose3 expectedPose(Rot3(), Point3(0, 0.5, 0)); +// const Vector3 expectedVelocity(0, 1, 0); +// EXPECT(assert_equal(expectedPose, actual.pose())); +// EXPECT(assert_equal(Vector(expectedVelocity), Vector(actual.velocity()))); +// } + +// /* ************************************************************************* */ +// TEST(CombinedImuFactor, PredictRotation) { +// const Bias bias(Vector3(0, 0, 0), Vector3(0, 0, 0)); // Biases (acc, rot) +// auto p = testing::Params(); +// PreintegratedCombinedMeasurements pim(p, bias); +// const Vector3 measuredAcc = - kGravityAlongNavZDown; +// const Vector3 measuredOmega(0, 0, M_PI / 10.0); +// const double deltaT = 0.01; +// const double tol = 1e-4; +// for (int i = 0; i < 100; ++i) +// pim.integrateMeasurement(measuredAcc, measuredOmega, deltaT); +// const CombinedImuFactor Combinedfactor(X(1), V(1), X(2), V(2), B(1), B(2), pim); + +// // Predict +// const Pose3 x(Rot3::Ypr(0, 0, 0), Point3(0, 0, 0)), x2; +// const Vector3 v(0, 0, 0), v2; +// const NavState actual = pim.predict(NavState(x, v), bias); +// const Pose3 expectedPose(Rot3::Ypr(M_PI / 10, 0, 0), Point3(0, 0, 0)); +// EXPECT(assert_equal(expectedPose, actual.pose(), tol)); +// } + +// /* ************************************************************************* */ +// // Testing covariance to check if all the jacobians are accounted for. +// TEST(CombinedImuFactor, CheckCovariance) { +// auto params = PreintegrationCombinedParams::MakeSharedU(9.81); + +// params->setAccelerometerCovariance(pow(0.01, 2) * I_3x3); +// params->setGyroscopeCovariance(pow(1.75e-4, 2) * I_3x3); +// params->setIntegrationCovariance(pow(0.0, 2) * I_3x3); +// params->setOmegaCoriolis(Vector3::Zero()); + +// imuBias::ConstantBias currentBias; + +// PreintegratedCombinedMeasurements actual(params, currentBias); + +// // Measurements +// Vector3 measuredAcc(0.1577, -0.8251, 9.6111); +// Vector3 measuredOmega(-0.0210, 0.0311, 0.0145); +// double deltaT = 0.01; + +// actual.integrateMeasurement(measuredAcc, measuredOmega, deltaT); + +// Eigen::Matrix expected; +// expected << 0.01, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, // +// 0, 0.01, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, // +// 0, 0, 0.01, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, // +// 0, 0, 0, 2.50025e-07, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, // +// 0, 0, 0, 0, 2.50025e-07, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, // +// 0, 0, 0, 0, 0, 2.50025e-07, 0, 0, 0, 0, 0, 0, 0, 0, 0, // +// 0, 0, 0, 0, 0, 0, 0.010001, 0, 0, 0, 0, 0, 0, 0, 0, // +// 0, 0, 0, 0, 0, 0, 0, 0.010001, 0, 0, 0, 0, 0, 0, 0, // +// 0, 0, 0, 0, 0, 0, 0, 0, 0.010001, 0, 0, 0, 0, 0, 0, // +// 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.01, 0, 0, 0, 0, 0, // +// 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.01, 0, 0, 0, 0, // +// 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.01, 0, 0, 0, // +// 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.01, 0, 0, // +// 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.01, 0, // +// 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.01; + +// // regression +// EXPECT(assert_equal(expected, actual.preintMeasCov())); +// } + +TEST(CombinedImuFactor, SameCovarianceCombined) { + auto params = PreintegrationCombinedParams::MakeSharedU(); - // Measurements - const Vector3 measuredOmega(0, 0.1, 0); // M_PI/10.0+0.3; - const Vector3 measuredAcc(0, 1.1, -kGravity); - const double deltaT = 0.01; - - PreintegratedCombinedMeasurements pim(p, bias); + params->setAccelerometerCovariance(pow(0.01, 2) * I_3x3); + params->setGyroscopeCovariance(pow(1.75e-4, 2) * I_3x3); + params->setIntegrationCovariance(pow(0, 2) * I_3x3); + params->setOmegaCoriolis(Vector3::Zero()); - for (int i = 0; i < 100; ++i) - pim.integrateMeasurement(measuredAcc, measuredOmega, deltaT); + imuBias::ConstantBias currentBias; - // Create factor - const noiseModel::Gaussian::shared_ptr combinedmodel = - noiseModel::Gaussian::Covariance(pim.preintMeasCov()); - const CombinedImuFactor Combinedfactor(X(1), V(1), X(2), V(2), B(1), B(2), pim); + PreintegratedCombinedMeasurements pim(params, currentBias); - // Predict - const NavState actual = pim.predict(NavState(), bias); - const Pose3 expectedPose(Rot3(), Point3(0, 0.5, 0)); - const Vector3 expectedVelocity(0, 1, 0); - EXPECT(assert_equal(expectedPose, actual.pose())); - EXPECT(assert_equal(Vector(expectedVelocity), Vector(actual.velocity()))); -} + Vector3 accMeas(0.1577, -0.8251, 9.6111); + Vector3 omegaMeas(-0.0210, 0.0311, 0.0145); + double deltaT = 0.01; + pim.integrateMeasurement(accMeas, omegaMeas, deltaT); -/* ************************************************************************* */ -TEST(CombinedImuFactor, PredictRotation) { - const Bias bias(Vector3(0, 0, 0), Vector3(0, 0, 0)); // Biases (acc, rot) - auto p = testing::Params(); - PreintegratedCombinedMeasurements pim(p, bias); - const Vector3 measuredAcc = - kGravityAlongNavZDown; - const Vector3 measuredOmega(0, 0, M_PI / 10.0); - const double deltaT = 0.01; - const double tol = 1e-4; - for (int i = 0; i < 100; ++i) - pim.integrateMeasurement(measuredAcc, measuredOmega, deltaT); - const CombinedImuFactor Combinedfactor(X(1), V(1), X(2), V(2), B(1), B(2), pim); - - // Predict - const Pose3 x(Rot3::Ypr(0, 0, 0), Point3(0, 0, 0)), x2; - const Vector3 v(0, 0, 0), v2; - const NavState actual = pim.predict(NavState(x, v), bias); - const Pose3 expectedPose(Rot3::Ypr(M_PI / 10, 0, 0), Point3(0, 0, 0)); - EXPECT(assert_equal(expectedPose, actual.pose(), tol)); + std::cout << pim.preintMeasCov() << std::endl << std::endl; } -/* ************************************************************************* */ -// Testing covariance to check if all the jacobians are accounted for. -TEST(CombinedImuFactor, CheckCovariance) { - auto params = PreintegrationCombinedParams::MakeSharedU(9.81); +TEST(CombinedImuFactor, SameCovariance) { + auto params = PreintegrationParams::MakeSharedU(); params->setAccelerometerCovariance(pow(0.01, 2) * I_3x3); params->setGyroscopeCovariance(pow(1.75e-4, 2) * I_3x3); - params->setIntegrationCovariance(pow(0.0, 2) * I_3x3); + params->setIntegrationCovariance(pow(0, 2) * I_3x3); params->setOmegaCoriolis(Vector3::Zero()); imuBias::ConstantBias currentBias; - PreintegratedCombinedMeasurements actual(params, currentBias); + PreintegratedImuMeasurements pim(params, currentBias); - // Measurements - Vector3 measuredAcc(0.1577, -0.8251, 9.6111); - Vector3 measuredOmega(-0.0210, 0.0311, 0.0145); + Vector3 accMeas(0.1577, -0.8251, 9.6111); + Vector3 omegaMeas(-0.0210, 0.0311, 0.0145); double deltaT = 0.01; + pim.integrateMeasurement(accMeas, omegaMeas, deltaT); - actual.integrateMeasurement(measuredAcc, measuredOmega, deltaT); - - Eigen::Matrix expected; - expected << 0.01, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, // - 0, 0.01, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, // - 0, 0, 0.01, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, // - 0, 0, 0, 2.50025e-07, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, // - 0, 0, 0, 0, 2.50025e-07, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, // - 0, 0, 0, 0, 0, 2.50025e-07, 0, 0, 0, 0, 0, 0, 0, 0, 0, // - 0, 0, 0, 0, 0, 0, 0.010001, 0, 0, 0, 0, 0, 0, 0, 0, // - 0, 0, 0, 0, 0, 0, 0, 0.010001, 0, 0, 0, 0, 0, 0, 0, // - 0, 0, 0, 0, 0, 0, 0, 0, 0.010001, 0, 0, 0, 0, 0, 0, // - 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.01, 0, 0, 0, 0, 0, // - 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.01, 0, 0, 0, 0, // - 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.01, 0, 0, 0, // - 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.01, 0, 0, // - 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.01, 0, // - 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.01; - - // regression - EXPECT(assert_equal(expected, actual.preintMeasCov())); + std::cout << pim.preintMeasCov() << std::endl << std::endl; } + /* ************************************************************************* */ int main() { TestResult tr; From a10c776fdae8a6df2ddb5a448648a3a7e50ad69b Mon Sep 17 00:00:00 2001 From: Varun Agrawal Date: Sun, 19 Sep 2021 10:53:25 -0400 Subject: [PATCH 02/24] print statements in ImuFactor --- gtsam/navigation/ImuFactor.cpp | 4 ++++ 1 file changed, 4 insertions(+) diff --git a/gtsam/navigation/ImuFactor.cpp b/gtsam/navigation/ImuFactor.cpp index 9b6affaaf8..c0797d0e15 100644 --- a/gtsam/navigation/ImuFactor.cpp +++ b/gtsam/navigation/ImuFactor.cpp @@ -75,12 +75,16 @@ void PreintegratedImuMeasurements::integrateMeasurement( // (1/dt) allows to pass from continuous time noise to discrete time noise // Update the uncertainty on the state (matrix A in [4]). preintMeasCov_ = A * preintMeasCov_ * A.transpose(); + // std::cout << "A * p * A\n" << preintMeasCov_ << std::endl; // These 2 updates account for uncertainty on the IMU measurement (matrix B in [4]). preintMeasCov_.noalias() += B * (aCov / dt) * B.transpose(); + // std::cout << "p + B\n" << preintMeasCov_ << std::endl; preintMeasCov_.noalias() += C * (wCov / dt) * C.transpose(); + // std::cout << "ApA' + B + C\n" << preintMeasCov_ << std::endl; // NOTE(frank): (Gi*dt)*(C/dt)*(Gi'*dt), with Gi << Z_3x3, I_3x3, Z_3x3 (9x3 matrix) preintMeasCov_.block<3, 3>(3, 3).noalias() += iCov * dt; + // std::cout << "p + iCov\n" << preintMeasCov_ << std::endl; } //------------------------------------------------------------------------------ From 65bbe6b577c0d28a91652a6247e087d63757fbf5 Mon Sep 17 00:00:00 2001 From: Varun Agrawal Date: Sun, 19 Sep 2021 10:53:41 -0400 Subject: [PATCH 03/24] typedef for Vector15 --- gtsam/base/Vector.h | 1 + 1 file changed, 1 insertion(+) diff --git a/gtsam/base/Vector.h b/gtsam/base/Vector.h index ed90a71269..9567d9980d 100644 --- a/gtsam/base/Vector.h +++ b/gtsam/base/Vector.h @@ -60,6 +60,7 @@ GTSAM_MAKE_VECTOR_DEFS(9); GTSAM_MAKE_VECTOR_DEFS(10); GTSAM_MAKE_VECTOR_DEFS(11); GTSAM_MAKE_VECTOR_DEFS(12); +GTSAM_MAKE_VECTOR_DEFS(15); typedef Eigen::VectorBlock SubVector; typedef Eigen::VectorBlock ConstSubVector; From 3a3640c5e0d94c1108eac9ef863de6bc9e0e849a Mon Sep 17 00:00:00 2001 From: Varun Agrawal Date: Sun, 19 Sep 2021 10:59:05 -0400 Subject: [PATCH 04/24] updated CombinedImuFactor covariance with additional off-diagonal elements --- gtsam/navigation/CombinedImuFactor.cpp | 15 +++++++++------ 1 file changed, 9 insertions(+), 6 deletions(-) diff --git a/gtsam/navigation/CombinedImuFactor.cpp b/gtsam/navigation/CombinedImuFactor.cpp index 24e2e3016e..cd579d716c 100644 --- a/gtsam/navigation/CombinedImuFactor.cpp +++ b/gtsam/navigation/CombinedImuFactor.cpp @@ -134,18 +134,19 @@ void PreintegratedCombinedMeasurements::integrateMeasurement( Eigen::Matrix G_measCov_Gt; G_measCov_Gt.setZero(15, 15); - Matrix3 aCov_updated = (aCov + p().biasAccOmegaInt.block<3, 3>(0, 0)); + Matrix3 aCov_updated = aCov + p().biasAccOmegaInt.block<3, 3>(0, 0); + Matrix3 wCov_updated = wCov + p().biasAccOmegaInt.block<3, 3>(3, 3); // BLOCK DIAGONAL TERMS - D_t_t(&G_measCov_Gt) = ((1 / dt) * pos_H_biasAcc - * aCov_updated - * (pos_H_biasAcc.transpose())) + (dt * iCov); + D_t_t(&G_measCov_Gt) = (pos_H_biasAcc + * (aCov / dt) // aCov_updated / dt + * pos_H_biasAcc.transpose()) + (dt * iCov); D_v_v(&G_measCov_Gt) = (1 / dt) * vel_H_biasAcc - * aCov_updated + * (aCov / dt) // aCov_updated / dt * (vel_H_biasAcc.transpose()); D_R_R(&G_measCov_Gt) = (1 / dt) * theta_H_biasOmega - * (wCov + p().biasAccOmegaInt.block<3, 3>(3, 3)) + * (wCov / dt) // wCov_updated / dt * (theta_H_biasOmega.transpose()); D_a_a(&G_measCov_Gt) = dt * p().biasAccCovariance; @@ -155,7 +156,9 @@ void PreintegratedCombinedMeasurements::integrateMeasurement( Matrix3 temp = vel_H_biasAcc * p().biasAccOmegaInt.block<3, 3>(3, 0) * theta_H_biasOmega.transpose(); D_v_R(&G_measCov_Gt) = temp; + D_v_t(&G_measCov_Gt) = vel_H_biasAcc * (aCov / dt) * pos_H_biasAcc.transpose(); D_R_v(&G_measCov_Gt) = temp.transpose(); + D_t_v(&G_measCov_Gt) = pos_H_biasAcc * (aCov / dt) * vel_H_biasAcc.transpose(); preintMeasCov_ = F * preintMeasCov_ * F.transpose() + G_measCov_Gt; } From 3132cfbc868f0e382e2be34b0eabb9ffe6761f92 Mon Sep 17 00:00:00 2001 From: Varun Agrawal Date: Sun, 19 Sep 2021 10:59:32 -0400 Subject: [PATCH 05/24] CombinedScenarioRunner --- gtsam/navigation/ScenarioRunner.cpp | 59 ++++++++++++++++++++++++++++- gtsam/navigation/ScenarioRunner.h | 44 +++++++++++++++++++-- 2 files changed, 98 insertions(+), 5 deletions(-) diff --git a/gtsam/navigation/ScenarioRunner.cpp b/gtsam/navigation/ScenarioRunner.cpp index 3938ce86c4..3a447dcab6 100644 --- a/gtsam/navigation/ScenarioRunner.cpp +++ b/gtsam/navigation/ScenarioRunner.cpp @@ -15,8 +15,8 @@ * @author Frank Dellaert */ -#include #include +#include #include #include @@ -105,4 +105,61 @@ Matrix6 ScenarioRunner::estimateNoiseCovariance(size_t N) const { return Q / (N - 1); } +PreintegratedCombinedMeasurements CombinedScenarioRunner::integrate( + double T, const Bias& estimatedBias, bool corrupted) const { + gttic_(integrate); + PreintegratedCombinedMeasurements pim(p_, estimatedBias); + + const double dt = imuSampleTime(); + const size_t nrSteps = T / dt; + double t = 0; + for (size_t k = 0; k < nrSteps; k++, t += dt) { + Vector3 measuredOmega = + corrupted ? measuredAngularVelocity(t) : actualAngularVelocity(t); + Vector3 measuredAcc = + corrupted ? measuredSpecificForce(t) : actualSpecificForce(t); + pim.integrateMeasurement(measuredAcc, measuredOmega, dt); + } + + return pim; +} + +NavState CombinedScenarioRunner::predict( + const PreintegratedCombinedMeasurements& pim, + const Bias& estimatedBias) const { + const NavState state_i(scenario().pose(0), scenario().velocity_n(0)); + return pim.predict(state_i, estimatedBias); +} + +Eigen::Matrix CombinedScenarioRunner::estimateCovariance( + double T, size_t N, const Bias& estimatedBias) const { + gttic_(estimateCovariance); + + // Get predict prediction from ground truth measurements + NavState prediction = predict(integrate(T)); + + // Sample ! + Matrix samples(15, N); + Vector15 sum = Vector15::Zero(); + for (size_t i = 0; i < N; i++) { + auto pim = integrate(T, estimatedBias, true); + NavState sampled = predict(pim); + Vector15 xi = Vector15::Zero(); + xi << sampled.localCoordinates(prediction), estimatedBias_.vector(); + samples.col(i) = xi; + sum += xi; + } + + // Compute MC covariance + Vector15 sampleMean = sum / N; + Eigen::Matrix Q; + Q.setZero(); + for (size_t i = 0; i < N; i++) { + Vector15 xi = samples.col(i) - sampleMean; + Q += xi * xi.transpose(); + } + + return Q / (N - 1); +} + } // namespace gtsam diff --git a/gtsam/navigation/ScenarioRunner.h b/gtsam/navigation/ScenarioRunner.h index 1577e36fe1..cee5a54ab6 100644 --- a/gtsam/navigation/ScenarioRunner.h +++ b/gtsam/navigation/ScenarioRunner.h @@ -16,9 +16,10 @@ */ #pragma once +#include +#include #include #include -#include namespace gtsam { @@ -66,10 +67,10 @@ class GTSAM_EXPORT ScenarioRunner { // also, uses g=10 for easy debugging const Vector3& gravity_n() const { return p_->n_gravity; } + const Scenario& scenario() const { return scenario_; } + // A gyro simply measures angular velocity in body frame - Vector3 actualAngularVelocity(double t) const { - return scenario_.omega_b(t); - } + Vector3 actualAngularVelocity(double t) const { return scenario_.omega_b(t); } // An accelerometer measures acceleration in body, but not gravity Vector3 actualSpecificForce(double t) const { @@ -106,4 +107,39 @@ class GTSAM_EXPORT ScenarioRunner { Matrix6 estimateNoiseCovariance(size_t N = 1000) const; }; +/* + * Simple class to test navigation scenarios with CombinedImuMeasurements. + * Takes a trajectory scenario as input, and can generate IMU measurements + */ +class GTSAM_EXPORT CombinedScenarioRunner : public ScenarioRunner { + public: + typedef boost::shared_ptr SharedParams; + + private: + const SharedParams p_; + const Bias estimatedBias_; + + public: + CombinedScenarioRunner(const Scenario& scenario, const SharedParams& p, + double imuSampleTime = 1.0 / 100.0, + const Bias& bias = Bias()) + : ScenarioRunner(scenario, static_cast(p), + imuSampleTime, bias), + p_(p), + estimatedBias_(bias) {} + + /// Integrate measurements for T seconds into a PIM + PreintegratedCombinedMeasurements integrate( + double T, const Bias& estimatedBias = Bias(), + bool corrupted = false) const; + + /// Predict predict given a PIM + NavState predict(const PreintegratedCombinedMeasurements& pim, + const Bias& estimatedBias = Bias()) const; + + /// Compute a Monte Carlo estimate of the predict covariance using N samples + Eigen::Matrix estimateCovariance( + double T, size_t N = 1000, const Bias& estimatedBias = Bias()) const; +}; + } // namespace gtsam From 53712149f98b8325ce91fdab22f8fc2b0f395e10 Mon Sep 17 00:00:00 2001 From: Varun Agrawal Date: Sun, 19 Sep 2021 21:15:51 -0400 Subject: [PATCH 06/24] actually test the covariances and fix bug --- gtsam/navigation/CombinedImuFactor.cpp | 4 +- .../tests/testCombinedImuFactor.cpp | 40 ++++++++----------- 2 files changed, 19 insertions(+), 25 deletions(-) diff --git a/gtsam/navigation/CombinedImuFactor.cpp b/gtsam/navigation/CombinedImuFactor.cpp index cd579d716c..c8d1b10fef 100644 --- a/gtsam/navigation/CombinedImuFactor.cpp +++ b/gtsam/navigation/CombinedImuFactor.cpp @@ -141,11 +141,11 @@ void PreintegratedCombinedMeasurements::integrateMeasurement( D_t_t(&G_measCov_Gt) = (pos_H_biasAcc * (aCov / dt) // aCov_updated / dt * pos_H_biasAcc.transpose()) + (dt * iCov); - D_v_v(&G_measCov_Gt) = (1 / dt) * vel_H_biasAcc + D_v_v(&G_measCov_Gt) = vel_H_biasAcc * (aCov / dt) // aCov_updated / dt * (vel_H_biasAcc.transpose()); - D_R_R(&G_measCov_Gt) = (1 / dt) * theta_H_biasOmega + D_R_R(&G_measCov_Gt) = theta_H_biasOmega * (wCov / dt) // wCov_updated / dt * (theta_H_biasOmega.transpose()); diff --git a/gtsam/navigation/tests/testCombinedImuFactor.cpp b/gtsam/navigation/tests/testCombinedImuFactor.cpp index f7acfa79e5..0dbf961fc6 100644 --- a/gtsam/navigation/tests/testCombinedImuFactor.cpp +++ b/gtsam/navigation/tests/testCombinedImuFactor.cpp @@ -269,27 +269,14 @@ static boost::shared_ptr Params() { // EXPECT(assert_equal(expected, actual.preintMeasCov())); // } -TEST(CombinedImuFactor, SameCovarianceCombined) { - auto params = PreintegrationCombinedParams::MakeSharedU(); - - params->setAccelerometerCovariance(pow(0.01, 2) * I_3x3); - params->setGyroscopeCovariance(pow(1.75e-4, 2) * I_3x3); - params->setIntegrationCovariance(pow(0, 2) * I_3x3); - params->setOmegaCoriolis(Vector3::Zero()); - - imuBias::ConstantBias currentBias; - - PreintegratedCombinedMeasurements pim(params, currentBias); +TEST(CombinedImuFactor, SameCovariance) { Vector3 accMeas(0.1577, -0.8251, 9.6111); Vector3 omegaMeas(-0.0210, 0.0311, 0.0145); double deltaT = 0.01; - pim.integrateMeasurement(accMeas, omegaMeas, deltaT); - - std::cout << pim.preintMeasCov() << std::endl << std::endl; -} -TEST(CombinedImuFactor, SameCovariance) { + imuBias::ConstantBias currentBias; + auto params = PreintegrationParams::MakeSharedU(); params->setAccelerometerCovariance(pow(0.01, 2) * I_3x3); @@ -297,16 +284,23 @@ TEST(CombinedImuFactor, SameCovariance) { params->setIntegrationCovariance(pow(0, 2) * I_3x3); params->setOmegaCoriolis(Vector3::Zero()); - imuBias::ConstantBias currentBias; - PreintegratedImuMeasurements pim(params, currentBias); - - Vector3 accMeas(0.1577, -0.8251, 9.6111); - Vector3 omegaMeas(-0.0210, 0.0311, 0.0145); - double deltaT = 0.01; pim.integrateMeasurement(accMeas, omegaMeas, deltaT); - std::cout << pim.preintMeasCov() << std::endl << std::endl; + // std::cout << pim.preintMeasCov() << std::endl << std::endl; + + auto combined_params = PreintegrationCombinedParams::MakeSharedU(); + + combined_params->setAccelerometerCovariance(pow(0.01, 2) * I_3x3); + combined_params->setGyroscopeCovariance(pow(1.75e-4, 2) * I_3x3); + combined_params->setIntegrationCovariance(pow(0, 2) * I_3x3); + combined_params->setOmegaCoriolis(Vector3::Zero()); + + PreintegratedCombinedMeasurements cpim(combined_params, currentBias); + cpim.integrateMeasurement(accMeas, omegaMeas, deltaT); + + // std::cout << cpim.preintMeasCov() << std::endl << std::endl; + EXPECT(assert_equal(pim.preintMeasCov(), cpim.preintMeasCov().block(0, 0, 9, 9))); } From 10a73338da8a785788bb954e26dfb7a625a3f3ff Mon Sep 17 00:00:00 2001 From: Varun Agrawal Date: Tue, 21 Sep 2021 12:28:59 -0400 Subject: [PATCH 07/24] update test with comments --- .../tests/testCombinedImuFactor.cpp | 26 +++++++++++-------- 1 file changed, 15 insertions(+), 11 deletions(-) diff --git a/gtsam/navigation/tests/testCombinedImuFactor.cpp b/gtsam/navigation/tests/testCombinedImuFactor.cpp index 0dbf961fc6..a8c0391449 100644 --- a/gtsam/navigation/tests/testCombinedImuFactor.cpp +++ b/gtsam/navigation/tests/testCombinedImuFactor.cpp @@ -75,16 +75,16 @@ static boost::shared_ptr Params() { // TEST(CombinedImuFactor, Accelerating) { // const double a = 0.2, v = 50; -// // Set up body pointing towards y axis, and start at 10,20,0 with velocity going in X -// // The body itself has Z axis pointing down +// // Set up body pointing towards y axis, and start at 10,20,0 with velocity +// // going in X The body itself has Z axis pointing down // const Rot3 nRb(Point3(0, 1, 0), Point3(1, 0, 0), Point3(0, 0, -1)); // const Point3 initial_position(10, 20, 0); // const Vector3 initial_velocity(v, 0, 0); // const AcceleratingScenario scenario(nRb, initial_position, initial_velocity, -// Vector3(a, 0, 0)); +// Vector3(a, 0, 0)); -// const double T = 3.0; // seconds +// const double T = 3.0; // seconds // CombinedScenarioRunner runner(scenario, testing::Params(), T / 10); // PreintegratedCombinedMeasurements pim = runner.integrate(T); @@ -92,7 +92,7 @@ static boost::shared_ptr Params() { // auto estimatedCov = runner.estimateCovariance(T, 100); // Eigen::Matrix expected = pim.preintMeasCov(); -// // EXPECT(assert_equal(estimatedCov, expected, 0.1)); +// EXPECT(assert_equal(estimatedCov, expected, 0.1)); // } // /* ************************************************************************* */ @@ -268,38 +268,42 @@ static boost::shared_ptr Params() { // // regression // EXPECT(assert_equal(expected, actual.preintMeasCov())); // } - +// Test that the covariance values for the ImuFactor and the CombinedImuFactor (top-left 9x9) are the same TEST(CombinedImuFactor, SameCovariance) { + // IMU measurements and time delta Vector3 accMeas(0.1577, -0.8251, 9.6111); Vector3 omegaMeas(-0.0210, 0.0311, 0.0145); double deltaT = 0.01; + // Assume zero bias imuBias::ConstantBias currentBias; + // Define params for ImuFactor auto params = PreintegrationParams::MakeSharedU(); - params->setAccelerometerCovariance(pow(0.01, 2) * I_3x3); params->setGyroscopeCovariance(pow(1.75e-4, 2) * I_3x3); params->setIntegrationCovariance(pow(0, 2) * I_3x3); params->setOmegaCoriolis(Vector3::Zero()); + // The IMU preintegration object for ImuFactor PreintegratedImuMeasurements pim(params, currentBias); pim.integrateMeasurement(accMeas, omegaMeas, deltaT); - // std::cout << pim.preintMeasCov() << std::endl << std::endl; - + // Define params for CombinedImuFactor auto combined_params = PreintegrationCombinedParams::MakeSharedU(); - combined_params->setAccelerometerCovariance(pow(0.01, 2) * I_3x3); combined_params->setGyroscopeCovariance(pow(1.75e-4, 2) * I_3x3); combined_params->setIntegrationCovariance(pow(0, 2) * I_3x3); combined_params->setOmegaCoriolis(Vector3::Zero()); + // Set bias integration covariance explicitly to zero + combined_params->setBiasAccOmegaInt(Z_6x6); + // The IMU preintegration object for CombinedImuFactor PreintegratedCombinedMeasurements cpim(combined_params, currentBias); cpim.integrateMeasurement(accMeas, omegaMeas, deltaT); - // std::cout << cpim.preintMeasCov() << std::endl << std::endl; + // Assert if the noise covariance EXPECT(assert_equal(pim.preintMeasCov(), cpim.preintMeasCov().block(0, 0, 9, 9))); } From 755c75278215739d39b36fed689d3ae0b6ca79c5 Mon Sep 17 00:00:00 2001 From: Varun Agrawal Date: Tue, 21 Sep 2021 12:29:36 -0400 Subject: [PATCH 08/24] update ImuFactor doc --- doc/ImuFactor.lyx | 41 ++++++++++++++++++++++++++++++++++------- doc/ImuFactor.pdf | Bin 225325 -> 225898 bytes 2 files changed, 34 insertions(+), 7 deletions(-) diff --git a/doc/ImuFactor.lyx b/doc/ImuFactor.lyx index bba8f212a7..c79a5f37a7 100644 --- a/doc/ImuFactor.lyx +++ b/doc/ImuFactor.lyx @@ -1427,15 +1427,34 @@ pose/velocity/bias \begin_layout Standard We expand the state vector as -\begin_inset Formula $\zeta_{k}=[\theta_{k},p_{k},v_{k},a_{k}^{b}, \omega_{k}^{b}]$ +\begin_inset Formula $\zeta_{k}=[\theta_{k},p_{k},v_{k},b_{k}^{a},b_{k}^{\omega}]$ \end_inset -. - For the jacobian + to include the bias terms. + This gives the noise propagation equation as +\end_layout + +\begin_layout Standard +\begin_inset Formula +\begin{equation} +\Sigma_{k+1}=F_{k}\Sigma_{k}F_{k}^{T}+G_{k}\Sigma_{k}G_{k}\label{eq:prop-combined} +\end{equation} + +\end_inset + + +\end_layout + +\begin_layout Standard +where \begin_inset Formula $F_{k}$ \end_inset - of + is the +\begin_inset Formula $15\times15$ +\end_inset + + derivative of \begin_inset Formula $f$ \end_inset @@ -1443,13 +1462,21 @@ We expand the state vector as \begin_inset Formula $\zeta$ \end_inset -, we get a +, and +\begin_inset Formula $G_{k}$ +\end_inset + + is the \begin_inset Formula $15\times15$ \end_inset - matrix. + matrix for first order uncertainty propagation. 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From bbde7b980c732a3e70db397e1d3f43a33eaa7e61 Mon Sep 17 00:00:00 2001 From: Varun Agrawal Date: Tue, 21 Sep 2021 12:29:45 -0400 Subject: [PATCH 09/24] remove print statements --- gtsam/navigation/ImuFactor.cpp | 4 ---- 1 file changed, 4 deletions(-) diff --git a/gtsam/navigation/ImuFactor.cpp b/gtsam/navigation/ImuFactor.cpp index c0797d0e15..9b6affaaf8 100644 --- a/gtsam/navigation/ImuFactor.cpp +++ b/gtsam/navigation/ImuFactor.cpp @@ -75,16 +75,12 @@ void PreintegratedImuMeasurements::integrateMeasurement( // (1/dt) allows to pass from continuous time noise to discrete time noise // Update the uncertainty on the state (matrix A in [4]). preintMeasCov_ = A * preintMeasCov_ * A.transpose(); - // std::cout << "A * p * A\n" << preintMeasCov_ << std::endl; // These 2 updates account for uncertainty on the IMU measurement (matrix B in [4]). preintMeasCov_.noalias() += B * (aCov / dt) * B.transpose(); - // std::cout << "p + B\n" << preintMeasCov_ << std::endl; preintMeasCov_.noalias() += C * (wCov / dt) * C.transpose(); - // std::cout << "ApA' + B + C\n" << preintMeasCov_ << std::endl; // NOTE(frank): (Gi*dt)*(C/dt)*(Gi'*dt), with Gi << Z_3x3, I_3x3, Z_3x3 (9x3 matrix) preintMeasCov_.block<3, 3>(3, 3).noalias() += iCov * dt; - // std::cout << "p + iCov\n" << preintMeasCov_ << std::endl; } //------------------------------------------------------------------------------ From a2bf0c4da4e3ac52a99da716f4067e0fc70b5b53 Mon Sep 17 00:00:00 2001 From: Varun Agrawal Date: Tue, 21 Sep 2021 12:30:04 -0400 Subject: [PATCH 10/24] minor refactoring --- gtsam/navigation/CombinedImuFactor.cpp | 17 ++++++++++------- 1 file changed, 10 insertions(+), 7 deletions(-) diff --git a/gtsam/navigation/CombinedImuFactor.cpp b/gtsam/navigation/CombinedImuFactor.cpp index c8d1b10fef..de4d3f66db 100644 --- a/gtsam/navigation/CombinedImuFactor.cpp +++ b/gtsam/navigation/CombinedImuFactor.cpp @@ -123,6 +123,9 @@ void PreintegratedCombinedMeasurements::integrateMeasurement( F.block<3, 3>(6, 9) = vel_H_biasAcc; F.block<6, 6>(9, 9) = I_6x6; + // Update the uncertainty on the state (matrix F in [4]). + preintMeasCov_ = F * preintMeasCov_ * F.transpose(); + // propagate uncertainty // TODO(frank): use noiseModel routine so we can have arbitrary noise models. const Matrix3& aCov = p().accelerometerCovariance; @@ -138,15 +141,15 @@ void PreintegratedCombinedMeasurements::integrateMeasurement( Matrix3 wCov_updated = wCov + p().biasAccOmegaInt.block<3, 3>(3, 3); // BLOCK DIAGONAL TERMS - D_t_t(&G_measCov_Gt) = (pos_H_biasAcc - * (aCov / dt) // aCov_updated / dt + D_t_t(&G_measCov_Gt) = (pos_H_biasAcc // + * (aCov_updated / dt) // * pos_H_biasAcc.transpose()) + (dt * iCov); - D_v_v(&G_measCov_Gt) = vel_H_biasAcc - * (aCov / dt) // aCov_updated / dt + D_v_v(&G_measCov_Gt) = vel_H_biasAcc // + * (aCov_updated / dt) // * (vel_H_biasAcc.transpose()); - D_R_R(&G_measCov_Gt) = theta_H_biasOmega - * (wCov / dt) // wCov_updated / dt + D_R_R(&G_measCov_Gt) = theta_H_biasOmega // + * (wCov_updated / dt) // * (theta_H_biasOmega.transpose()); D_a_a(&G_measCov_Gt) = dt * p().biasAccCovariance; @@ -160,7 +163,7 @@ void PreintegratedCombinedMeasurements::integrateMeasurement( D_R_v(&G_measCov_Gt) = temp.transpose(); D_t_v(&G_measCov_Gt) = pos_H_biasAcc * (aCov / dt) * vel_H_biasAcc.transpose(); - preintMeasCov_ = F * preintMeasCov_ * F.transpose() + G_measCov_Gt; + preintMeasCov_.noalias() += G_measCov_Gt; } //------------------------------------------------------------------------------ From aa4a163480424688835c68384c6ae7aad239ca15 Mon Sep 17 00:00:00 2001 From: Varun Agrawal Date: Tue, 28 Sep 2021 11:45:31 -0400 Subject: [PATCH 11/24] updated ImuFactor doc with details about CombinedImuFactor --- doc/ImuFactor.lyx | 542 ++++++++++++++++++++++++++++++++++++++++++---- doc/ImuFactor.pdf | Bin 225898 -> 243257 bytes doc/refs.bib | 68 ++++-- 3 files changed, 547 insertions(+), 63 deletions(-) diff --git a/doc/ImuFactor.lyx b/doc/ImuFactor.lyx index c79a5f37a7..4b71a29ed7 100644 --- a/doc/ImuFactor.lyx +++ b/doc/ImuFactor.lyx @@ -108,6 +108,222 @@ filename "macros.lyx" \end_layout +\begin_layout Standard +\begin_inset FormulaMacro +\newcommand{\Rnine}{\mathfrak{\mathbb{R}^{9}}} +{\mathfrak{\mathbb{R}^{9}}} +\end_inset + + +\end_layout + +\begin_layout Standard +\begin_inset FormulaMacro +\newcommand{\Rninethree}{\mathfrak{\mathbb{R}^{9\times3}}} +{\mathfrak{\mathbb{R}^{9\times3}}} +\end_inset + + +\end_layout + +\begin_layout Standard +\begin_inset FormulaMacro +\newcommand{\Rninesix}{\mathfrak{\mathbb{R}^{9\times6}}} +{\mathfrak{\mathbb{R}^{9\times6}}} +\end_inset + + +\end_layout + +\begin_layout Standard +\begin_inset FormulaMacro +\newcommand{\Rninenine}{\mathfrak{\mathbb{R}^{9\times9}}} +{\mathfrak{\mathbb{R}^{9\times9}}} +\end_inset + + +\end_layout + +\begin_layout Subsubsection* +IMU Factor +\end_layout + +\begin_layout Standard +The IMU factor has 2 variants: +\end_layout + +\begin_layout Enumerate +ImuFactor is a 5-way factor between the previous pose and velocity, the + current pose and velocity, and the current IMU bias. +\end_layout + +\begin_layout Enumerate +ImuFactor2 is a 3-way factor between the previous NavState, the current + NavState and the current IMU bias. +\end_layout + +\begin_layout Standard +Both variants take a PreintegratedMeasurements object which encodes all + the IMU measurements between the previous timestep and the current timestep. +\end_layout + +\begin_layout Standard +There are also 2 variants of this class: +\end_layout + +\begin_layout Enumerate +Manifold Preintegration: This version keeps track of the incremental NavState + +\begin_inset Formula $\Delta X_{ij}$ +\end_inset + + with respect to the previous NavState, on the NavState manifold itself. + It also keeps track of the +\begin_inset Formula $\Rninesix$ +\end_inset + + Jacobian of +\begin_inset Formula $\Delta X_{ij}$ +\end_inset + + w.r.t. + the bias. + This corresponds to Forster et. + al. +\begin_inset CommandInset citation +LatexCommand cite +key "Forster15rss" +literal "false" + +\end_inset + + +\end_layout + +\begin_layout Enumerate +Tangent Preintegration: This version keeps track of the incremental NavState + in the NavState tangent space instead. + This is a +\begin_inset Formula $\Rnine$ +\end_inset + + vector +\emph on +preintegrated_ +\emph default +. + It also keeps track of the +\begin_inset Formula $\Rninesix$ +\end_inset + + jacobian of the +\emph on +preintegrated_ +\emph default + w.r.t. + the bias. + +\end_layout + +\begin_layout Standard +The main function of a factor is to calculate an error. + The easiest case to look at is the NavState variant in ImuFactor2, which + is given as: +\begin_inset Formula +\begin{equation} +\Delta X_{ij}=X_{j}-\hat{X_{ij}}\label{eq:imu-factor-error} +\end{equation} + +\end_inset + + +\end_layout + +\begin_layout Subsubsection* +Combined IMU Factor +\end_layout + +\begin_layout Standard +The IMU factor above requires that bias drift over time be modeled as a + separate stochastic process (using a BetweenFactor for example), a crucial + aspect given that the preintegrated measurements depend on these bias values + and are thus correlated. + For this reason, we provide another type of IMU factor which we term the + Combined IMU Factor. + This factor similarly has 2 variants: +\end_layout + +\begin_layout Enumerate +CombinedImuFactor is a 6-way factor between the previous pose, velocity + and IMU bias and the current pose, velocity and IMU bias. +\end_layout + +\begin_layout Enumerate +CombinedImuFactor2 is a 4-way factor between the previous NavState and IMU + bias and the current NavState and IMU bias. +\end_layout + +\begin_layout Subsubsection* +Covariance Matrices +\end_layout + +\begin_layout Standard +For IMU preintegration, it is important to propagate the uncertainty accurately + as well. + As such, we detail the various covariance matrices used in the preintegration + step. +\end_layout + +\begin_layout Itemize +Gyroscope Covariance +\begin_inset Formula $Q_{\omega}$ +\end_inset + +: Measurement uncertainty of the gyroscope. +\end_layout + +\begin_layout Itemize +Accelerometer Covariance +\begin_inset Formula $Q_{acc}$ +\end_inset + + : Measurement uncertainty of the accelerometer. +\end_layout + +\begin_layout Itemize +Accelerometer Bias Covariance +\begin_inset Formula $Q_{\Delta b^{acc}}$ +\end_inset + + : The covariance associated with the accelerometer bias random walk. +\end_layout + +\begin_layout Itemize +Gyroscope Bias Covariance +\begin_inset Formula $Q_{\Delta b^{\omega}}$ +\end_inset + + : The covariance associated with the gyroscope bias random walk. +\end_layout + +\begin_layout Itemize +Integration Covariance +\begin_inset Formula $Q_{int}$ +\end_inset + + : This is the uncertainty due to modeling errors in the integration from + acceleration to velocity and position. +\end_layout + +\begin_layout Itemize +Initial Bias Estimate Covariance +\begin_inset Formula $Q_{init}$ +\end_inset + + : This is the uncertainty associated with the estimation of the bias (since + we jointly estimate the bias as well). +\end_layout + \begin_layout Subsubsection* Navigation States \end_layout @@ -725,15 +941,6 @@ In other words, the vector field Retractions \end_layout -\begin_layout Standard -\begin_inset FormulaMacro -\newcommand{\Rnine}{\mathfrak{\mathbb{R}^{9}}} -{\mathfrak{\mathbb{R}^{9}}} -\end_inset - - -\end_layout - \begin_layout Standard Note that the use of the exponential map in local coordinate mappings is not obligatory, even in the context of Lie groups. @@ -1018,7 +1225,15 @@ In the IMU factor, we need to predict the NavState needs to be known in order to compensate properly for the initial velocity and rotated gravity vector. - Hence, the idea of Lupton was to split up + Hence, the idea of Lupton +\begin_inset CommandInset citation +LatexCommand cite +key "Lupton12tro" +literal "false" + +\end_inset + + was to split up \begin_inset Formula $v(t)$ \end_inset @@ -1075,8 +1290,11 @@ p_{g}(t) & = & R_{i}^{T}\frac{gt^{2}}{2} \end_inset -The recipe for the IMU factor is then, in summary. - Solve the ordinary differential equations +The recipe for the IMU factor is then, in summary: +\end_layout + +\begin_layout Enumerate +Solve the ordinary differential equations \begin_inset Formula \begin{eqnarray*} \dot{\theta}(t) & = & H(\theta(t))^{-1}\,\omega^{b}(t)\\ @@ -1095,7 +1313,10 @@ starting from zero, up to time \end_inset at all times. - Form the local coordinate vector as +\end_layout + +\begin_layout Enumerate +Form the local coordinate vector as \begin_inset Formula \[ \zeta(t_{ij})=\left[\theta(t_{ij}),p(t_{ij}),v(t_{ij})\right]=\left[\theta(t_{ij}),R_{i}^{T}V_{i}t_{ij}+R_{i}^{T}\frac{gt_{ij}^{2}}{2}+p_{v}(t_{ij}),R_{i}^{T}gt_{ij}+v_{a}(t_{ij})\right] @@ -1103,6 +1324,10 @@ starting from zero, up to time \end_inset + +\end_layout + +\begin_layout Enumerate Predict the NavState \begin_inset Formula $X_{j}$ \end_inset @@ -1197,7 +1422,50 @@ where we defined the rotation matrix \end_layout \begin_layout Subsubsection* -Noise Propagation +Noise Modeling +\end_layout + +\begin_layout Standard +Given the above solutions to the differential equations, we add noise modeling + to account for the various sources of error in the system +\end_layout + +\begin_layout Standard +\begin_inset Formula +\begin{eqnarray} +\theta_{k+1} & = & \theta_{k}+H(\theta_{k})^{-1}\,(\omega_{k}^{b}+\epsilon_{k}^{\omega} -b_{k}^{\omega}-\epsilon_{init}^{\omega})\Delta_{t}\nonumber \\ +p_{k+1} & = & p_{k}+v_{k}\Delta_{t}+R_{k}(a_{k}^{b}+\epsilon_{k}^{a}-b_{k}^{a}-\epsilon_{init}^{a})\frac{\Delta_{t}^{2}}{2}+\epsilon_{k}^{int}\label{eq:preintegration}\\ +v_{k+1} & = & v_{k}+R_{k}(a_{k}^{b}+\epsilon_{k}^{a}-b_{k}^{a}-\epsilon_{init}^{a})\Delta_{t}\nonumber \\ +b_{k+1}^{a} & = & b_{k}^{a}+\epsilon_{k}^{b^{a}}\nonumber \\ +b_{k+1}^{\omega} & = & b_{k}^{\omega}+\epsilon_{k}^{b^{\omega}}\nonumber +\end{eqnarray} + +\end_inset + + +\end_layout + +\begin_layout Standard +which we can write compactly as, +\end_layout + +\begin_layout Standard +\begin_inset Formula +\begin{eqnarray} +\theta_{k+1} & = & f_{\theta}(\theta_{k},b_{k}^{w},\epsilon_{k}^{\omega},\epsilon_{init}^{b^{\omega}})\label{eq:compact-preintegration}\\ +p_{k+1} & = & f_{p}(p_{k},v_{k},\theta_{k},b_{k}^{a},\epsilon_{k}^{a},\epsilon_{init}^{a},\epsilon_{k}^{int})\nonumber \\ +v_{k+1} & = & f_{v}(v_{k,}\theta_{k,}b_{k}^{a},\epsilon_{k}^{a},\epsilon_{init}^{a})\nonumber \\ +b_{k+1}^{a} & = & f_{b^{a}}(b_{k}^{a},\epsilon_{k}^{b^{a}})\nonumber \\ +b_{k+1}^{\omega} & = & f_{b^{\omega}}(b_{k}^{\omega},\epsilon_{k}^{b^{\omega}})\nonumber +\end{eqnarray} + +\end_inset + + +\end_layout + +\begin_layout Subsubsection* +Noise Propagation in IMU Factor \end_layout \begin_layout Standard @@ -1257,7 +1525,7 @@ Then the noise on propagates as \begin_inset Formula \begin{equation} -\Sigma_{k+1}=A_{k}\Sigma_{k}A_{k}^{T}+B_{k}\Sigma_{\eta}^{ad}B_{k}+C_{k}\Sigma_{\eta}^{gd}C_{k}\label{eq:prop} +\Sigma_{k+1}=A_{k}\Sigma_{k}A_{k}^{T}+B_{k}\Sigma_{\eta}^{ad}B_{k}^{T}+C_{k}\Sigma_{\eta}^{gd}C_{k}^{T}\label{eq:prop} \end{equation} \end_inset @@ -1313,7 +1581,7 @@ We start with the noise propagation on \begin_layout Standard \begin_inset Formula \[ -\deriv{\theta_{k+1}}{\theta_{k}}=I_{3x3}+\deriv{H(\theta_{k})^{-1}\omega_{k}^{b}}{\theta_{k}}\Delta_{t} +\deriv{\theta_{k+1}}{\theta_{k}}=I_{3\times3}+\deriv{H(\theta_{k})^{-1}\omega_{k}^{b}}{\theta_{k}}\Delta_{t} \] \end_inset @@ -1325,7 +1593,7 @@ It can be shown that for small we have \begin_inset Formula \[ -\deriv{H(\theta_{k})^{-1}\omega_{k}^{b}}{\theta_{k}}\approx-\frac{1}{2}\Skew{\omega_{k}^{b}}\mbox{ and hence }\deriv{\theta_{k+1}}{\theta_{k}}=I_{3x3}-\frac{\Delta t}{2}\Skew{\omega_{k}^{b}} +\deriv{H(\theta_{k})^{-1}\omega_{k}^{b}}{\theta_{k}}\approx-\frac{1}{2}\Skew{\omega_{k}^{b}}\mbox{ and hence }\deriv{\theta_{k+1}}{\theta_{k}}=I_{3\times3}-\frac{\Delta t}{2}\Skew{\omega_{k}^{b}} \] \end_inset @@ -1375,9 +1643,9 @@ Putting all this together, we finally obtain \begin_inset Formula \[ A_{k}\approx\left[\begin{array}{ccc} -I_{3\times3}-\frac{\Delta_{t}}{2}\Skew{\omega_{k}^{b}}\\ +I_{3\times3}-\frac{\Delta_{t}}{2}\Skew{\omega_{k}^{b}} & 0_{3\times3} & 0_{3\times3}\\ R_{k}\Skew{-a_{k}^{b}}H(\theta_{k})\frac{\Delta_{t}}{2}^{2} & I_{3\times3} & I_{3\times3}\Delta_{t}\\ -R_{k}\Skew{-a_{k}^{b}}H(\theta_{k})\Delta_{t} & & I_{3\times3} +R_{k}\Skew{-a_{k}^{b}}H(\theta_{k})\Delta_{t} & 0_{3\times3} & I_{3\times3} \end{array}\right] \] @@ -1403,26 +1671,12 @@ H(\theta_{k})^{-1}\Delta_{t}\\ \end_layout \begin_layout Subsubsection* -Combined IMU Factor +Noise Propagation in Combined IMU Factor \end_layout \begin_layout Standard We can similarly account for bias drift over time, as is commonly seen in commercial grade IMUs. - This is accomplished via the -\emph on -CombinedImuFactor -\emph default - which is a 6-way factor between the previous -\emph on -pose/velocity/bias -\emph default - and the -\emph on -pose/velocity/bias -\emph default - at the next timestep. - \end_layout \begin_layout Standard @@ -1430,14 +1684,18 @@ We expand the state vector as \begin_inset Formula $\zeta_{k}=[\theta_{k},p_{k},v_{k},b_{k}^{a},b_{k}^{\omega}]$ \end_inset - to include the bias terms. + to include the bias terms and define the augmented noise vector +\begin_inset Formula $\epsilon=[\epsilon_{k}^{\omega},\epsilon_{k}^{a},\epsilon_{k}^{b^{a}},\epsilon_{k}^{b^{\omega}},\epsilon_{k}^{int},\epsilon_{init}^{b^{a}},\epsilon_{init}^{b^{\omega}}]$ +\end_inset + +. This gives the noise propagation equation as \end_layout \begin_layout Standard \begin_inset Formula \begin{equation} -\Sigma_{k+1}=F_{k}\Sigma_{k}F_{k}^{T}+G_{k}\Sigma_{k}G_{k}\label{eq:prop-combined} +\Sigma_{k+1}=F_{k}\Sigma_{k}F_{k}^{T}+G_{k}Q_{k}G_{k}^{T}\label{eq:prop-combined} \end{equation} \end_inset @@ -1467,10 +1725,19 @@ where \end_inset is the -\begin_inset Formula $15\times15$ +\begin_inset Formula $15\times21$ \end_inset matrix for first order uncertainty propagation. + +\begin_inset Formula $Q_{k}$ +\end_inset + + defines the uncertainty of +\begin_inset Formula $\eta$ +\end_inset + +. The top-left \begin_inset Formula $9\times9$ \end_inset @@ -1509,22 +1776,213 @@ derivation as matrices \begin_inset Formula \[ F_{k}\approx\left[\begin{array}{ccccc} -I_{3\times3}-\frac{\Delta_{t}}{2}\Skew{\omega_{k}^{b}} & & & & H(\theta_{k})^{-1}\Delta_{t}\\ -R_{k}\Skew{-a_{k}^{b}}H(\theta_{k})\frac{\Delta_{t}}{2}^{2} & I_{3\times3} & I_{3\times3}\Delta_{t} & R_{k}\frac{\Delta_{t}}{2}^{2}\\ -R_{k}\Skew{-a_{k}^{b}}H(\theta_{k})\Delta_{t} & & I_{3\times3} & R_{k}\Delta_{t}\\ - & & & I_{3\times3}\\ - & & & & I_{3\times3} +I_{3\times3}-\frac{\Delta_{t}}{2}\Skew{\omega_{k}^{b}} & 0_{3\times3} & 0_{3\times3} & 0_{3\times3} & H(\theta_{k})^{-1}\Delta_{t}\\ +R_{k}\Skew{-a_{k}^{b}}H(\theta_{k})\frac{\Delta_{t}}{2}^{2} & I_{3\times3} & I_{3\times3}\Delta_{t} & R_{k}\frac{\Delta_{t}}{2}^{2} & 0_{3\times3}\\ +R_{k}\Skew{-a_{k}^{b}}H(\theta_{k})\Delta_{t} & 0_{3\times3} & I_{3\times3} & R_{k}\Delta_{t} & 0_{3\times3}\\ +0_{3\times3} & 0_{3\times3} & 0_{3\times3} & I_{3\times3} & 0_{3\times3}\\ +0_{3\times3} & 0_{3\times3} & 0_{3\times3} & 0_{3\times3} & I_{3\times3} \end{array}\right] \] \end_inset +\end_layout + +\begin_layout Standard +Similarly for +\begin_inset Formula $Q_{k},$ +\end_inset + +we get +\end_layout + +\begin_layout Standard +\begin_inset Formula +\[ +Q_{k}=\left[\begin{array}{ccccccc} +\Sigma^{\omega}\\ + & \Sigma^{a}\\ + & & \Sigma^{b^{a}}\\ + & & & \Sigma^{b^{\omega}}\\ + & & & & \Sigma^{int}\\ + & & & & & \Sigma^{init_{11}} & \Sigma^{init_{12}}\\ + & & & & & \Sigma^{init_{21}} & \Sigma^{init_{22}} +\end{array}\right] +\] + +\end_inset + + +\end_layout + +\begin_layout Standard +and for +\begin_inset Formula $G_{k}$ +\end_inset + + we get +\end_layout + +\begin_layout Standard +\begin_inset Formula +\[ +G_{k}=\left[\begin{array}{ccccccc} +\deriv{\theta}{\epsilon^{\omega}} & \deriv{\theta}{\epsilon^{a}} & \deriv{\theta}{\epsilon^{b^{a}}} & \deriv{\theta}{\epsilon^{b^{\omega}}} & \deriv{\theta}{\epsilon^{int}} & \deriv{\theta}{\epsilon_{init}^{b^{a}}} & \deriv{\theta}{\epsilon_{init}^{b^{\omega}}}\\ +\deriv p{\epsilon^{\omega}} & \deriv p{\epsilon^{a}} & \deriv p{\epsilon^{b^{a}}} & \deriv p{\epsilon^{b^{\omega}}} & \deriv p{\epsilon^{int}} & \deriv p{\epsilon_{init}^{b^{a}}} & \deriv p{\epsilon_{init}^{b^{\omega}}}\\ +\deriv v{\epsilon^{\omega}} & \deriv v{\epsilon^{a}} & \deriv v{\epsilon^{b^{a}}} & \deriv v{\epsilon^{b^{\omega}}} & \deriv v{\epsilon^{int}} & \deriv v{\epsilon_{init}^{b^{a}}} & \deriv v{\epsilon_{init}^{b^{\omega}}}\\ +\deriv{b^{a}}{\epsilon^{\omega}} & \deriv{b^{a}}{\epsilon^{a}} & \deriv{b^{a}}{\epsilon^{b^{a}}} & \deriv{b^{a}}{\epsilon^{b^{\omega}}} & \deriv{b^{a}}{\epsilon^{int}} & \deriv{b^{a}}{\epsilon_{init}^{b^{a}}} & \deriv{b^{a}}{\epsilon_{init}^{b^{\omega}}}\\ +\deriv{b^{\omega}}{\epsilon^{\omega}} & \deriv{b^{\omega}}{\epsilon^{a}} & \deriv{b^{\omega}}{\epsilon^{b^{a}}} & \deriv{b^{\omega}}{\epsilon^{b^{\omega}}} & \deriv{b^{\omega}}{\epsilon^{int}} & \deriv{b^{\omega}}{\epsilon_{init}^{b^{a}}} & \deriv{b^{\omega}}{\epsilon_{init}^{b^{\omega}}} +\end{array}\right]=\left[\begin{array}{ccccccc} +\deriv{\theta}{\epsilon^{\omega}} & 0 & 0 & 0 & 0 & 0 & \deriv{\theta}{\eta_{init}^{b^{\omega}}}\\ +0 & \deriv p{\epsilon^{a}} & 0 & 0 & \deriv p{\epsilon^{int}} & \deriv p{\eta_{init}^{b^{a}}} & 0\\ +0 & \deriv v{\epsilon^{a}} & 0 & 0 & 0 & \deriv v{\eta_{init}^{b^{a}}} & 0\\ +0 & 0 & I_{3\times3} & 0 & 0 & 0 & 0\\ +0 & 0 & 0 & I_{3\times3} & 0 & 0 & 0 +\end{array}\right] +\] + +\end_inset + + +\end_layout + +\begin_layout Standard +We can perform the block-wise computation of +\begin_inset Formula $G_{k}Q_{k}G_{k}^{T}$ +\end_inset + + +\end_layout + +\begin_layout Standard +\begin_inset Formula +\[ +G_{k}Q_{k}G_{k}^{T}=\left[\begin{array}{ccccccc} +\deriv{\theta}{\epsilon^{\omega}} & 0 & 0 & 0 & 0 & 0 & \deriv{\theta}{\eta_{init}^{b^{\omega}}}\\ +0 & \deriv p{\epsilon^{a}} & 0 & 0 & \deriv p{\epsilon^{int}} & \deriv p{\eta_{init}^{b^{a}}} & 0\\ +0 & \deriv v{\epsilon^{a}} & 0 & 0 & 0 & \deriv v{\eta_{init}^{b^{a}}} & 0\\ +0 & 0 & I_{3\times3} & 0 & 0 & 0 & 0\\ +0 & 0 & 0 & I_{3\times3} & 0 & 0 & 0 +\end{array}\right]\left[\begin{array}{ccccccc} +\Sigma^{\omega}\\ + & \Sigma^{a}\\ + & & \Sigma^{b^{a}}\\ + & & & \Sigma^{b^{\omega}}\\ + & & & & \Sigma^{int}\\ + & & & & & \Sigma^{init_{11}} & \Sigma^{init_{12}}\\ + & & & & & \Sigma^{init_{21}} & \Sigma^{init_{22}} +\end{array}\right]G_{k}^{T} +\] + +\end_inset + + +\end_layout + +\begin_layout Standard +\begin_inset Formula +\[ +G_{k}Q_{k}G_{k}^{T}=\left[\begin{array}{ccccccc} +\deriv{\theta}{\epsilon^{\omega}}\Sigma^{\omega} & 0 & 0 & 0 & 0 & \deriv{\theta}{\eta_{init}^{b^{\omega}}}\Sigma^{init_{21}} & \deriv{\theta}{\eta_{init}^{b^{\omega}}}\Sigma^{init_{22}}\\ +0 & \deriv p{\epsilon^{a}}\Sigma^{a} & 0 & 0 & \deriv p{\epsilon^{int}}\Sigma^{int} & \deriv p{\eta_{init}^{b^{a}}}\Sigma^{init_{11}} & \deriv p{\eta_{init}^{b^{a}}}\Sigma^{init_{12}}\\ +0 & \deriv v{\epsilon^{a}}\Sigma^{a} & 0 & 0 & 0 & \deriv v{\eta_{init}^{b^{a}}}\Sigma^{init_{11}} & \deriv v{\eta_{init}^{b^{a}}}\Sigma^{init_{12}}\\ +0 & 0 & \Sigma^{b^{a}} & 0 & 0 & 0 & 0\\ +0 & 0 & 0 & \Sigma^{b^{\omega}} & 0 & 0 & 0 +\end{array}\right]G_{k}^{T} +\] + +\end_inset + + +\end_layout + +\begin_layout Standard +\begin_inset Formula +\begin{multline*} +G_{k}Q_{k}G_{k}^{T}=\left[\begin{array}{ccccccc} +\deriv{\theta}{\epsilon^{\omega}}\Sigma^{\omega} & 0 & 0 & 0 & 0 & \deriv{\theta}{\eta_{init}^{b^{\omega}}}\Sigma^{init_{21}} & \deriv{\theta}{\eta_{init}^{b^{\omega}}}\Sigma^{init_{22}}\\ +0 & \deriv p{\epsilon^{a}}\Sigma^{a} & 0 & 0 & \deriv p{\epsilon^{int}}\Sigma^{int} & \deriv p{\eta_{init}^{b^{a}}}\Sigma^{init_{11}} & \deriv p{\eta_{init}^{b^{a}}}\Sigma^{init_{12}}\\ +0 & \deriv v{\epsilon^{a}}\Sigma^{a} & 0 & 0 & 0 & \deriv v{\eta_{init}^{b^{a}}}\Sigma^{init_{11}} & \deriv v{\eta_{init}^{b^{a}}}\Sigma^{init_{12}}\\ +0 & 0 & \Sigma^{b^{a}} & 0 & 0 & 0 & 0\\ +0 & 0 & 0 & \Sigma^{b^{\omega}} & 0 & 0 & 0 +\end{array}\right]\\ +\left[\begin{array}{ccccc} +\deriv{\theta}{\epsilon^{\omega}} & 0 & 0 & 0 & 0\\ +0 & \deriv p{\epsilon^{a}} & \deriv v{\epsilon^{a}} & 0 & 0\\ +0 & 0 & 0 & I_{3\times3} & 0\\ +0 & 0 & 0 & 0 & I_{3\times3}\\ +0 & \deriv p{\epsilon^{int}} & 0 & 0 & 0\\ +0 & \deriv p{\eta_{init}^{b^{a}}} & \deriv v{\eta_{init}^{b^{a}}} & 0 & 0\\ +\deriv{\theta}{\eta_{init}^{b^{\omega}}} & 0 & 0 & 0 & 0 +\end{array}\right] +\end{multline*} + +\end_inset + + +\end_layout + +\begin_layout Standard +\begin_inset Formula +\begin{multline*} +=\\ +\left[\begin{array}{ccccc} +\deriv{\theta}{\epsilon^{\omega}}\Sigma^{\omega}\deriv{\theta}{\epsilon^{\omega}}+\deriv{\theta}{\eta_{init}^{b^{\omega}}}\Sigma^{init_{22}}\deriv{\theta}{\eta_{init}^{b^{\omega}}} & \deriv{\theta}{\eta_{init}^{b^{\omega}}}\Sigma^{init_{21}}\deriv p{\eta_{init}^{b^{a}}} & \deriv{\theta}{\eta_{init}^{b^{\omega}}}\Sigma^{init_{21}}\deriv v{\eta_{init}^{b^{a}}} & 0 & 0\\ +\deriv p{\eta_{init}^{b^{a}}}\Sigma^{init_{12}}\deriv{\theta}{\eta_{init}^{b^{\omega}}} & \deriv p{\epsilon^{a}}\Sigma^{a}\deriv p{\epsilon^{a}}+\deriv p{\epsilon^{int}}\Sigma^{int}\deriv p{\epsilon^{int}}\\ + & +\deriv p{\eta_{init}^{b^{a}}}\Sigma^{init_{11}}\deriv p{\eta_{init}^{b^{a}}} & \deriv p{\epsilon^{a}}\Sigma^{a}\deriv v{\epsilon^{a}}+\deriv p{\eta_{init}^{b^{a}}}\Sigma^{init_{11}}\deriv v{\eta_{init}^{b^{a}}} & 0 & 0\\ +\deriv v{\eta_{init}^{b^{a}}}\Sigma^{init_{12}}\deriv{\theta}{\eta_{init}^{b^{\omega}}} & \deriv v{\epsilon^{a}}\Sigma^{a}\deriv p{\epsilon^{a}}+\deriv v{\eta_{init}^{b^{a}}}\Sigma^{init_{11}}\deriv p{\eta_{init}^{b^{a}}} & \deriv v{\epsilon^{a}}\Sigma^{a}\deriv v{\epsilon^{a}}+\deriv v{\eta_{init}^{b^{a}}}\Sigma^{init_{11}}\deriv v{\eta_{init}^{b^{a}}} & 0 & 0\\ +0 & 0 & 0 & \Sigma^{b^{a}} & 0\\ +0 & 0 & 0 & 0 & \Sigma^{b^{\omega}} +\end{array}\right] +\end{multline*} + +\end_inset + + +\end_layout + +\begin_layout Standard +which we can break into 3 matrices for clarity, representing the main diagonal + and off-diagonal elements +\end_layout + +\begin_layout Standard +\begin_inset Formula +\begin{multline*} +=\\ +\left[\begin{array}{ccccc} +\deriv{\theta}{\epsilon^{\omega}}\Sigma^{\omega}\deriv{\theta}{\epsilon^{\omega}} & 0 & 0 & 0 & 0\\ +0 & \deriv p{\epsilon^{a}}\Sigma^{a}\deriv p{\epsilon^{a}} & 0 & 0 & 0\\ +0 & 0 & \deriv v{\epsilon^{a}}\Sigma^{a}\deriv v{\epsilon^{a}} & 0 & 0\\ +0 & 0 & 0 & \Sigma^{b^{a}} & 0\\ +0 & 0 & 0 & 0 & \Sigma^{b^{\omega}} +\end{array}\right]+\\ +\left[\begin{array}{ccccc} +\deriv{\theta}{\eta_{init}^{b^{\omega}}}\Sigma^{init_{22}}\deriv{\theta}{\eta_{init}^{b^{\omega}}} & 0 & 0 & 0 & 0\\ +0 & \deriv p{\epsilon^{int}}\Sigma^{int}\deriv p{\epsilon^{int}}+\deriv p{\eta_{init}^{b^{a}}}\Sigma^{init_{11}}\deriv p{\eta_{init}^{b^{a}}} & 0 & 0 & 0\\ +0 & 0 & \deriv v{\eta_{init}^{b^{a}}}\Sigma^{init_{11}}\deriv v{\eta_{init}^{b^{a}}} & 0 & 0\\ +0 & 0 & 0 & 0 & 0\\ +0 & 0 & 0 & 0 & 0 +\end{array}\right]+\\ +\left[\begin{array}{ccccc} +0 & \deriv{\theta}{\eta_{init}^{b^{\omega}}}\Sigma^{init_{21}}\deriv p{\eta_{init}^{b^{a}}} & \deriv{\theta}{\eta_{init}^{b^{\omega}}}\Sigma^{init_{21}}\deriv v{\eta_{init}^{b^{a}}} & 0 & 0\\ +\deriv p{\eta_{init}^{b^{a}}}\Sigma^{init_{12}}\deriv{\theta}{\eta_{init}^{b^{\omega}}} & 0 & \deriv p{\epsilon^{a}}\Sigma^{a}\deriv v{\epsilon^{a}}+\deriv p{\eta_{init}^{b^{a}}}\Sigma^{init_{11}}\deriv v{\eta_{init}^{b^{a}}} & 0 & 0\\ +\deriv v{\eta_{init}^{b^{a}}}\Sigma^{init_{12}}\deriv{\theta}{\eta_{init}^{b^{\omega}}} & \deriv v{\epsilon^{a}}\Sigma^{a}\deriv p{\epsilon^{a}}+\deriv v{\eta_{init}^{b^{a}}}\Sigma^{init_{11}}\deriv p{\eta_{init}^{b^{a}}} & 0 & 0 & 0\\ +0 & 0 & 0 & 0 & 0\\ +0 & 0 & 0 & 0 & 0 +\end{array}\right] +\end{multline*} + +\end_inset + + \end_layout \begin_layout Standard \begin_inset CommandInset bibtex LatexCommand bibtex +btprint "btPrintCited" bibfiles "refs" options "plain" diff --git a/doc/ImuFactor.pdf b/doc/ImuFactor.pdf index 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zJTOB!GDJc)GB+?oIWi(RHZ?RcMmaY)IWjddI6^f=MMXYc3NK7$ZfA68ATl>IAeS+Q z0VsbZ(7Q5&Q5c2cwf-M*N+Qn3I40s8BF-WR8fi75Z~6x`O&%EEaXZD`i0Pq_C5eg89Lsb+TqQLN|;9W_CA|ROcZcWUK1+gp^#fsPz+af2n z#Hy$kRYWZ6Tb4v#L_`hIb>)LPQA=dbJvM)cdLn=AF)A8~;*-Z65f?FH|Hr#^F(;Zt zLNtpO(JIiML{jvN0pj4&ZwwM=AFd(d@zym=yuP_cNM5*72mk_oC9SkxxGdD2`B_%~qMhe49R$%}D diff --git a/doc/refs.bib b/doc/refs.bib index 414773483f..97960d8534 100644 --- a/doc/refs.bib +++ b/doc/refs.bib @@ -1,26 +1,52 @@ +%% This BibTeX bibliography file was created using BibDesk. +%% https://bibdesk.sourceforge.io/ + +%% Created for Varun Agrawal at 2021-09-27 17:39:09 -0400 + + +%% Saved with string encoding Unicode (UTF-8) + + + +@article{Lupton12tro, + author = {Lupton, Todd and Sukkarieh, Salah}, + date-added = {2021-09-27 17:38:56 -0400}, + date-modified = {2021-09-27 17:39:09 -0400}, + doi = {10.1109/TRO.2011.2170332}, + journal = {IEEE Transactions on Robotics}, + number = {1}, + pages = {61-76}, + title = {Visual-Inertial-Aided Navigation for High-Dynamic Motion in Built Environments Without Initial Conditions}, + volume = {28}, + year = {2012}, + Bdsk-Url-1 = {https://doi.org/10.1109/TRO.2011.2170332}} + +@inproceedings{Forster15rss, + author = {Christian Forster and Luca Carlone and Frank Dellaert and Davide Scaramuzza}, + booktitle = {Robotics: Science and Systems}, + date-added = {2021-09-26 20:44:41 -0400}, + date-modified = {2021-09-26 20:45:03 -0400}, + title = {IMU Preintegration on Manifold for Efficient Visual-Inertial Maximum-a-Posteriori Estimation}, + year = {2015}} + @article{Iserles00an, - title = {Lie-group methods}, - author = {Iserles, Arieh and Munthe-Kaas, Hans Z and - N{\o}rsett, Syvert P and Zanna, Antonella}, - journal = {Acta Numerica 2000}, - volume = {9}, - pages = {215--365}, - year = {2000}, - publisher = {Cambridge Univ Press} -} + author = {Iserles, Arieh and Munthe-Kaas, Hans Z and N{\o}rsett, Syvert P and Zanna, Antonella}, + journal = {Acta Numerica 2000}, + pages = {215--365}, + publisher = {Cambridge Univ Press}, + title = {Lie-group methods}, + volume = {9}, + year = {2000}} @book{Murray94book, - title = {A mathematical introduction to robotic manipulation}, - author = {Murray, Richard M and Li, Zexiang and Sastry, S - Shankar and Sastry, S Shankara}, - year = {1994}, - publisher = {CRC press} -} + author = {Murray, Richard M and Li, Zexiang and Sastry, S Shankar and Sastry, S Shankara}, + publisher = {CRC press}, + title = {A mathematical introduction to robotic manipulation}, + year = {1994}} @book{Spivak65book, - title = {Calculus on manifolds}, - author = {Spivak, Michael}, - volume = {1}, - year = {1965}, - publisher = {WA Benjamin New York} -} \ No newline at end of file + author = {Spivak, Michael}, + publisher = {WA Benjamin New York}, + title = {Calculus on manifolds}, + volume = {1}, + year = {1965}} From 0968c6005e9a74a56588ab55dec44c4c304cb834 Mon Sep 17 00:00:00 2001 From: Varun Agrawal Date: Tue, 28 Sep 2021 18:26:03 -0400 Subject: [PATCH 12/24] added details about covariance discretization with references --- doc/ImuFactor.lyx | 105 +++++++++++++++++++++++++++++++++++++--------- doc/ImuFactor.pdf | Bin 243257 -> 248399 bytes doc/refs.bib | 20 +++++++++ 3 files changed, 106 insertions(+), 19 deletions(-) diff --git a/doc/ImuFactor.lyx b/doc/ImuFactor.lyx index 4b71a29ed7..f76ede023f 100644 --- a/doc/ImuFactor.lyx +++ b/doc/ImuFactor.lyx @@ -1433,7 +1433,7 @@ Given the above solutions to the differential equations, we add noise modeling \begin_layout Standard \begin_inset Formula \begin{eqnarray} -\theta_{k+1} & = & \theta_{k}+H(\theta_{k})^{-1}\,(\omega_{k}^{b}+\epsilon_{k}^{\omega} -b_{k}^{\omega}-\epsilon_{init}^{\omega})\Delta_{t}\nonumber \\ +\theta_{k+1} & = & \theta_{k}+H(\theta_{k})^{-1}\,(\omega_{k}^{b}+\epsilon_{k}^{\omega}-b_{k}^{\omega}-\epsilon_{init}^{\omega})\Delta_{t}\nonumber \\ p_{k+1} & = & p_{k}+v_{k}\Delta_{t}+R_{k}(a_{k}^{b}+\epsilon_{k}^{a}-b_{k}^{a}-\epsilon_{init}^{a})\frac{\Delta_{t}^{2}}{2}+\epsilon_{k}^{int}\label{eq:preintegration}\\ v_{k+1} & = & v_{k}+R_{k}(a_{k}^{b}+\epsilon_{k}^{a}-b_{k}^{a}-\epsilon_{init}^{a})\Delta_{t}\nonumber \\ b_{k+1}^{a} & = & b_{k}^{a}+\epsilon_{k}^{b^{a}}\nonumber \\ @@ -1908,13 +1908,13 @@ G_{k}Q_{k}G_{k}^{T}=\left[\begin{array}{ccccccc} 0 & 0 & 0 & \Sigma^{b^{\omega}} & 0 & 0 & 0 \end{array}\right]\\ \left[\begin{array}{ccccc} -\deriv{\theta}{\epsilon^{\omega}} & 0 & 0 & 0 & 0\\ -0 & \deriv p{\epsilon^{a}} & \deriv v{\epsilon^{a}} & 0 & 0\\ +\deriv{\theta}{\epsilon^{\omega}}^{T} & 0 & 0 & 0 & 0\\ +0 & \deriv p{\epsilon^{a}}^{T} & \deriv v{\epsilon^{a}}^{T} & 0 & 0\\ 0 & 0 & 0 & I_{3\times3} & 0\\ 0 & 0 & 0 & 0 & I_{3\times3}\\ -0 & \deriv p{\epsilon^{int}} & 0 & 0 & 0\\ -0 & \deriv p{\eta_{init}^{b^{a}}} & \deriv v{\eta_{init}^{b^{a}}} & 0 & 0\\ -\deriv{\theta}{\eta_{init}^{b^{\omega}}} & 0 & 0 & 0 & 0 +0 & \deriv p{\epsilon^{int}}^{T} & 0 & 0 & 0\\ +0 & \deriv p{\eta_{init}^{b^{a}}}^{T} & \deriv v{\eta_{init}^{b^{a}}}^{T} & 0 & 0\\ +\deriv{\theta}{\eta_{init}^{b^{\omega}}}^{T} & 0 & 0 & 0 & 0 \end{array}\right] \end{multline*} @@ -1928,10 +1928,10 @@ G_{k}Q_{k}G_{k}^{T}=\left[\begin{array}{ccccccc} \begin{multline*} =\\ \left[\begin{array}{ccccc} -\deriv{\theta}{\epsilon^{\omega}}\Sigma^{\omega}\deriv{\theta}{\epsilon^{\omega}}+\deriv{\theta}{\eta_{init}^{b^{\omega}}}\Sigma^{init_{22}}\deriv{\theta}{\eta_{init}^{b^{\omega}}} & \deriv{\theta}{\eta_{init}^{b^{\omega}}}\Sigma^{init_{21}}\deriv p{\eta_{init}^{b^{a}}} & \deriv{\theta}{\eta_{init}^{b^{\omega}}}\Sigma^{init_{21}}\deriv v{\eta_{init}^{b^{a}}} & 0 & 0\\ -\deriv p{\eta_{init}^{b^{a}}}\Sigma^{init_{12}}\deriv{\theta}{\eta_{init}^{b^{\omega}}} & \deriv p{\epsilon^{a}}\Sigma^{a}\deriv p{\epsilon^{a}}+\deriv p{\epsilon^{int}}\Sigma^{int}\deriv p{\epsilon^{int}}\\ - & +\deriv p{\eta_{init}^{b^{a}}}\Sigma^{init_{11}}\deriv p{\eta_{init}^{b^{a}}} & \deriv p{\epsilon^{a}}\Sigma^{a}\deriv v{\epsilon^{a}}+\deriv p{\eta_{init}^{b^{a}}}\Sigma^{init_{11}}\deriv v{\eta_{init}^{b^{a}}} & 0 & 0\\ -\deriv v{\eta_{init}^{b^{a}}}\Sigma^{init_{12}}\deriv{\theta}{\eta_{init}^{b^{\omega}}} & \deriv v{\epsilon^{a}}\Sigma^{a}\deriv p{\epsilon^{a}}+\deriv v{\eta_{init}^{b^{a}}}\Sigma^{init_{11}}\deriv p{\eta_{init}^{b^{a}}} & \deriv v{\epsilon^{a}}\Sigma^{a}\deriv v{\epsilon^{a}}+\deriv v{\eta_{init}^{b^{a}}}\Sigma^{init_{11}}\deriv v{\eta_{init}^{b^{a}}} & 0 & 0\\ +\deriv{\theta}{\epsilon^{\omega}}\Sigma^{\omega}\deriv{\theta}{\epsilon^{\omega}}^{T}+\deriv{\theta}{\eta_{init}^{b^{\omega}}}\Sigma^{init_{22}}\deriv{\theta}{\eta_{init}^{b^{\omega}}}^{T} & \deriv{\theta}{\eta_{init}^{b^{\omega}}}\Sigma^{init_{21}}\deriv p{\eta_{init}^{b^{a}}}^{T} & \deriv{\theta}{\eta_{init}^{b^{\omega}}}\Sigma^{init_{21}}\deriv v{\eta_{init}^{b^{a}}}^{T} & 0 & 0\\ +\deriv p{\eta_{init}^{b^{a}}}\Sigma^{init_{12}}\deriv{\theta}{\eta_{init}^{b^{\omega}}}^{T} & \deriv p{\epsilon^{a}}\Sigma^{a}\deriv p{\epsilon^{a}}^{T}+\deriv p{\epsilon^{int}}\Sigma^{int}\deriv p{\epsilon^{int}}^{T}\\ + & +\deriv p{\eta_{init}^{b^{a}}}\Sigma^{init_{11}}\deriv p{\eta_{init}^{b^{a}}}^{T} & \deriv p{\epsilon^{a}}\Sigma^{a}\deriv v{\epsilon^{a}}^{T}+\deriv p{\eta_{init}^{b^{a}}}\Sigma^{init_{11}}\deriv v{\eta_{init}^{b^{a}}}^{T} & 0 & 0\\ +\deriv v{\eta_{init}^{b^{a}}}\Sigma^{init_{12}}\deriv{\theta}{\eta_{init}^{b^{\omega}}}^{T} & \deriv v{\epsilon^{a}}\Sigma^{a}\deriv p{\epsilon^{a}}^{T}+\deriv v{\eta_{init}^{b^{a}}}\Sigma^{init_{11}}\deriv p{\eta_{init}^{b^{a}}}^{T} & \deriv v{\epsilon^{a}}\Sigma^{a}\deriv v{\epsilon^{a}}^{T}+\deriv v{\eta_{init}^{b^{a}}}\Sigma^{init_{11}}\deriv v{\eta_{init}^{b^{a}}}^{T} & 0 & 0\\ 0 & 0 & 0 & \Sigma^{b^{a}} & 0\\ 0 & 0 & 0 & 0 & \Sigma^{b^{\omega}} \end{array}\right] @@ -1952,23 +1952,23 @@ which we can break into 3 matrices for clarity, representing the main diagonal \begin{multline*} =\\ \left[\begin{array}{ccccc} -\deriv{\theta}{\epsilon^{\omega}}\Sigma^{\omega}\deriv{\theta}{\epsilon^{\omega}} & 0 & 0 & 0 & 0\\ -0 & \deriv p{\epsilon^{a}}\Sigma^{a}\deriv p{\epsilon^{a}} & 0 & 0 & 0\\ -0 & 0 & \deriv v{\epsilon^{a}}\Sigma^{a}\deriv v{\epsilon^{a}} & 0 & 0\\ +\deriv{\theta}{\epsilon^{\omega}}\Sigma^{\omega}\deriv{\theta}{\epsilon^{\omega}}^{T} & 0 & 0 & 0 & 0\\ +0 & \deriv p{\epsilon^{a}}\Sigma^{a}\deriv p{\epsilon^{a}}^{T} & 0 & 0 & 0\\ +0 & 0 & \deriv v{\epsilon^{a}}\Sigma^{a}\deriv v{\epsilon^{a}}^{T} & 0 & 0\\ 0 & 0 & 0 & \Sigma^{b^{a}} & 0\\ 0 & 0 & 0 & 0 & \Sigma^{b^{\omega}} \end{array}\right]+\\ \left[\begin{array}{ccccc} -\deriv{\theta}{\eta_{init}^{b^{\omega}}}\Sigma^{init_{22}}\deriv{\theta}{\eta_{init}^{b^{\omega}}} & 0 & 0 & 0 & 0\\ -0 & \deriv p{\epsilon^{int}}\Sigma^{int}\deriv p{\epsilon^{int}}+\deriv p{\eta_{init}^{b^{a}}}\Sigma^{init_{11}}\deriv p{\eta_{init}^{b^{a}}} & 0 & 0 & 0\\ -0 & 0 & \deriv v{\eta_{init}^{b^{a}}}\Sigma^{init_{11}}\deriv v{\eta_{init}^{b^{a}}} & 0 & 0\\ +\deriv{\theta}{\eta_{init}^{b^{\omega}}}\Sigma^{init_{22}}\deriv{\theta}{\eta_{init}^{b^{\omega}}}^{T} & 0 & 0 & 0 & 0\\ +0 & \deriv p{\epsilon^{int}}\Sigma^{int}\deriv p{\epsilon^{int}}^{T}+\deriv p{\eta_{init}^{b^{a}}}\Sigma^{init_{11}}\deriv p{\eta_{init}^{b^{a}}}^{T} & 0 & 0 & 0\\ +0 & 0 & \deriv v{\eta_{init}^{b^{a}}}\Sigma^{init_{11}}\deriv v{\eta_{init}^{b^{a}}}^{T} & 0 & 0\\ 0 & 0 & 0 & 0 & 0\\ 0 & 0 & 0 & 0 & 0 \end{array}\right]+\\ \left[\begin{array}{ccccc} -0 & \deriv{\theta}{\eta_{init}^{b^{\omega}}}\Sigma^{init_{21}}\deriv p{\eta_{init}^{b^{a}}} & \deriv{\theta}{\eta_{init}^{b^{\omega}}}\Sigma^{init_{21}}\deriv v{\eta_{init}^{b^{a}}} & 0 & 0\\ -\deriv p{\eta_{init}^{b^{a}}}\Sigma^{init_{12}}\deriv{\theta}{\eta_{init}^{b^{\omega}}} & 0 & \deriv p{\epsilon^{a}}\Sigma^{a}\deriv v{\epsilon^{a}}+\deriv p{\eta_{init}^{b^{a}}}\Sigma^{init_{11}}\deriv v{\eta_{init}^{b^{a}}} & 0 & 0\\ -\deriv v{\eta_{init}^{b^{a}}}\Sigma^{init_{12}}\deriv{\theta}{\eta_{init}^{b^{\omega}}} & \deriv v{\epsilon^{a}}\Sigma^{a}\deriv p{\epsilon^{a}}+\deriv v{\eta_{init}^{b^{a}}}\Sigma^{init_{11}}\deriv p{\eta_{init}^{b^{a}}} & 0 & 0 & 0\\ +0 & \deriv{\theta}{\eta_{init}^{b^{\omega}}}\Sigma^{init_{21}}\deriv p{\eta_{init}^{b^{a}}}^{T} & \deriv{\theta}{\eta_{init}^{b^{\omega}}}\Sigma^{init_{21}}\deriv v{\eta_{init}^{b^{a}}}^{T} & 0 & 0\\ +\deriv p{\eta_{init}^{b^{a}}}\Sigma^{init_{12}}\deriv{\theta}{\eta_{init}^{b^{\omega}}}^{T} & 0 & \deriv p{\epsilon^{a}}\Sigma^{a}\deriv v{\epsilon^{a}}^{T}+\deriv p{\eta_{init}^{b^{a}}}\Sigma^{init_{11}}\deriv v{\eta_{init}^{b^{a}}}^{T} & 0 & 0\\ +\deriv v{\eta_{init}^{b^{a}}}\Sigma^{init_{12}}\deriv{\theta}{\eta_{init}^{b^{\omega}}}^{T} & \deriv v{\epsilon^{a}}\Sigma^{a}\deriv p{\epsilon^{a}}^{T}+\deriv v{\eta_{init}^{b^{a}}}\Sigma^{init_{11}}\deriv p{\eta_{init}^{b^{a}}}^{T} & 0 & 0 & 0\\ 0 & 0 & 0 & 0 & 0\\ 0 & 0 & 0 & 0 & 0 \end{array}\right] @@ -1979,6 +1979,73 @@ which we can break into 3 matrices for clarity, representing the main diagonal \end_layout +\begin_layout Subsubsection* +Covariance Discretization +\end_layout + +\begin_layout Standard +So far, all the covariances are assumed to be continuous since the state + and measurement models are considered to be continuous-time stochastic + processes. + However, we sample measurements in a discrete-time fashion, necessitating + the need to convert the covariances to their discrete time equivalents. +\end_layout + +\begin_layout Standard +The IMU is modeled as a first order Gauss-Markov process, with a measurement + noise and a process noise. + Following +\begin_inset CommandInset citation +LatexCommand cite +after "Alg. 1 Page 57" +key "Nikolic16thesis" +literal "false" + +\end_inset + + and +\begin_inset CommandInset citation +LatexCommand cite +after "Eqns 129-130" +key "Trawny05report_IndirectKF" +literal "false" + +\end_inset + +, the measurement noises +\begin_inset Formula $[\epsilon^{a},\epsilon^{\omega},\epsilon_{init}]$ +\end_inset + + are simply scaled by +\begin_inset Formula $\frac{1}{\Delta t}$ +\end_inset + +, and the process noises +\begin_inset Formula $[\epsilon^{int},\epsilon^{b^{a}},\epsilon^{b^{\omega}}]$ +\end_inset + + are scaled by +\begin_inset Formula $\Delta t$ +\end_inset + + where +\begin_inset Formula $\Delta t$ +\end_inset + + is the time interval between 2 consecutive samples. + For a thorough explanation of the discretization process, please refer + to +\begin_inset CommandInset citation +LatexCommand cite +after "Section 8.1" +key "Simon06book" +literal "false" + +\end_inset + +. +\end_layout + \begin_layout Standard \begin_inset CommandInset bibtex LatexCommand bibtex diff --git a/doc/ImuFactor.pdf b/doc/ImuFactor.pdf index 041d8bf1a2d3e93d115dcfee3a9b001f5a6ea52d..a4ec57fb7baa660508d5c6872185270e178b1d0f 100644 GIT binary patch delta 103379 zcmV(@K-Ryx><-VA50E4RFd&yPh5;ylEso7f1TheV@ADLWk_1dlcm9vcI-uam=tVq4 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zWlJwpB4%a|7)Es>ZDt}?BIch-C3}09pGj6CCL$#mMrk`U`=1fp|3+d&+I%dWVjRq( z;vC#!?83ratm5n<>}<@e>>@0}ESyYC!Xg4h|9=U>&yD`q+hqN@cw&GM6@YwBno-mc zYv|VbO1#{Yj=j>#IwvBdJpY*3hW=u3d|2cn!w%`9Q zRZ!u|cjr(KXq3l476eQtUkja{tMkXxD-Km|5^eK=- zEdpkr$&6#IeF&!ORElv> S0$3IfE>0M7a&ZL-nEwFqjx=5X diff --git a/doc/refs.bib b/doc/refs.bib index 97960d8534..ec42fb0328 100644 --- a/doc/refs.bib +++ b/doc/refs.bib @@ -50,3 +50,23 @@ @book{Spivak65book title = {Calculus on manifolds}, volume = {1}, year = {1965}} + +@phdthesis{Nikolic16thesis, + title={Characterisation, calibration, and design of visual-inertial sensor systems for robot navigation}, + author={Nikolic, Janosch}, + year={2016}, + school={ETH Zurich} +} + +@book{Simon06book, + title={Optimal state estimation: Kalman, H infinity, and nonlinear approaches}, + author={Simon, Dan}, + year={2006}, + publisher={John Wiley \& Sons} +} + +@inproceedings{Trawny05report_IndirectKF, + title={Indirect Kalman Filter for 3 D Attitude Estimation}, + author={Nikolas Trawny and Stergios I. Roumeliotis}, + year={2005} +} From 6bc9b50a46ac7cfdae0d1ec82c61779d25c3a6cf Mon Sep 17 00:00:00 2001 From: Varun Agrawal Date: Thu, 30 Sep 2021 09:05:02 -0400 Subject: [PATCH 13/24] add test for MC based covariance estimation --- .../tests/testCombinedImuFactor.cpp | 465 +++++++++--------- 1 file changed, 236 insertions(+), 229 deletions(-) diff --git a/gtsam/navigation/tests/testCombinedImuFactor.cpp b/gtsam/navigation/tests/testCombinedImuFactor.cpp index a8c0391449..2f12983c37 100644 --- a/gtsam/navigation/tests/testCombinedImuFactor.cpp +++ b/gtsam/navigation/tests/testCombinedImuFactor.cpp @@ -16,6 +16,7 @@ * @author Frank Dellaert * @author Richard Roberts * @author Stephen Williams + * @author Varun Agrawal */ #include @@ -40,237 +41,218 @@ static boost::shared_ptr Params() { p->gyroscopeCovariance = kGyroSigma * kGyroSigma * I_3x3; p->accelerometerCovariance = kAccelSigma * kAccelSigma * I_3x3; p->integrationCovariance = 0.0001 * I_3x3; + p->biasAccCovariance = Z_3x3; + p->biasOmegaCovariance = Z_3x3; + p->biasAccOmegaInit = Z_6x6; return p; } +} // namespace testing + +/* ************************************************************************* */ +TEST(CombinedImuFactor, PreintegratedMeasurements ) { + // Linearization point + Bias bias(Vector3(0, 0, 0), Vector3(0, 0, 0)); ///< Current estimate of acceleration and angular rate biases + + // Measurements + Vector3 measuredAcc(0.1, 0.0, 0.0); + Vector3 measuredOmega(M_PI / 100.0, 0.0, 0.0); + double deltaT = 0.5; + double tol = 1e-6; + + auto p = testing::Params(); + + // Actual preintegrated values + PreintegratedImuMeasurements expected1(p, bias); + expected1.integrateMeasurement(measuredAcc, measuredOmega, deltaT); + + PreintegratedCombinedMeasurements actual1(p, bias); + + actual1.integrateMeasurement(measuredAcc, measuredOmega, deltaT); + + EXPECT(assert_equal(Vector(expected1.deltaPij()), actual1.deltaPij(), tol)); + EXPECT(assert_equal(Vector(expected1.deltaVij()), actual1.deltaVij(), tol)); + EXPECT(assert_equal(expected1.deltaRij(), actual1.deltaRij(), tol)); + DOUBLES_EQUAL(expected1.deltaTij(), actual1.deltaTij(), tol); } -// /* ************************************************************************* */ -// TEST(CombinedImuFactor, PreintegratedMeasurements ) { -// // Linearization point -// Bias bias(Vector3(0, 0, 0), Vector3(0, 0, 0)); ///< Current estimate of acceleration and angular rate biases - -// // Measurements -// Vector3 measuredAcc(0.1, 0.0, 0.0); -// Vector3 measuredOmega(M_PI / 100.0, 0.0, 0.0); -// double deltaT = 0.5; -// double tol = 1e-6; - -// auto p = testing::Params(); - -// // Actual preintegrated values -// PreintegratedImuMeasurements expected1(p, bias); -// expected1.integrateMeasurement(measuredAcc, measuredOmega, deltaT); - -// PreintegratedCombinedMeasurements actual1(p, bias); - -// actual1.integrateMeasurement(measuredAcc, measuredOmega, deltaT); - -// EXPECT(assert_equal(Vector(expected1.deltaPij()), actual1.deltaPij(), tol)); -// EXPECT(assert_equal(Vector(expected1.deltaVij()), actual1.deltaVij(), tol)); -// EXPECT(assert_equal(expected1.deltaRij(), actual1.deltaRij(), tol)); -// DOUBLES_EQUAL(expected1.deltaTij(), actual1.deltaTij(), tol); -// } - -// /* ************************************************************************* */ -// TEST(CombinedImuFactor, Accelerating) { -// const double a = 0.2, v = 50; - -// // Set up body pointing towards y axis, and start at 10,20,0 with velocity -// // going in X The body itself has Z axis pointing down -// const Rot3 nRb(Point3(0, 1, 0), Point3(1, 0, 0), Point3(0, 0, -1)); -// const Point3 initial_position(10, 20, 0); -// const Vector3 initial_velocity(v, 0, 0); - -// const AcceleratingScenario scenario(nRb, initial_position, initial_velocity, -// Vector3(a, 0, 0)); - -// const double T = 3.0; // seconds -// CombinedScenarioRunner runner(scenario, testing::Params(), T / 10); - -// PreintegratedCombinedMeasurements pim = runner.integrate(T); -// EXPECT(assert_equal(scenario.pose(T), runner.predict(pim).pose(), 1e-9)); - -// auto estimatedCov = runner.estimateCovariance(T, 100); -// Eigen::Matrix expected = pim.preintMeasCov(); -// EXPECT(assert_equal(estimatedCov, expected, 0.1)); -// } - -// /* ************************************************************************* */ -// TEST(CombinedImuFactor, ErrorWithBiases ) { -// Bias bias(Vector3(0.2, 0, 0), Vector3(0, 0, 0.3)); // Biases (acc, rot) -// Bias bias2(Vector3(0.2, 0.2, 0), Vector3(1, 0, 0.3)); // Biases (acc, rot) -// Pose3 x1(Rot3::Expmap(Vector3(0, 0, M_PI / 4.0)), Point3(5.0, 1.0, -50.0)); -// Vector3 v1(0.5, 0.0, 0.0); -// Pose3 x2(Rot3::Expmap(Vector3(0, 0, M_PI / 4.0 + M_PI / 10.0)), -// Point3(5.5, 1.0, -50.0)); -// Vector3 v2(0.5, 0.0, 0.0); - -// auto p = testing::Params(); -// p->omegaCoriolis = Vector3(0,0.1,0.1); -// PreintegratedImuMeasurements pim( -// p, Bias(Vector3(0.2, 0.0, 0.0), Vector3(0.0, 0.0, 0.0))); - -// // Measurements -// Vector3 measuredOmega; -// measuredOmega << 0, 0, M_PI / 10.0 + 0.3; -// Vector3 measuredAcc = -// x1.rotation().unrotate(-p->n_gravity) + Vector3(0.2, 0.0, 0.0); -// double deltaT = 1.0; -// double tol = 1e-6; - -// pim.integrateMeasurement(measuredAcc, measuredOmega, deltaT); - -// PreintegratedCombinedMeasurements combined_pim(p, -// Bias(Vector3(0.2, 0.0, 0.0), Vector3(0.0, 0.0, 0.0))); - -// combined_pim.integrateMeasurement(measuredAcc, measuredOmega, deltaT); - -// // Create factor -// ImuFactor imuFactor(X(1), V(1), X(2), V(2), B(1), pim); - -// noiseModel::Gaussian::shared_ptr Combinedmodel = -// noiseModel::Gaussian::Covariance(combined_pim.preintMeasCov()); -// CombinedImuFactor combinedfactor(X(1), V(1), X(2), V(2), B(1), B(2), -// combined_pim); - -// Vector errorExpected = imuFactor.evaluateError(x1, v1, x2, v2, bias); -// Vector errorActual = combinedfactor.evaluateError(x1, v1, x2, v2, bias, -// bias2); -// EXPECT(assert_equal(errorExpected, errorActual.head(9), tol)); - -// // Expected Jacobians -// Matrix H1e, H2e, H3e, H4e, H5e; -// (void) imuFactor.evaluateError(x1, v1, x2, v2, bias, H1e, H2e, H3e, H4e, H5e); - -// // Actual Jacobians -// Matrix H1a, H2a, H3a, H4a, H5a, H6a; -// (void) combinedfactor.evaluateError(x1, v1, x2, v2, bias, bias2, H1a, H2a, -// H3a, H4a, H5a, H6a); - -// EXPECT(assert_equal(H1e, H1a.topRows(9))); -// EXPECT(assert_equal(H2e, H2a.topRows(9))); -// EXPECT(assert_equal(H3e, H3a.topRows(9))); -// EXPECT(assert_equal(H4e, H4a.topRows(9))); -// EXPECT(assert_equal(H5e, H5a.topRows(9))); -// } - -// /* ************************************************************************* */ -// #ifdef GTSAM_TANGENT_PREINTEGRATION -// TEST(CombinedImuFactor, FirstOrderPreIntegratedMeasurements) { -// auto p = testing::Params(); -// testing::SomeMeasurements measurements; - -// auto preintegrated = [=](const Vector3& a, const Vector3& w) { -// PreintegratedImuMeasurements pim(p, Bias(a, w)); -// testing::integrateMeasurements(measurements, &pim); -// return pim.preintegrated(); -// }; - -// // Actual pre-integrated values -// PreintegratedCombinedMeasurements pim(p); -// testing::integrateMeasurements(measurements, &pim); - -// EXPECT(assert_equal(numericalDerivative21(preintegrated, Z_3x1, Z_3x1), -// pim.preintegrated_H_biasAcc())); -// EXPECT(assert_equal(numericalDerivative22(preintegrated, Z_3x1, Z_3x1), -// pim.preintegrated_H_biasOmega(), 1e-3)); -// } -// #endif - -// /* ************************************************************************* */ -// TEST(CombinedImuFactor, PredictPositionAndVelocity) { -// const Bias bias(Vector3(0, 0.1, 0), Vector3(0, 0.1, 0)); // Biases (acc, rot) - -// auto p = testing::Params(); - -// // Measurements -// const Vector3 measuredOmega(0, 0.1, 0); // M_PI/10.0+0.3; -// const Vector3 measuredAcc(0, 1.1, -kGravity); -// const double deltaT = 0.01; - -// PreintegratedCombinedMeasurements pim(p, bias); - -// for (int i = 0; i < 100; ++i) -// pim.integrateMeasurement(measuredAcc, measuredOmega, deltaT); - -// // Create factor -// const noiseModel::Gaussian::shared_ptr combinedmodel = -// noiseModel::Gaussian::Covariance(pim.preintMeasCov()); -// const CombinedImuFactor Combinedfactor(X(1), V(1), X(2), V(2), B(1), B(2), pim); - -// // Predict -// const NavState actual = pim.predict(NavState(), bias); -// const Pose3 expectedPose(Rot3(), Point3(0, 0.5, 0)); -// const Vector3 expectedVelocity(0, 1, 0); -// EXPECT(assert_equal(expectedPose, actual.pose())); -// EXPECT(assert_equal(Vector(expectedVelocity), Vector(actual.velocity()))); -// } - -// /* ************************************************************************* */ -// TEST(CombinedImuFactor, PredictRotation) { -// const Bias bias(Vector3(0, 0, 0), Vector3(0, 0, 0)); // Biases (acc, rot) -// auto p = testing::Params(); -// PreintegratedCombinedMeasurements pim(p, bias); -// const Vector3 measuredAcc = - kGravityAlongNavZDown; -// const Vector3 measuredOmega(0, 0, M_PI / 10.0); -// const double deltaT = 0.01; -// const double tol = 1e-4; -// for (int i = 0; i < 100; ++i) -// pim.integrateMeasurement(measuredAcc, measuredOmega, deltaT); -// const CombinedImuFactor Combinedfactor(X(1), V(1), X(2), V(2), B(1), B(2), pim); - -// // Predict -// const Pose3 x(Rot3::Ypr(0, 0, 0), Point3(0, 0, 0)), x2; -// const Vector3 v(0, 0, 0), v2; -// const NavState actual = pim.predict(NavState(x, v), bias); -// const Pose3 expectedPose(Rot3::Ypr(M_PI / 10, 0, 0), Point3(0, 0, 0)); -// EXPECT(assert_equal(expectedPose, actual.pose(), tol)); -// } - -// /* ************************************************************************* */ -// // Testing covariance to check if all the jacobians are accounted for. -// TEST(CombinedImuFactor, CheckCovariance) { -// auto params = PreintegrationCombinedParams::MakeSharedU(9.81); - -// params->setAccelerometerCovariance(pow(0.01, 2) * I_3x3); -// params->setGyroscopeCovariance(pow(1.75e-4, 2) * I_3x3); -// params->setIntegrationCovariance(pow(0.0, 2) * I_3x3); -// params->setOmegaCoriolis(Vector3::Zero()); - -// imuBias::ConstantBias currentBias; - -// PreintegratedCombinedMeasurements actual(params, currentBias); - -// // Measurements -// Vector3 measuredAcc(0.1577, -0.8251, 9.6111); -// Vector3 measuredOmega(-0.0210, 0.0311, 0.0145); -// double deltaT = 0.01; - -// actual.integrateMeasurement(measuredAcc, measuredOmega, deltaT); - -// Eigen::Matrix expected; -// expected << 0.01, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, // -// 0, 0.01, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, // -// 0, 0, 0.01, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, // -// 0, 0, 0, 2.50025e-07, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, // -// 0, 0, 0, 0, 2.50025e-07, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, // -// 0, 0, 0, 0, 0, 2.50025e-07, 0, 0, 0, 0, 0, 0, 0, 0, 0, // -// 0, 0, 0, 0, 0, 0, 0.010001, 0, 0, 0, 0, 0, 0, 0, 0, // -// 0, 0, 0, 0, 0, 0, 0, 0.010001, 0, 0, 0, 0, 0, 0, 0, // -// 0, 0, 0, 0, 0, 0, 0, 0, 0.010001, 0, 0, 0, 0, 0, 0, // -// 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.01, 0, 0, 0, 0, 0, // -// 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.01, 0, 0, 0, 0, // -// 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.01, 0, 0, 0, // -// 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.01, 0, 0, // -// 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.01, 0, // -// 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.01; - -// // regression -// EXPECT(assert_equal(expected, actual.preintMeasCov())); -// } -// Test that the covariance values for the ImuFactor and the CombinedImuFactor (top-left 9x9) are the same -TEST(CombinedImuFactor, SameCovariance) { +/* ************************************************************************* */ +TEST(CombinedImuFactor, ErrorWithBiases ) { + Bias bias(Vector3(0.2, 0, 0), Vector3(0, 0, 0.3)); // Biases (acc, rot) + Bias bias2(Vector3(0.2, 0.2, 0), Vector3(1, 0, 0.3)); // Biases (acc, rot) + Pose3 x1(Rot3::Expmap(Vector3(0, 0, M_PI / 4.0)), Point3(5.0, 1.0, -50.0)); + Vector3 v1(0.5, 0.0, 0.0); + Pose3 x2(Rot3::Expmap(Vector3(0, 0, M_PI / 4.0 + M_PI / 10.0)), + Point3(5.5, 1.0, -50.0)); + Vector3 v2(0.5, 0.0, 0.0); + + auto p = testing::Params(); + p->omegaCoriolis = Vector3(0,0.1,0.1); + PreintegratedImuMeasurements pim( + p, Bias(Vector3(0.2, 0.0, 0.0), Vector3(0.0, 0.0, 0.0))); + + // Measurements + Vector3 measuredOmega; + measuredOmega << 0, 0, M_PI / 10.0 + 0.3; + Vector3 measuredAcc = + x1.rotation().unrotate(-p->n_gravity) + Vector3(0.2, 0.0, 0.0); + double deltaT = 1.0; + double tol = 1e-6; + + pim.integrateMeasurement(measuredAcc, measuredOmega, deltaT); + + PreintegratedCombinedMeasurements combined_pim(p, + Bias(Vector3(0.2, 0.0, 0.0), Vector3(0.0, 0.0, 0.0))); + + combined_pim.integrateMeasurement(measuredAcc, measuredOmega, deltaT); + + // Create factor + ImuFactor imuFactor(X(1), V(1), X(2), V(2), B(1), pim); + + noiseModel::Gaussian::shared_ptr Combinedmodel = + noiseModel::Gaussian::Covariance(combined_pim.preintMeasCov()); + CombinedImuFactor combinedfactor(X(1), V(1), X(2), V(2), B(1), B(2), + combined_pim); + + Vector errorExpected = imuFactor.evaluateError(x1, v1, x2, v2, bias); + Vector errorActual = combinedfactor.evaluateError(x1, v1, x2, v2, bias, + bias2); + EXPECT(assert_equal(errorExpected, errorActual.head(9), tol)); + + // Expected Jacobians + Matrix H1e, H2e, H3e, H4e, H5e; + (void) imuFactor.evaluateError(x1, v1, x2, v2, bias, H1e, H2e, H3e, H4e, H5e); + + // Actual Jacobians + Matrix H1a, H2a, H3a, H4a, H5a, H6a; + (void) combinedfactor.evaluateError(x1, v1, x2, v2, bias, bias2, H1a, H2a, + H3a, H4a, H5a, H6a); + + EXPECT(assert_equal(H1e, H1a.topRows(9))); + EXPECT(assert_equal(H2e, H2a.topRows(9))); + EXPECT(assert_equal(H3e, H3a.topRows(9))); + EXPECT(assert_equal(H4e, H4a.topRows(9))); + EXPECT(assert_equal(H5e, H5a.topRows(9))); +} + +/* ************************************************************************* */ +#ifdef GTSAM_TANGENT_PREINTEGRATION +TEST(CombinedImuFactor, FirstOrderPreIntegratedMeasurements) { + auto p = testing::Params(); + testing::SomeMeasurements measurements; + + auto preintegrated = [=](const Vector3& a, const Vector3& w) { + PreintegratedImuMeasurements pim(p, Bias(a, w)); + testing::integrateMeasurements(measurements, &pim); + return pim.preintegrated(); + }; + + // Actual pre-integrated values + PreintegratedCombinedMeasurements pim(p); + testing::integrateMeasurements(measurements, &pim); + + EXPECT(assert_equal(numericalDerivative21(preintegrated, Z_3x1, Z_3x1), + pim.preintegrated_H_biasAcc())); + EXPECT(assert_equal(numericalDerivative22(preintegrated, Z_3x1, Z_3x1), + pim.preintegrated_H_biasOmega(), 1e-3)); +} +#endif + +/* ************************************************************************* */ +TEST(CombinedImuFactor, PredictPositionAndVelocity) { + const Bias bias(Vector3(0, 0.1, 0), Vector3(0, 0.1, 0)); // Biases (acc, rot) + + auto p = testing::Params(); + + // Measurements + const Vector3 measuredOmega(0, 0.1, 0); // M_PI/10.0+0.3; + const Vector3 measuredAcc(0, 1.1, -kGravity); + const double deltaT = 0.01; + + PreintegratedCombinedMeasurements pim(p, bias); + + for (int i = 0; i < 100; ++i) + pim.integrateMeasurement(measuredAcc, measuredOmega, deltaT); + + // Create factor + const noiseModel::Gaussian::shared_ptr combinedmodel = + noiseModel::Gaussian::Covariance(pim.preintMeasCov()); + const CombinedImuFactor Combinedfactor(X(1), V(1), X(2), V(2), B(1), B(2), pim); + + // Predict + const NavState actual = pim.predict(NavState(), bias); + const Pose3 expectedPose(Rot3(), Point3(0, 0.5, 0)); + const Vector3 expectedVelocity(0, 1, 0); + EXPECT(assert_equal(expectedPose, actual.pose())); + EXPECT(assert_equal(Vector(expectedVelocity), Vector(actual.velocity()))); +} + +/* ************************************************************************* */ +TEST(CombinedImuFactor, PredictRotation) { + const Bias bias(Vector3(0, 0, 0), Vector3(0, 0, 0)); // Biases (acc, rot) + auto p = testing::Params(); + PreintegratedCombinedMeasurements pim(p, bias); + const Vector3 measuredAcc = - kGravityAlongNavZDown; + const Vector3 measuredOmega(0, 0, M_PI / 10.0); + const double deltaT = 0.01; + const double tol = 1e-4; + for (int i = 0; i < 100; ++i) + pim.integrateMeasurement(measuredAcc, measuredOmega, deltaT); + const CombinedImuFactor Combinedfactor(X(1), V(1), X(2), V(2), B(1), B(2), pim); + + // Predict + const Pose3 x(Rot3::Ypr(0, 0, 0), Point3(0, 0, 0)), x2; + const Vector3 v(0, 0, 0), v2; + const NavState actual = pim.predict(NavState(x, v), bias); + const Pose3 expectedPose(Rot3::Ypr(M_PI / 10, 0, 0), Point3(0, 0, 0)); + EXPECT(assert_equal(expectedPose, actual.pose(), tol)); +} + +/* ************************************************************************* */ +// Testing covariance to check if all the jacobians are accounted for. +TEST(CombinedImuFactor, CheckCovariance) { + auto params = PreintegrationCombinedParams::MakeSharedU(9.81); + + params->setAccelerometerCovariance(pow(0.01, 2) * I_3x3); + params->setGyroscopeCovariance(pow(1.75e-4, 2) * I_3x3); + params->setIntegrationCovariance(pow(0.0, 2) * I_3x3); + params->setOmegaCoriolis(Vector3::Zero()); + + imuBias::ConstantBias currentBias; + + PreintegratedCombinedMeasurements actual(params, currentBias); + + // Measurements + Vector3 measuredAcc(0.1577, -0.8251, 9.6111); + Vector3 measuredOmega(-0.0210, 0.0311, 0.0145); + double deltaT = 0.01; + + actual.integrateMeasurement(measuredAcc, measuredOmega, deltaT); + + Eigen::Matrix expected; + expected << 0.01, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, // + 0, 0.01, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, // + 0, 0, 0.01, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, // + 0, 0, 0, 2.50025e-07, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, // + 0, 0, 0, 0, 2.50025e-07, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, // + 0, 0, 0, 0, 0, 2.50025e-07, 0, 0, 0, 0, 0, 0, 0, 0, 0, // + 0, 0, 0, 0, 0, 0, 0.010001, 0, 0, 0, 0, 0, 0, 0, 0, // + 0, 0, 0, 0, 0, 0, 0, 0.010001, 0, 0, 0, 0, 0, 0, 0, // + 0, 0, 0, 0, 0, 0, 0, 0, 0.010001, 0, 0, 0, 0, 0, 0, // + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.01, 0, 0, 0, 0, 0, // + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.01, 0, 0, 0, 0, // + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.01, 0, 0, 0, // + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.01, 0, 0, // + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.01, 0, // + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.01; + + // regression + EXPECT(assert_equal(expected, actual.preintMeasCov())); +} + +// Test that the covariance values for the ImuFactor and the CombinedImuFactor +// (top-left 9x9) are the same +TEST(CombinedImuFactor, SameCovariance) { // IMU measurements and time delta Vector3 accMeas(0.1577, -0.8251, 9.6111); Vector3 omegaMeas(-0.0210, 0.0311, 0.0145); @@ -278,7 +260,7 @@ TEST(CombinedImuFactor, SameCovariance) { // Assume zero bias imuBias::ConstantBias currentBias; - + // Define params for ImuFactor auto params = PreintegrationParams::MakeSharedU(); params->setAccelerometerCovariance(pow(0.01, 2) * I_3x3); @@ -303,10 +285,35 @@ TEST(CombinedImuFactor, SameCovariance) { PreintegratedCombinedMeasurements cpim(combined_params, currentBias); cpim.integrateMeasurement(accMeas, omegaMeas, deltaT); - // Assert if the noise covariance - EXPECT(assert_equal(pim.preintMeasCov(), cpim.preintMeasCov().block(0, 0, 9, 9))); + // Assert if the noise covariance + EXPECT(assert_equal(pim.preintMeasCov(), + cpim.preintMeasCov().block(0, 0, 9, 9))); } +/* ************************************************************************* */ +TEST(CombinedImuFactor, Accelerating) { + const double a = 0.2, v = 50; + + // Set up body pointing towards y axis, and start at 10,20,0 with velocity + // going in X The body itself has Z axis pointing down + const Rot3 nRb(Point3(0, 1, 0), Point3(1, 0, 0), Point3(0, 0, -1)); + const Point3 initial_position(10, 20, 0); + const Vector3 initial_velocity(v, 0, 0); + + const AcceleratingScenario scenario(nRb, initial_position, initial_velocity, + Vector3(a, 0, 0)); + + const double T = 3.0; // seconds + + CombinedScenarioRunner runner(scenario, testing::Params(), T / 10); + + PreintegratedCombinedMeasurements pim = runner.integrate(T); + EXPECT(assert_equal(scenario.pose(T), runner.predict(pim).pose(), 1e-9)); + + auto estimatedCov = runner.estimateCovariance(T, 100); + Eigen::Matrix expected = pim.preintMeasCov(); + EXPECT(assert_equal(estimatedCov, expected, 0.1)); +} /* ************************************************************************* */ int main() { From af714cdb5a756a744dd0000a89782a55fb14d66c Mon Sep 17 00:00:00 2001 From: Varun Agrawal Date: Tue, 28 Sep 2021 13:43:04 -0400 Subject: [PATCH 14/24] undo name change from 984a90 --- examples/CombinedImuFactorsExample.cpp | 4 ++-- examples/ImuFactorsExample.cpp | 4 ++-- gtsam/navigation/CombinedImuFactor.cpp | 10 +++++----- gtsam/navigation/CombinedImuFactor.h | 12 ++++++------ .../examples/ISAM2_SmartFactorStereo_IMU.cpp | 2 +- tests/testImuPreintegration.cpp | 4 ++-- 6 files changed, 18 insertions(+), 18 deletions(-) diff --git a/examples/CombinedImuFactorsExample.cpp b/examples/CombinedImuFactorsExample.cpp index 49cdb68354..35ed387c40 100644 --- a/examples/CombinedImuFactorsExample.cpp +++ b/examples/CombinedImuFactorsExample.cpp @@ -107,7 +107,7 @@ boost::shared_ptr imuParams() { I_3x3 * 1e-8; // error committed in integrating position from velocities Matrix33 bias_acc_cov = I_3x3 * pow(accel_bias_rw_sigma, 2); Matrix33 bias_omega_cov = I_3x3 * pow(gyro_bias_rw_sigma, 2); - Matrix66 bias_acc_omega_int = + Matrix66 bias_acc_omega_init = I_6x6 * 1e-5; // error in the bias used for preintegration auto p = PreintegratedCombinedMeasurements::Params::MakeSharedD(0.0); @@ -123,7 +123,7 @@ boost::shared_ptr imuParams() { // PreintegrationCombinedMeasurements params: p->biasAccCovariance = bias_acc_cov; // acc bias in continuous p->biasOmegaCovariance = bias_omega_cov; // gyro bias in continuous - p->biasAccOmegaInt = bias_acc_omega_int; + p->biasAccOmegaInit = bias_acc_omega_init; return p; } diff --git a/examples/ImuFactorsExample.cpp b/examples/ImuFactorsExample.cpp index 38ee4c7c76..12167a19d1 100644 --- a/examples/ImuFactorsExample.cpp +++ b/examples/ImuFactorsExample.cpp @@ -94,7 +94,7 @@ boost::shared_ptr imuParams() { I_3x3 * 1e-8; // error committed in integrating position from velocities Matrix33 bias_acc_cov = I_3x3 * pow(accel_bias_rw_sigma, 2); Matrix33 bias_omega_cov = I_3x3 * pow(gyro_bias_rw_sigma, 2); - Matrix66 bias_acc_omega_int = + Matrix66 bias_acc_omega_init = I_6x6 * 1e-5; // error in the bias used for preintegration auto p = PreintegratedCombinedMeasurements::Params::MakeSharedD(0.0); @@ -110,7 +110,7 @@ boost::shared_ptr imuParams() { // PreintegrationCombinedMeasurements params: p->biasAccCovariance = bias_acc_cov; // acc bias in continuous p->biasOmegaCovariance = bias_omega_cov; // gyro bias in continuous - p->biasAccOmegaInt = bias_acc_omega_int; + p->biasAccOmegaInit = bias_acc_omega_init; return p; } diff --git a/gtsam/navigation/CombinedImuFactor.cpp b/gtsam/navigation/CombinedImuFactor.cpp index de4d3f66db..5d49e4c0b9 100644 --- a/gtsam/navigation/CombinedImuFactor.cpp +++ b/gtsam/navigation/CombinedImuFactor.cpp @@ -39,7 +39,7 @@ void PreintegrationCombinedParams::print(const string& s) const { << endl; cout << "biasOmegaCovariance:\n[\n" << biasOmegaCovariance << "\n]" << endl; - cout << "biasAccOmegaInt:\n[\n" << biasAccOmegaInt << "\n]" + cout << "biasAccOmegaInit:\n[\n" << biasAccOmegaInit << "\n]" << endl; } @@ -52,7 +52,7 @@ bool PreintegrationCombinedParams::equals(const PreintegratedRotationParams& oth tol) && equal_with_abs_tol(biasOmegaCovariance, e->biasOmegaCovariance, tol) && - equal_with_abs_tol(biasAccOmegaInt, e->biasAccOmegaInt, tol); + equal_with_abs_tol(biasAccOmegaInit, e->biasAccOmegaInit, tol); } //------------------------------------------------------------------------------ @@ -137,8 +137,8 @@ void PreintegratedCombinedMeasurements::integrateMeasurement( Eigen::Matrix G_measCov_Gt; G_measCov_Gt.setZero(15, 15); - Matrix3 aCov_updated = aCov + p().biasAccOmegaInt.block<3, 3>(0, 0); - Matrix3 wCov_updated = wCov + p().biasAccOmegaInt.block<3, 3>(3, 3); + Matrix3 aCov_updated = aCov + p().biasAccOmegaInit.block<3, 3>(0, 0); + Matrix3 wCov_updated = wCov + p().biasAccOmegaInit.block<3, 3>(3, 3); // BLOCK DIAGONAL TERMS D_t_t(&G_measCov_Gt) = (pos_H_biasAcc // @@ -156,7 +156,7 @@ void PreintegratedCombinedMeasurements::integrateMeasurement( D_g_g(&G_measCov_Gt) = dt * p().biasOmegaCovariance; // OFF BLOCK DIAGONAL TERMS - Matrix3 temp = vel_H_biasAcc * p().biasAccOmegaInt.block<3, 3>(3, 0) + Matrix3 temp = vel_H_biasAcc * p().biasAccOmegaInit.block<3, 3>(3, 0) * theta_H_biasOmega.transpose(); D_v_R(&G_measCov_Gt) = temp; D_v_t(&G_measCov_Gt) = vel_H_biasAcc * (aCov / dt) * pos_H_biasAcc.transpose(); diff --git a/gtsam/navigation/CombinedImuFactor.h b/gtsam/navigation/CombinedImuFactor.h index ce169c1d0b..5849f6f247 100644 --- a/gtsam/navigation/CombinedImuFactor.h +++ b/gtsam/navigation/CombinedImuFactor.h @@ -62,19 +62,19 @@ typedef ManifoldPreintegration PreintegrationType; struct GTSAM_EXPORT PreintegrationCombinedParams : PreintegrationParams { Matrix3 biasAccCovariance; ///< continuous-time "Covariance" describing accelerometer bias random walk Matrix3 biasOmegaCovariance; ///< continuous-time "Covariance" describing gyroscope bias random walk - Matrix6 biasAccOmegaInt; ///< covariance of bias used for pre-integration + Matrix6 biasAccOmegaInit; ///< covariance of bias used as initial estimate. /// Default constructor makes uninitialized params struct. /// Used for serialization. PreintegrationCombinedParams() : biasAccCovariance(I_3x3), biasOmegaCovariance(I_3x3), - biasAccOmegaInt(I_6x6) {} + biasAccOmegaInit(I_6x6) {} /// See two named constructors below for good values of n_gravity in body frame PreintegrationCombinedParams(const Vector3& n_gravity) : PreintegrationParams(n_gravity), biasAccCovariance(I_3x3), - biasOmegaCovariance(I_3x3), biasAccOmegaInt(I_6x6) { + biasOmegaCovariance(I_3x3), biasAccOmegaInit(I_6x6) { } @@ -93,11 +93,11 @@ struct GTSAM_EXPORT PreintegrationCombinedParams : PreintegrationParams { void setBiasAccCovariance(const Matrix3& cov) { biasAccCovariance=cov; } void setBiasOmegaCovariance(const Matrix3& cov) { biasOmegaCovariance=cov; } - void setBiasAccOmegaInt(const Matrix6& cov) { biasAccOmegaInt=cov; } + void setBiasAccOmegaInt(const Matrix6& cov) { biasAccOmegaInit=cov; } const Matrix3& getBiasAccCovariance() const { return biasAccCovariance; } const Matrix3& getBiasOmegaCovariance() const { return biasOmegaCovariance; } - const Matrix6& getBiasAccOmegaInt() const { return biasAccOmegaInt; } + const Matrix6& getBiasAccOmegaInt() const { return biasAccOmegaInit; } private: @@ -109,7 +109,7 @@ struct GTSAM_EXPORT PreintegrationCombinedParams : PreintegrationParams { ar & BOOST_SERIALIZATION_BASE_OBJECT_NVP(PreintegrationParams); ar & BOOST_SERIALIZATION_NVP(biasAccCovariance); ar & BOOST_SERIALIZATION_NVP(biasOmegaCovariance); - ar & BOOST_SERIALIZATION_NVP(biasAccOmegaInt); + ar & BOOST_SERIALIZATION_NVP(biasAccOmegaInit); } public: diff --git a/gtsam_unstable/examples/ISAM2_SmartFactorStereo_IMU.cpp b/gtsam_unstable/examples/ISAM2_SmartFactorStereo_IMU.cpp index c0a102d111..27d87d217f 100644 --- a/gtsam_unstable/examples/ISAM2_SmartFactorStereo_IMU.cpp +++ b/gtsam_unstable/examples/ISAM2_SmartFactorStereo_IMU.cpp @@ -57,7 +57,7 @@ struct IMUHelper { p->biasAccCovariance = I_3x3 * pow(0.00002, 2.0); // acc bias in continuous p->biasOmegaCovariance = I_3x3 * pow(0.001, 2.0); // gyro bias in continuous - p->biasAccOmegaInt = Matrix::Identity(6, 6) * 1e-5; + p->biasAccOmegaInit = Matrix::Identity(6, 6) * 1e-5; // body to IMU rotation Rot3 iRb(0.036129, -0.998727, 0.035207, diff --git a/tests/testImuPreintegration.cpp b/tests/testImuPreintegration.cpp index 1f584be0ed..94e6fb89f2 100644 --- a/tests/testImuPreintegration.cpp +++ b/tests/testImuPreintegration.cpp @@ -43,7 +43,7 @@ TEST(TestImuPreintegration, LoadedSimulationData) { double gyrNoiseSigma = 0.000208; double gyrBiasRwSigma = 0.000004; double integrationCovariance = 1e-8; - double biasAccOmegaInt = 1e-5; + double biasAccOmegaInit = 1e-5; double gravity = 9.81; double rate = 400.0; // Hz @@ -76,7 +76,7 @@ TEST(TestImuPreintegration, LoadedSimulationData) { imuPreintegratedParams->gyroscopeCovariance = I_3x3 * pow(gyrNoiseSigma, 2); imuPreintegratedParams->biasOmegaCovariance = I_3x3 * pow(gyrBiasRwSigma, 2); imuPreintegratedParams->integrationCovariance = I_3x3 * integrationCovariance; - imuPreintegratedParams->biasAccOmegaInt = I_6x6 * biasAccOmegaInt; + imuPreintegratedParams->biasAccOmegaInit = I_6x6 * biasAccOmegaInit; // Initial state Pose3 priorPose; From e38ea502d7df488fdbec8072284715c977547e32 Mon Sep 17 00:00:00 2001 From: Varun Agrawal Date: Tue, 28 Sep 2021 18:22:15 -0400 Subject: [PATCH 15/24] detailed implementation of CombinedImuFactor noise propagation --- gtsam/navigation/CombinedImuFactor.cpp | 70 +++++++++++++++++--------- 1 file changed, 45 insertions(+), 25 deletions(-) diff --git a/gtsam/navigation/CombinedImuFactor.cpp b/gtsam/navigation/CombinedImuFactor.cpp index 5d49e4c0b9..2dfaae2fd9 100644 --- a/gtsam/navigation/CombinedImuFactor.cpp +++ b/gtsam/navigation/CombinedImuFactor.cpp @@ -110,17 +110,22 @@ void PreintegratedCombinedMeasurements::integrateMeasurement( // and preintegrated measurements // Single Jacobians to propagate covariance - Matrix3 theta_H_biasOmega = C.topRows<3>(); - Matrix3 pos_H_biasAcc = B.middleRows<3>(3); - Matrix3 vel_H_biasAcc = B.bottomRows<3>(); + Matrix3 theta_H_omega = C.topRows<3>(); + Matrix3 pos_H_acc = B.middleRows<3>(3); + Matrix3 vel_H_acc = B.bottomRows<3>(); + + Matrix3 theta_H_biasOmegaInit = -theta_H_omega; + Matrix3 pos_H_biasAccInit = -pos_H_acc; + Matrix3 vel_H_biasAcc = -vel_H_acc; + Matrix3 vel_H_biasAccInit = -vel_H_acc; // overall Jacobian wrt preintegrated measurements (df/dx) Eigen::Matrix F; F.setZero(); F.block<9, 9>(0, 0) = A; - F.block<3, 3>(0, 12) = theta_H_biasOmega; - F.block<3, 3>(3, 9) = pos_H_biasAcc; - F.block<3, 3>(6, 9) = vel_H_biasAcc; + F.block<3, 3>(0, 12) = theta_H_omega; + F.block<3, 3>(3, 9) = pos_H_acc; + F.block<3, 3>(6, 9) = vel_H_acc; F.block<6, 6>(9, 9) = I_6x6; // Update the uncertainty on the state (matrix F in [4]). @@ -131,37 +136,52 @@ void PreintegratedCombinedMeasurements::integrateMeasurement( const Matrix3& aCov = p().accelerometerCovariance; const Matrix3& wCov = p().gyroscopeCovariance; const Matrix3& iCov = p().integrationCovariance; + const Matrix6& bInitCov = p().biasAccOmegaInit; // first order uncertainty propagation // Optimized matrix mult: (1/dt) * G * measurementCovariance * G.transpose() Eigen::Matrix G_measCov_Gt; G_measCov_Gt.setZero(15, 15); - Matrix3 aCov_updated = aCov + p().biasAccOmegaInit.block<3, 3>(0, 0); - Matrix3 wCov_updated = wCov + p().biasAccOmegaInit.block<3, 3>(3, 3); - // BLOCK DIAGONAL TERMS - D_t_t(&G_measCov_Gt) = (pos_H_biasAcc // - * (aCov_updated / dt) // - * pos_H_biasAcc.transpose()) + (dt * iCov); - D_v_v(&G_measCov_Gt) = vel_H_biasAcc // - * (aCov_updated / dt) // - * (vel_H_biasAcc.transpose()); - - D_R_R(&G_measCov_Gt) = theta_H_biasOmega // - * (wCov_updated / dt) // - * (theta_H_biasOmega.transpose()); + D_R_R(&G_measCov_Gt) = + (theta_H_omega * (wCov / dt) * theta_H_omega.transpose()) + // + (theta_H_biasOmegaInit * (bInitCov.block<3, 3>(3, 3) / dt) * + theta_H_biasOmegaInit.transpose()); + + D_t_t(&G_measCov_Gt) = + (pos_H_acc * (aCov / dt) * pos_H_acc.transpose()) // + + (pos_H_biasAccInit * (bInitCov.block<3, 3>(0, 0) / dt) * + pos_H_biasAccInit.transpose()) // + + (dt * iCov); + + D_v_v(&G_measCov_Gt) = + (vel_H_acc * (aCov / dt) * vel_H_acc.transpose()) // + + (vel_H_biasAccInit * (bInitCov.block<3, 3>(0, 0) / dt) * + vel_H_biasAccInit.transpose()); D_a_a(&G_measCov_Gt) = dt * p().biasAccCovariance; D_g_g(&G_measCov_Gt) = dt * p().biasOmegaCovariance; // OFF BLOCK DIAGONAL TERMS - Matrix3 temp = vel_H_biasAcc * p().biasAccOmegaInit.block<3, 3>(3, 0) - * theta_H_biasOmega.transpose(); - D_v_R(&G_measCov_Gt) = temp; - D_v_t(&G_measCov_Gt) = vel_H_biasAcc * (aCov / dt) * pos_H_biasAcc.transpose(); - D_R_v(&G_measCov_Gt) = temp.transpose(); - D_t_v(&G_measCov_Gt) = pos_H_biasAcc * (aCov / dt) * vel_H_biasAcc.transpose(); + D_R_t(&G_measCov_Gt) = theta_H_biasOmegaInit * + (bInitCov.block<3, 3>(3, 0) / dt) * + pos_H_biasAccInit.transpose(); + D_R_v(&G_measCov_Gt) = theta_H_biasOmegaInit * + (bInitCov.block<3, 3>(3, 0) / dt) * + vel_H_biasAccInit.transpose(); + D_t_R(&G_measCov_Gt) = pos_H_biasAccInit * (bInitCov.block<3, 3>(0, 3) / dt) * + theta_H_biasOmegaInit.transpose(); + D_t_v(&G_measCov_Gt) = + (pos_H_acc * (aCov / dt) * vel_H_acc.transpose()) + + (pos_H_biasAccInit * (bInitCov.block<3, 3>(0, 0) / dt) * + vel_H_biasAccInit.transpose()); + D_v_R(&G_measCov_Gt) = vel_H_biasAccInit * (bInitCov.block<3, 3>(0, 3) / dt) * + theta_H_biasOmegaInit.transpose(); + D_v_t(&G_measCov_Gt) = + (vel_H_acc * (aCov / dt) * pos_H_acc.transpose()) + + (vel_H_biasAccInit * (bInitCov.block<3, 3>(0, 0) / dt) * + pos_H_biasAccInit.transpose()); preintMeasCov_.noalias() += G_measCov_Gt; } From 3cee1b71ec55d157e7a4654c984fb9d40ae15550 Mon Sep 17 00:00:00 2001 From: Varun Agrawal Date: Thu, 30 Sep 2021 09:01:23 -0400 Subject: [PATCH 16/24] test passes --- gtsam/navigation/CombinedImuFactor.cpp | 6 +++--- gtsam/navigation/ScenarioRunner.cpp | 3 ++- 2 files changed, 5 insertions(+), 4 deletions(-) diff --git a/gtsam/navigation/CombinedImuFactor.cpp b/gtsam/navigation/CombinedImuFactor.cpp index 2dfaae2fd9..64d555e2e6 100644 --- a/gtsam/navigation/CombinedImuFactor.cpp +++ b/gtsam/navigation/CombinedImuFactor.cpp @@ -145,9 +145,9 @@ void PreintegratedCombinedMeasurements::integrateMeasurement( // BLOCK DIAGONAL TERMS D_R_R(&G_measCov_Gt) = - (theta_H_omega * (wCov / dt) * theta_H_omega.transpose()) + // - (theta_H_biasOmegaInit * (bInitCov.block<3, 3>(3, 3) / dt) * - theta_H_biasOmegaInit.transpose()); + (theta_H_omega * (wCov / dt) * theta_H_omega.transpose()) // + + (theta_H_biasOmegaInit * (bInitCov.block<3, 3>(3, 3) / dt) * + theta_H_biasOmegaInit.transpose()); D_t_t(&G_measCov_Gt) = (pos_H_acc * (aCov / dt) * pos_H_acc.transpose()) // diff --git a/gtsam/navigation/ScenarioRunner.cpp b/gtsam/navigation/ScenarioRunner.cpp index 3a447dcab6..9d3e258de9 100644 --- a/gtsam/navigation/ScenarioRunner.cpp +++ b/gtsam/navigation/ScenarioRunner.cpp @@ -145,7 +145,8 @@ Eigen::Matrix CombinedScenarioRunner::estimateCovariance( auto pim = integrate(T, estimatedBias, true); NavState sampled = predict(pim); Vector15 xi = Vector15::Zero(); - xi << sampled.localCoordinates(prediction), estimatedBias_.vector(); + xi << sampled.localCoordinates(prediction), + (estimatedBias_.vector() - estimatedBias.vector()); samples.col(i) = xi; sum += xi; } From dfa32e50207a3b69be71ad3b17df9093ae98d8c9 Mon Sep 17 00:00:00 2001 From: Varun Agrawal Date: Sat, 9 Oct 2021 22:51:48 -0400 Subject: [PATCH 17/24] lyx update --- doc/ImuFactor.lyx | 80 ++++++++++++++++++++++++++++++++++++++--------- 1 file changed, 66 insertions(+), 14 deletions(-) diff --git a/doc/ImuFactor.lyx b/doc/ImuFactor.lyx index f76ede023f..80c160e6ee 100644 --- a/doc/ImuFactor.lyx +++ b/doc/ImuFactor.lyx @@ -227,16 +227,62 @@ preintegrated_ \begin_layout Standard The main function of a factor is to calculate an error. - The easiest case to look at is the NavState variant in ImuFactor2, which - is given as: + This is done exactly the same in both variants: \begin_inset Formula \begin{equation} -\Delta X_{ij}=X_{j}-\hat{X_{ij}}\label{eq:imu-factor-error} +e(X_{i},X_{j})=X_{j}\ominus\widehat{X_{j}}\label{eq:imu-factor-error} \end{equation} \end_inset +where the predicted NavState +\begin_inset Formula $\widehat{X_{j}}$ +\end_inset + + at time +\begin_inset Formula $t_{j}$ +\end_inset + + is a function of the NavState +\begin_inset Formula $X_{i}$ +\end_inset + + at time +\begin_inset Formula $t_{i}$ +\end_inset + + and the preintegrated measurements +\begin_inset Formula $PIM$ +\end_inset + +: +\begin_inset Formula +\[ +\widehat{X_{j}}=f(X_{i},PIM) +\] + +\end_inset + +The noise model associated with this factor is assumed to be zero-mean Gaussian + with a +\begin_inset Formula $9\times9$ +\end_inset + + covariance matrix +\begin_inset Formula $\Sigma_{ij}$ +\end_inset +, which is defined in the tangent space +\begin_inset Formula $T_{X_{j}}\mathcal{N}$ +\end_inset + + of the NavState manifold at the NavState +\begin_inset Formula $X_{j}$ +\end_inset + +. + This covariance matrix is computed in the preintegrated measurement class, + of which there are two variants as discussed above. \end_layout \begin_layout Subsubsection* @@ -282,6 +328,14 @@ Gyroscope Covariance : Measurement uncertainty of the gyroscope. \end_layout +\begin_layout Itemize +Gyroscope Bias Covariance +\begin_inset Formula $Q_{\Delta b^{\omega}}$ +\end_inset + + : The covariance associated with the gyroscope bias random walk. +\end_layout + \begin_layout Itemize Accelerometer Covariance \begin_inset Formula $Q_{acc}$ @@ -298,14 +352,6 @@ Accelerometer Bias Covariance : The covariance associated with the accelerometer bias random walk. \end_layout -\begin_layout Itemize -Gyroscope Bias Covariance -\begin_inset Formula $Q_{\Delta b^{\omega}}$ -\end_inset - - : The covariance associated with the gyroscope bias random walk. -\end_layout - \begin_layout Itemize Integration Covariance \begin_inset Formula $Q_{int}$ @@ -1469,7 +1515,12 @@ Noise Propagation in IMU Factor \end_layout \begin_layout Standard -Even when we assume uncorrelated noise on +We wish to compute the ImuFactor covariance matrix +\begin_inset Formula $\Sigma_{ij}$ +\end_inset + +. + Even when we assume uncorrelated noise on \begin_inset Formula $\omega^{b}$ \end_inset @@ -1487,11 +1538,12 @@ Even when we assume uncorrelated noise on \end_inset appear in multiple places. - To model the noise propagation, let us define + To model the noise propagation, let us define the preintegrated navigation + state \begin_inset Formula $\zeta_{k}=[\theta_{k},p_{k},v_{k}]$ \end_inset - and rewrite Eqns. +, as a 9D vector on tangent space at and rewrite Eqns. ( \begin_inset CommandInset ref LatexCommand ref From 40e6d8be9b146a0caf43ea231610239bf716ed42 Mon Sep 17 00:00:00 2001 From: Varun Agrawal Date: Sat, 9 Oct 2021 22:52:01 -0400 Subject: [PATCH 18/24] formatting --- doc/ImuFactor.lyx | 2 +- gtsam/navigation/PreintegrationBase.cpp | 4 ++-- 2 files changed, 3 insertions(+), 3 deletions(-) diff --git a/doc/ImuFactor.lyx b/doc/ImuFactor.lyx index 80c160e6ee..7b176f484e 100644 --- a/doc/ImuFactor.lyx +++ b/doc/ImuFactor.lyx @@ -82,7 +82,7 @@ \begin_body \begin_layout Title -The new IMU Factor +The New IMU Factor \end_layout \begin_layout Author diff --git a/gtsam/navigation/PreintegrationBase.cpp b/gtsam/navigation/PreintegrationBase.cpp index 8840c34e9d..f6e9fccb8d 100644 --- a/gtsam/navigation/PreintegrationBase.cpp +++ b/gtsam/navigation/PreintegrationBase.cpp @@ -157,9 +157,9 @@ Vector9 PreintegrationBase::computeError(const NavState& state_i, state_j.localCoordinates(predictedState_j, H2 ? &D_error_state_j : 0, H1 || H3 ? &D_error_predict : 0); - if (H1) *H1 << D_error_predict* D_predict_state_i; + if (H1) *H1 << D_error_predict * D_predict_state_i; if (H2) *H2 << D_error_state_j; - if (H3) *H3 << D_error_predict* D_predict_bias_i; + if (H3) *H3 << D_error_predict * D_predict_bias_i; return error; } From 995710f8fdf0e91f29ec15158c8a376ee4a8883f Mon Sep 17 00:00:00 2001 From: Varun Agrawal Date: Thu, 5 May 2022 11:38:18 -0400 Subject: [PATCH 19/24] update PDF doc --- doc/ImuFactor.pdf | Bin 248399 -> 249424 bytes 1 file changed, 0 insertions(+), 0 deletions(-) diff --git a/doc/ImuFactor.pdf b/doc/ImuFactor.pdf index a4ec57fb7baa660508d5c6872185270e178b1d0f..9d7026d0978944949f5f6d4932c85dbe112a2a10 100644 GIT binary patch delta 100260 zcmV)GK)%1vln>CH50E1RFft&Mfj}sKEsxDg1TheV@ADLWk_1eguKXVr9Z*>zM=PIr0w2Xrt&T$3IFCj&JzGn0WpD1WsXYmeNv@wRRGg7yj&NP>Xg)%oP?N?S?mM}K|iL29Wz-q{zYpF|CZoZ-xHUVM4;?7LUmtz;qU zqL!!J1CMpf%+e1Q~JvJ_$=yqOEtlw_7FwsmnO^8j? z@yvt=z`sX+ 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8dbbb1fe1f3eca333602e4673d8c976a5375984b Mon Sep 17 00:00:00 2001 From: Varun Agrawal Date: Fri, 6 May 2022 16:45:37 -0400 Subject: [PATCH 20/24] fix test --- .../tests/testCombinedImuFactor.cpp | 30 +++++++++---------- 1 file changed, 15 insertions(+), 15 deletions(-) diff --git a/gtsam/navigation/tests/testCombinedImuFactor.cpp b/gtsam/navigation/tests/testCombinedImuFactor.cpp index 2f12983c37..8091e3ad21 100644 --- a/gtsam/navigation/tests/testCombinedImuFactor.cpp +++ b/gtsam/navigation/tests/testCombinedImuFactor.cpp @@ -230,21 +230,21 @@ TEST(CombinedImuFactor, CheckCovariance) { actual.integrateMeasurement(measuredAcc, measuredOmega, deltaT); Eigen::Matrix expected; - expected << 0.01, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, // - 0, 0.01, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, // - 0, 0, 0.01, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, // - 0, 0, 0, 2.50025e-07, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, // - 0, 0, 0, 0, 2.50025e-07, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, // - 0, 0, 0, 0, 0, 2.50025e-07, 0, 0, 0, 0, 0, 0, 0, 0, 0, // - 0, 0, 0, 0, 0, 0, 0.010001, 0, 0, 0, 0, 0, 0, 0, 0, // - 0, 0, 0, 0, 0, 0, 0, 0.010001, 0, 0, 0, 0, 0, 0, 0, // - 0, 0, 0, 0, 0, 0, 0, 0, 0.010001, 0, 0, 0, 0, 0, 0, // - 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.01, 0, 0, 0, 0, 0, // - 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.01, 0, 0, 0, 0, // - 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.01, 0, 0, 0, // - 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.01, 0, 0, // - 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.01, 0, // - 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.01; + expected << 0.01, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, // + 0, 0.01, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, // + 0, 0, 0.01, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, // + 0, 0, 0, 2.50025e-07, 0, 0, 5.0005e-05, 0, 0, 0, 0, 0, 0, 0, 0, // + 0, 0, 0, 0, 2.50025e-07, 0, 0, 5.0005e-05, 0, 0, 0, 0, 0, 0, 0, // + 0, 0, 0, 0, 0, 2.50025e-07, 0, 0, 5.0005e-05, 0, 0, 0, 0, 0, 0, // + 0, 0, 0, 5.0005e-05, 0, 0, 0.010001, 0, 0, 0, 0, 0, 0, 0, 0, // + 0, 0, 0, 0, 5.0005e-05, 0, 0, 0.010001, 0, 0, 0, 0, 0, 0, 0, // + 0, 0, 0, 0, 0, 5.0005e-05, 0, 0, 0.010001, 0, 0, 0, 0, 0, 0, // + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.01, 0, 0, 0, 0, 0, // + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.01, 0, 0, 0, 0, // + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.01, 0, 0, 0, // + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.01, 0, 0, // + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.01, 0, // + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.0; // regression EXPECT(assert_equal(expected, actual.preintMeasCov())); From ce7c71b7d77e8d92a04de8fdd0dbd11dd2115f4c Mon Sep 17 00:00:00 2001 From: Varun Agrawal Date: Sun, 8 May 2022 16:51:21 -0400 Subject: [PATCH 21/24] fix test --- gtsam/navigation/tests/testCombinedImuFactor.cpp | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/gtsam/navigation/tests/testCombinedImuFactor.cpp b/gtsam/navigation/tests/testCombinedImuFactor.cpp index 8091e3ad21..48a89d7a05 100644 --- a/gtsam/navigation/tests/testCombinedImuFactor.cpp +++ b/gtsam/navigation/tests/testCombinedImuFactor.cpp @@ -244,7 +244,7 @@ TEST(CombinedImuFactor, CheckCovariance) { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.01, 0, 0, 0, // 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.01, 0, 0, // 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.01, 0, // - 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.0; + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.01; // regression EXPECT(assert_equal(expected, actual.preintMeasCov())); From a17134dd6a6c462ca488c27a487f84d8d528e7d6 Mon Sep 17 00:00:00 2001 From: Varun Agrawal Date: Sun, 8 May 2022 17:34:14 -0400 Subject: [PATCH 22/24] minor refactor to follow the math better --- gtsam/navigation/CombinedImuFactor.cpp | 45 ++++++++++++-------------- 1 file changed, 21 insertions(+), 24 deletions(-) diff --git a/gtsam/navigation/CombinedImuFactor.cpp b/gtsam/navigation/CombinedImuFactor.cpp index f2349a96e4..c9f0a926b2 100644 --- a/gtsam/navigation/CombinedImuFactor.cpp +++ b/gtsam/navigation/CombinedImuFactor.cpp @@ -116,7 +116,6 @@ void PreintegratedCombinedMeasurements::integrateMeasurement( Matrix3 theta_H_biasOmegaInit = -theta_H_omega; Matrix3 pos_H_biasAccInit = -pos_H_acc; - Matrix3 vel_H_biasAcc = -vel_H_acc; Matrix3 vel_H_biasAccInit = -vel_H_acc; // overall Jacobian wrt preintegrated measurements (df/dx) @@ -143,45 +142,44 @@ void PreintegratedCombinedMeasurements::integrateMeasurement( Eigen::Matrix G_measCov_Gt; G_measCov_Gt.setZero(15, 15); + const Matrix3& bInitCov11 = bInitCov.block<3, 3>(0, 0) / dt; + const Matrix3& bInitCov12 = bInitCov.block<3, 3>(0, 3) / dt; + const Matrix3& bInitCov21 = bInitCov.block<3, 3>(3, 0) / dt; + const Matrix3& bInitCov22 = bInitCov.block<3, 3>(3, 3) / dt; + // BLOCK DIAGONAL TERMS D_R_R(&G_measCov_Gt) = (theta_H_omega * (wCov / dt) * theta_H_omega.transpose()) // - + (theta_H_biasOmegaInit * (bInitCov.block<3, 3>(3, 3) / dt) * - theta_H_biasOmegaInit.transpose()); + + + (theta_H_biasOmegaInit * bInitCov22 * theta_H_biasOmegaInit.transpose()); D_t_t(&G_measCov_Gt) = - (pos_H_acc * (aCov / dt) * pos_H_acc.transpose()) // - + (pos_H_biasAccInit * (bInitCov.block<3, 3>(0, 0) / dt) * - pos_H_biasAccInit.transpose()) // + (pos_H_acc * (aCov / dt) * pos_H_acc.transpose()) // + + (pos_H_biasAccInit * bInitCov11 * pos_H_biasAccInit.transpose()) // + (dt * iCov); D_v_v(&G_measCov_Gt) = (vel_H_acc * (aCov / dt) * vel_H_acc.transpose()) // - + (vel_H_biasAccInit * (bInitCov.block<3, 3>(0, 0) / dt) * - vel_H_biasAccInit.transpose()); + + (vel_H_biasAccInit * bInitCov11 * vel_H_biasAccInit.transpose()); D_a_a(&G_measCov_Gt) = dt * p().biasAccCovariance; D_g_g(&G_measCov_Gt) = dt * p().biasOmegaCovariance; // OFF BLOCK DIAGONAL TERMS - D_R_t(&G_measCov_Gt) = theta_H_biasOmegaInit * - (bInitCov.block<3, 3>(3, 0) / dt) * - pos_H_biasAccInit.transpose(); - D_R_v(&G_measCov_Gt) = theta_H_biasOmegaInit * - (bInitCov.block<3, 3>(3, 0) / dt) * - vel_H_biasAccInit.transpose(); - D_t_R(&G_measCov_Gt) = pos_H_biasAccInit * (bInitCov.block<3, 3>(0, 3) / dt) * - theta_H_biasOmegaInit.transpose(); + D_R_t(&G_measCov_Gt) = + theta_H_biasOmegaInit * bInitCov21 * pos_H_biasAccInit.transpose(); + D_R_v(&G_measCov_Gt) = + theta_H_biasOmegaInit * bInitCov21 * vel_H_biasAccInit.transpose(); + D_t_R(&G_measCov_Gt) = + pos_H_biasAccInit * bInitCov12 * theta_H_biasOmegaInit.transpose(); D_t_v(&G_measCov_Gt) = (pos_H_acc * (aCov / dt) * vel_H_acc.transpose()) + - (pos_H_biasAccInit * (bInitCov.block<3, 3>(0, 0) / dt) * - vel_H_biasAccInit.transpose()); - D_v_R(&G_measCov_Gt) = vel_H_biasAccInit * (bInitCov.block<3, 3>(0, 3) / dt) * - theta_H_biasOmegaInit.transpose(); + (pos_H_biasAccInit * bInitCov11 * vel_H_biasAccInit.transpose()); + D_v_R(&G_measCov_Gt) = + vel_H_biasAccInit * bInitCov12 * theta_H_biasOmegaInit.transpose(); D_v_t(&G_measCov_Gt) = (vel_H_acc * (aCov / dt) * pos_H_acc.transpose()) + - (vel_H_biasAccInit * (bInitCov.block<3, 3>(0, 0) / dt) * - pos_H_biasAccInit.transpose()); + (vel_H_biasAccInit * bInitCov11 * pos_H_biasAccInit.transpose()); preintMeasCov_.noalias() += G_measCov_Gt; } @@ -291,6 +289,5 @@ std::ostream& operator<<(std::ostream& os, const CombinedImuFactor& f) { os << " noise model sigmas: " << f.noiseModel_->sigmas().transpose(); return os; } -} - /// namespace gtsam +} // namespace gtsam From cb75d92bf6938007fe7e3d358138584995e5b3f4 Mon Sep 17 00:00:00 2001 From: Varun Agrawal Date: Sun, 22 May 2022 16:39:06 -0400 Subject: [PATCH 23/24] use prior naming scheme for bias jacobians --- gtsam/navigation/CombinedImuFactor.cpp | 28 +++++++++++++------------- 1 file changed, 14 insertions(+), 14 deletions(-) diff --git a/gtsam/navigation/CombinedImuFactor.cpp b/gtsam/navigation/CombinedImuFactor.cpp index c9f0a926b2..0813bbfd12 100644 --- a/gtsam/navigation/CombinedImuFactor.cpp +++ b/gtsam/navigation/CombinedImuFactor.cpp @@ -110,21 +110,21 @@ void PreintegratedCombinedMeasurements::integrateMeasurement( // and preintegrated measurements // Single Jacobians to propagate covariance - Matrix3 theta_H_omega = C.topRows<3>(); - Matrix3 pos_H_acc = B.middleRows<3>(3); - Matrix3 vel_H_acc = B.bottomRows<3>(); + Matrix3 theta_H_biasOmega = C.topRows<3>(); + Matrix3 pos_H_biasAcc = B.middleRows<3>(3); + Matrix3 vel_H_biasAcc = B.bottomRows<3>(); - Matrix3 theta_H_biasOmegaInit = -theta_H_omega; - Matrix3 pos_H_biasAccInit = -pos_H_acc; - Matrix3 vel_H_biasAccInit = -vel_H_acc; + Matrix3 theta_H_biasOmegaInit = -theta_H_biasOmega; + Matrix3 pos_H_biasAccInit = -pos_H_biasAcc; + Matrix3 vel_H_biasAccInit = -vel_H_biasAcc; // overall Jacobian wrt preintegrated measurements (df/dx) Eigen::Matrix F; F.setZero(); F.block<9, 9>(0, 0) = A; - F.block<3, 3>(0, 12) = theta_H_omega; - F.block<3, 3>(3, 9) = pos_H_acc; - F.block<3, 3>(6, 9) = vel_H_acc; + F.block<3, 3>(0, 12) = theta_H_biasOmega; + F.block<3, 3>(3, 9) = pos_H_biasAcc; + F.block<3, 3>(6, 9) = vel_H_biasAcc; F.block<6, 6>(9, 9) = I_6x6; // Update the uncertainty on the state (matrix F in [4]). @@ -149,17 +149,17 @@ void PreintegratedCombinedMeasurements::integrateMeasurement( // BLOCK DIAGONAL TERMS D_R_R(&G_measCov_Gt) = - (theta_H_omega * (wCov / dt) * theta_H_omega.transpose()) // + (theta_H_biasOmega * (wCov / dt) * theta_H_biasOmega.transpose()) // + (theta_H_biasOmegaInit * bInitCov22 * theta_H_biasOmegaInit.transpose()); D_t_t(&G_measCov_Gt) = - (pos_H_acc * (aCov / dt) * pos_H_acc.transpose()) // + (pos_H_biasAcc * (aCov / dt) * pos_H_biasAcc.transpose()) // + (pos_H_biasAccInit * bInitCov11 * pos_H_biasAccInit.transpose()) // + (dt * iCov); D_v_v(&G_measCov_Gt) = - (vel_H_acc * (aCov / dt) * vel_H_acc.transpose()) // + (vel_H_biasAcc * (aCov / dt) * vel_H_biasAcc.transpose()) // + (vel_H_biasAccInit * bInitCov11 * vel_H_biasAccInit.transpose()); D_a_a(&G_measCov_Gt) = dt * p().biasAccCovariance; @@ -173,12 +173,12 @@ void PreintegratedCombinedMeasurements::integrateMeasurement( D_t_R(&G_measCov_Gt) = pos_H_biasAccInit * bInitCov12 * theta_H_biasOmegaInit.transpose(); D_t_v(&G_measCov_Gt) = - (pos_H_acc * (aCov / dt) * vel_H_acc.transpose()) + + (pos_H_biasAcc * (aCov / dt) * vel_H_biasAcc.transpose()) + (pos_H_biasAccInit * bInitCov11 * vel_H_biasAccInit.transpose()); D_v_R(&G_measCov_Gt) = vel_H_biasAccInit * bInitCov12 * theta_H_biasOmegaInit.transpose(); D_v_t(&G_measCov_Gt) = - (vel_H_acc * (aCov / dt) * pos_H_acc.transpose()) + + (vel_H_biasAcc * (aCov / dt) * pos_H_biasAcc.transpose()) + (vel_H_biasAccInit * bInitCov11 * pos_H_biasAccInit.transpose()); preintMeasCov_.noalias() += G_measCov_Gt; From bbd1e3f07a9e8b03322d9a1b51efded5f123956f Mon Sep 17 00:00:00 2001 From: Varun Agrawal Date: Sun, 3 Jul 2022 15:57:54 -0400 Subject: [PATCH 24/24] update Lyx document based on Luca's review --- doc/ImuFactor.lyx | 73 +++++++++++++++++++++++++++++++++++++++++++--- doc/ImuFactor.pdf | Bin 249424 -> 250191 bytes 2 files changed, 69 insertions(+), 4 deletions(-) diff --git a/doc/ImuFactor.lyx b/doc/ImuFactor.lyx index 7b176f484e..c335e69496 100644 --- a/doc/ImuFactor.lyx +++ b/doc/ImuFactor.lyx @@ -281,8 +281,8 @@ The noise model associated with this factor is assumed to be zero-mean Gaussian \end_inset . - This covariance matrix is computed in the preintegrated measurement class, - of which there are two variants as discussed above. + This (discrete-time) covariance matrix is computed in the preintegrated + measurement class, of which there are two variants as discussed above. \end_layout \begin_layout Subsubsection* @@ -309,6 +309,20 @@ CombinedImuFactor2 is a 4-way factor between the previous NavState and IMU bias and the current NavState and IMU bias. \end_layout +\begin_layout Standard +Since the Combined IMU Factor has a larger state variable due to the inclusion + of IMU biases, the noise model associated with this factor is assumed to + be a zero mean Gaussian with a +\begin_inset Formula $15\times15$ +\end_inset + + covariance matrix +\begin_inset Formula $\Sigma$ +\end_inset + +, similarly defined on the tangent space of the NavState manifold. +\end_layout + \begin_layout Subsubsection* Covariance Matrices \end_layout @@ -564,7 +578,15 @@ acceleration \end_inset in the body frame. - We know (from Murray84book) that the derivative of + We know (from +\begin_inset CommandInset citation +LatexCommand cite +key "Murray94book" +literal "false" + +\end_inset + +) that the derivative of \begin_inset Formula $R$ \end_inset @@ -1618,6 +1640,42 @@ where \begin_inset Formula $\omega^{b}$ \end_inset +. + Note that +\begin_inset Formula $\Sigma_{k},$ +\end_inset + + +\begin_inset Formula $\Sigma_{\eta}^{ad}$ +\end_inset + +, and +\begin_inset Formula $\Sigma_{\eta}^{gd}$ +\end_inset + + are discrete time covariances with +\begin_inset Formula $\Sigma_{\eta}^{ad}$ +\end_inset + +, and +\begin_inset Formula $\Sigma_{\eta}^{gd}$ +\end_inset + +divided by +\begin_inset Formula $\Delta_{t}$ +\end_inset + +. + Please see the section on Covariance Discretization +\begin_inset CommandInset ref +LatexCommand vpageref +reference "subsec:Covariance-Discretization" +plural "false" +caps "false" +noprefix "false" + +\end_inset + . \end_layout @@ -1645,7 +1703,7 @@ It can be shown that for small we have \begin_inset Formula \[ -\deriv{H(\theta_{k})^{-1}\omega_{k}^{b}}{\theta_{k}}\approx-\frac{1}{2}\Skew{\omega_{k}^{b}}\mbox{ and hence }\deriv{\theta_{k+1}}{\theta_{k}}=I_{3\times3}-\frac{\Delta t}{2}\Skew{\omega_{k}^{b}} +\deriv{H(\theta_{k})^{-1}\omega_{k}^{b}}{\theta_{k}}\approx-\frac{1}{2}\Skew{\omega_{k}^{b}}\mbox{ and hence }\deriv{\theta_{k+1}}{\theta_{k}}=I_{3\times3}-\frac{\Delta_{t}}{2}\Skew{\omega_{k}^{b}} \] \end_inset @@ -2033,6 +2091,13 @@ which we can break into 3 matrices for clarity, representing the main diagonal \begin_layout Subsubsection* Covariance Discretization +\begin_inset CommandInset label +LatexCommand label +name "subsec:Covariance-Discretization" + +\end_inset + + \end_layout \begin_layout Standard diff --git a/doc/ImuFactor.pdf b/doc/ImuFactor.pdf index 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