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gtsam/gtsam/navigation/tests/testImuFactor.cpp

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/* ----------------------------------------------------------------------------
* GTSAM Copyright 2010, Georgia Tech Research Corporation,
* Atlanta, Georgia 30332-0415
* All Rights Reserved
* Authors: Frank Dellaert, et al. (see THANKS for the full author list)
* See LICENSE for the license information
* -------------------------------------------------------------------------- */
/**
* @file testImuFactor.cpp
* @brief Unit test for ImuFactor
* @author Luca Carlone
* @author Frank Dellaert
* @author Richard Roberts
* @author Stephen Williams
*/
// #define ENABLE_TIMING // uncomment for timing results
#include <gtsam/navigation/ImuFactor.h>
#include <gtsam/navigation/ScenarioRunner.h>
#include <gtsam/geometry/Pose3.h>
#include <gtsam/nonlinear/Values.h>
#include <gtsam/nonlinear/factorTesting.h>
#include <gtsam/linear/Sampler.h>
#include <gtsam/base/TestableAssertions.h>
#include <gtsam/base/numericalDerivative.h>
#include <CppUnitLite/TestHarness.h>
#include <boost/bind.hpp>
#include <list>
#include "imuFactorTesting.h"
namespace testing {
// Create default parameters with Z-down and above noise parameters
static boost::shared_ptr<PreintegrationParams> Params() {
auto p = PreintegrationParams::MakeSharedD(kGravity);
p->gyroscopeCovariance = kGyroSigma * kGyroSigma * I_3x3;
p->accelerometerCovariance = kAccelSigma * kAccelSigma * I_3x3;
p->integrationCovariance = 0.0001 * I_3x3;
return p;
}
}
/* ************************************************************************* */
namespace {
// Auxiliary functions to test evaluate error in ImuFactor
/* ************************************************************************* */
Rot3 evaluateRotationError(const ImuFactor& factor, const Pose3& pose_i,
const Vector3& vel_i, const Pose3& pose_j, const Vector3& vel_j,
const Bias& bias) {
return Rot3::Expmap(
factor.evaluateError(pose_i, vel_i, pose_j, vel_j, bias).head(3));
}
} // namespace
/* ************************************************************************* */
TEST(ImuFactor, PreintegratedMeasurementsConstruction) {
// Actual pre-integrated values
PreintegratedImuMeasurements actual(testing::Params());
EXPECT(assert_equal(Rot3(), actual.deltaRij()));
EXPECT(assert_equal(kZero, actual.deltaPij()));
EXPECT(assert_equal(kZero, actual.deltaVij()));
DOUBLES_EQUAL(0.0, actual.deltaTij(), 1e-9);
}
/* ************************************************************************* */
TEST(ImuFactor, PreintegratedMeasurementsReset) {
auto p = testing::Params();
// Create a preintegrated measurement struct and integrate
PreintegratedImuMeasurements pimActual(p);
Vector3 measuredAcc(0.5, 1.0, 0.5);
Vector3 measuredOmega(0.1, 0.3, 0.1);
double deltaT = 1.0;
pimActual.integrateMeasurement(measuredAcc, measuredOmega, deltaT);
// reset and make sure that it is the same as a fresh one
pimActual.resetIntegration();
CHECK(assert_equal(pimActual, PreintegratedImuMeasurements(p)));
// Now create one with a different bias ..
Bias nonZeroBias(Vector3(0.2, 0, 0), Vector3(0.1, 0, 0.3));
PreintegratedImuMeasurements pimExpected(p, nonZeroBias);
// integrate again, then reset to a new bias
pimActual.integrateMeasurement(measuredAcc, measuredOmega, deltaT);
pimActual.resetIntegrationAndSetBias(nonZeroBias);
CHECK(assert_equal(pimActual, pimExpected));
}
/* ************************************************************************* */
TEST(ImuFactor, 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
ScenarioRunner runner(scenario, testing::Params(), T / 10);
PreintegratedImuMeasurements pim = runner.integrate(T);
EXPECT(assert_equal(scenario.pose(T), runner.predict(pim).pose(), 1e-9));
Matrix9 estimatedCov = runner.estimateCovariance(T, 100);
EXPECT(assert_equal(estimatedCov, pim.preintMeasCov(), 0.1));
}
/* ************************************************************************* */
TEST(ImuFactor, PreintegratedMeasurements) {
// Measurements
const double a = 0.1, w = M_PI / 100.0;
Vector3 measuredAcc(a, 0.0, 0.0);
Vector3 measuredOmega(w, 0.0, 0.0);
double deltaT = 0.5;
// Expected pre-integrated values
Vector3 expectedDeltaR1(w * deltaT, 0.0, 0.0);
Vector3 expectedDeltaP1(0.5 * a * deltaT*deltaT, 0, 0);
Vector3 expectedDeltaV1(0.05, 0.0, 0.0);
// Actual pre-integrated values
PreintegratedImuMeasurements actual(testing::Params());
actual.integrateMeasurement(measuredAcc, measuredOmega, deltaT);
EXPECT(assert_equal(Rot3::Expmap(expectedDeltaR1), actual.deltaRij()));
EXPECT(assert_equal(expectedDeltaP1, actual.deltaPij()));
EXPECT(assert_equal(expectedDeltaV1, actual.deltaVij()));
DOUBLES_EQUAL(0.5, actual.deltaTij(), 1e-9);
// Check derivatives of computeError
Bias bias(Vector3(0.2, 0, 0), Vector3(0.1, 0, 0.3)); // Biases (acc, rot)
NavState x1, x2 = actual.predict(x1, bias);
{
Matrix9 aH1, aH2;
Matrix96 aH3;
actual.computeError(x1, x2, bias, aH1, aH2, aH3);
boost::function<Vector9(const NavState&, const NavState&, const Bias&)> f =
boost::bind(&PreintegrationBase::computeError, actual, _1, _2, _3,
boost::none, boost::none, boost::none);
EXPECT(assert_equal(numericalDerivative31(f, x1, x2, bias), aH1, 1e-9));
EXPECT(assert_equal(numericalDerivative32(f, x1, x2, bias), aH2, 1e-9));
EXPECT(assert_equal(numericalDerivative33(f, x1, x2, bias), aH3, 1e-9));
}
// Integrate again
Vector3 expectedDeltaR2(2.0 * 0.5 * M_PI / 100.0, 0.0, 0.0);
Vector3 expectedDeltaP2(0.025 + expectedDeltaP1(0) + 0.5 * 0.1 * 0.5 * 0.5, 0, 0);
Vector3 expectedDeltaV2 = Vector3(0.05, 0.0, 0.0) +
Rot3::Expmap(expectedDeltaR1) * measuredAcc * 0.5;
// Actual pre-integrated values
actual.integrateMeasurement(measuredAcc, measuredOmega, deltaT);
EXPECT(assert_equal(Rot3::Expmap(expectedDeltaR2), actual.deltaRij()));
EXPECT(assert_equal(expectedDeltaP2, actual.deltaPij()));
EXPECT(assert_equal(expectedDeltaV2, actual.deltaVij()));
DOUBLES_EQUAL(1.0, actual.deltaTij(), 1e-9);
}
/* ************************************************************************* */
// Common linearization point and measurements for tests
namespace common {
static const Pose3 x1(Rot3::RzRyRx(M_PI / 12.0, M_PI / 6.0, M_PI / 4.0),
Point3(5.0, 1.0, 0));
static const Vector3 v1(Vector3(0.5, 0.0, 0.0));
static const NavState state1(x1, v1);
// Measurements
static const double w = M_PI / 100;
static const Vector3 measuredOmega(w, 0, 0);
static const Vector3 measuredAcc = x1.rotation().unrotate(
-kGravityAlongNavZDown);
static const double deltaT = 1.0;
static const Pose3 x2(Rot3::RzRyRx(M_PI / 12.0 + w, M_PI / 6.0, M_PI / 4.0),
Point3(5.5, 1.0, 0));
static const Vector3 v2(Vector3(0.5, 0.0, 0.0));
static const NavState state2(x2, v2);
} // namespace common
/* ************************************************************************* */
TEST(ImuFactor, PreintegrationBaseMethods) {
using namespace common;
auto p = testing::Params();
p->omegaCoriolis = Vector3(0.02, 0.03, 0.04);
p->use2ndOrderCoriolis = true;
PreintegratedImuMeasurements pim(p, kZeroBiasHat);
pim.integrateMeasurement(measuredAcc, measuredOmega, deltaT);
pim.integrateMeasurement(measuredAcc, measuredOmega, deltaT);
// biasCorrectedDelta
Matrix96 actualH;
pim.biasCorrectedDelta(kZeroBias, actualH);
Matrix expectedH = numericalDerivative11<Vector9, Bias>(
boost::bind(&PreintegrationBase::biasCorrectedDelta, pim, _1,
boost::none), kZeroBias);
EXPECT(assert_equal(expectedH, actualH));
Matrix9 aH1;
Matrix96 aH2;
NavState predictedState = pim.predict(state1, kZeroBias, aH1, aH2);
Matrix eH1 = numericalDerivative11<NavState, NavState>(
boost::bind(&PreintegrationBase::predict, pim, _1, kZeroBias, boost::none,
boost::none), state1);
EXPECT(assert_equal(eH1, aH1));
Matrix eH2 = numericalDerivative11<NavState, Bias>(
boost::bind(&PreintegrationBase::predict, pim, state1, _1, boost::none,
boost::none), kZeroBias);
EXPECT(assert_equal(eH2, aH2));
}
/* ************************************************************************* */
TEST(ImuFactor, MultipleMeasurements) {
using namespace common;
PreintegratedImuMeasurements expected(testing::Params(), kZeroBiasHat);
expected.integrateMeasurement(measuredAcc, measuredOmega, deltaT);
expected.integrateMeasurement(measuredAcc, measuredOmega, deltaT);
Matrix32 acc,gyro;
Matrix12 dts;
acc << measuredAcc, measuredAcc;
gyro << measuredOmega, measuredOmega;
dts << deltaT, deltaT;
PreintegratedImuMeasurements actual(testing::Params(), kZeroBiasHat);
actual.integrateMeasurements(acc,gyro,dts);
EXPECT(assert_equal(expected,actual));
}
/* ************************************************************************* */
TEST(ImuFactor, ErrorAndJacobians) {
using namespace common;
PreintegratedImuMeasurements pim(testing::Params());
pim.integrateMeasurement(measuredAcc, measuredOmega, deltaT);
EXPECT(assert_equal(state2, pim.predict(state1, kZeroBias)));
// Create factor
ImuFactor factor(X(1), V(1), X(2), V(2), B(1), pim);
// Expected error
Vector expectedError(9);
expectedError << 0, 0, 0, 0, 0, 0, 0, 0, 0;
EXPECT(
assert_equal(expectedError,
factor.evaluateError(x1, v1, x2, v2, kZeroBias)));
Values values;
values.insert(X(1), x1);
values.insert(V(1), v1);
values.insert(X(2), x2);
values.insert(V(2), v2);
values.insert(B(1), kZeroBias);
EXPECT(assert_equal(expectedError, factor.unwhitenedError(values)));
// Make sure linearization is correct
double diffDelta = 1e-7;
EXPECT_CORRECT_FACTOR_JACOBIANS(factor, values, diffDelta, 1e-3);
// Actual Jacobians
Matrix H1a, H2a, H3a, H4a, H5a;
(void) factor.evaluateError(x1, v1, x2, v2, kZeroBias, H1a, H2a, H3a, H4a,
H5a);
// Make sure rotation part is correct when error is interpreted as axis-angle
// Jacobians are around zero, so the rotation part is the same as:
Matrix H1Rot3 = numericalDerivative11<Rot3, Pose3>(
boost::bind(&evaluateRotationError, factor, _1, v1, x2, v2, kZeroBias),
x1);
EXPECT(assert_equal(H1Rot3, H1a.topRows(3)));
Matrix H3Rot3 = numericalDerivative11<Rot3, Pose3>(
boost::bind(&evaluateRotationError, factor, x1, v1, _1, v2, kZeroBias),
x2);
EXPECT(assert_equal(H3Rot3, H3a.topRows(3)));
// Evaluate error with wrong values
Vector3 v2_wrong = v2 + Vector3(0.1, 0.1, 0.1);
values.update(V(2), v2_wrong);
expectedError << 0, 0, 0, 0, 0, 0, -0.0724744871, -0.040715657, -0.151952901;
EXPECT(
assert_equal(expectedError,
factor.evaluateError(x1, v1, x2, v2_wrong, kZeroBias), 1e-2));
EXPECT(assert_equal(expectedError, factor.unwhitenedError(values), 1e-2));
// Make sure the whitening is done correctly
Matrix cov = pim.preintMeasCov();
Matrix R = RtR(cov.inverse());
Vector whitened = R * expectedError;
EXPECT(assert_equal(0.5 * whitened.squaredNorm(), factor.error(values), 1e-4));
// Make sure linearization is correct
EXPECT_CORRECT_FACTOR_JACOBIANS(factor, values, diffDelta, 1e-3);
}
/* ************************************************************************* */
TEST(ImuFactor, ErrorAndJacobianWithBiases) {
using common::x1;
using common::v1;
using common::v2;
Bias bias(Vector3(0.2, 0, 0), Vector3(0.1, 0, 0.3)); // Biases (acc, rot)
Pose3 x2(Rot3::Expmap(Vector3(0, 0, M_PI / 10.0 + M_PI / 10.0)),
Point3(5.5, 1.0, -50.0));
// Measurements
Vector3 measuredOmega;
measuredOmega << 0, 0, M_PI / 10.0 + 0.3;
Vector3 measuredAcc = x1.rotation().unrotate(-kGravityAlongNavZDown)
+ Vector3(0.2, 0.0, 0.0);
double deltaT = 1.0;
auto p = testing::Params();
p->omegaCoriolis = kNonZeroOmegaCoriolis;
Bias biasHat(Vector3(0.2, 0.0, 0.0), Vector3(0.0, 0.0, 0.1));
PreintegratedImuMeasurements pim(p, biasHat);
pim.integrateMeasurement(measuredAcc, measuredOmega, deltaT);
// Make sure of biasCorrectedDelta
Matrix96 actualH;
pim.biasCorrectedDelta(bias, actualH);
Matrix expectedH = numericalDerivative11<Vector9, Bias>(
boost::bind(&PreintegrationBase::biasCorrectedDelta, pim, _1,
boost::none), bias);
EXPECT(assert_equal(expectedH, actualH));
// Create factor
ImuFactor factor(X(1), V(1), X(2), V(2), B(1), pim);
Values values;
values.insert(X(1), x1);
values.insert(V(1), v1);
values.insert(X(2), x2);
values.insert(V(2), v2);
values.insert(B(1), bias);
// Make sure linearization is correct
double diffDelta = 1e-7;
EXPECT_CORRECT_FACTOR_JACOBIANS(factor, values, diffDelta, 1e-3);
}
/* ************************************************************************* */
TEST(ImuFactor, ErrorAndJacobianWith2ndOrderCoriolis) {
using common::x1;
using common::v1;
using common::v2;
Bias bias(Vector3(0.2, 0, 0), Vector3(0.1, 0, 0.3)); // Biases (acc, rot)
Pose3 x2(Rot3::Expmap(Vector3(0, 0, M_PI / 10.0 + M_PI / 10.0)),
Point3(5.5, 1.0, -50.0));
// Measurements
Vector3 measuredOmega;
measuredOmega << 0, 0, M_PI / 10.0 + 0.3;
Vector3 measuredAcc = x1.rotation().unrotate(-kGravityAlongNavZDown)
+ Vector3(0.2, 0.0, 0.0);
double deltaT = 1.0;
auto p = testing::Params();
p->omegaCoriolis = kNonZeroOmegaCoriolis;
p->use2ndOrderCoriolis = true;
PreintegratedImuMeasurements pim(p,
Bias(Vector3(0.2, 0.0, 0.0), Vector3(0.0, 0.0, 0.1)));
pim.integrateMeasurement(measuredAcc, measuredOmega, deltaT);
// Create factor
ImuFactor factor(X(1), V(1), X(2), V(2), B(1), pim);
Values values;
values.insert(X(1), x1);
values.insert(V(1), v1);
values.insert(X(2), x2);
values.insert(V(2), v2);
values.insert(B(1), bias);
// Make sure linearization is correct
double diffDelta = 1e-7;
EXPECT_CORRECT_FACTOR_JACOBIANS(factor, values, diffDelta, 1e-3);
}
/* ************************************************************************* */
TEST(ImuFactor, PartialDerivative_wrt_Bias) {
// Linearization point
Vector3 biasOmega(0, 0, 0); // Current estimate of rotation rate bias
// Measurements
Vector3 measuredOmega(0.1, 0, 0);
double deltaT = 0.5;
auto evaluateRotation = [=](const Vector3 biasOmega) {
return Rot3::Expmap((measuredOmega - biasOmega) * deltaT);
};
// Compute numerical derivatives
Matrix expectedDelRdelBiasOmega =
numericalDerivative11<Rot3, Vector3>(evaluateRotation, biasOmega);
const Matrix3 Jr =
Rot3::ExpmapDerivative((measuredOmega - biasOmega) * deltaT);
Matrix3 actualdelRdelBiasOmega = -Jr * deltaT; // the delta bias appears with the minus sign
// Compare Jacobians
EXPECT(assert_equal(expectedDelRdelBiasOmega, actualdelRdelBiasOmega, 1e-9));
}
/* ************************************************************************* */
TEST(ImuFactor, PartialDerivativeLogmap) {
// Linearization point
Vector3 thetahat(0.1, 0.1, 0); // Current estimate of rotation rate bias
// Measurements
Vector3 deltatheta(0, 0, 0);
auto evaluateLogRotation = [=](const Vector3 deltatheta) {
return Rot3::Logmap(
Rot3::Expmap(thetahat).compose(Rot3::Expmap(deltatheta)));
};
// Compute numerical derivatives
Matrix expectedDelFdeltheta =
numericalDerivative11<Vector, Vector3>(evaluateLogRotation, deltatheta);
Matrix3 actualDelFdeltheta = Rot3::LogmapDerivative(thetahat);
// Compare Jacobians
EXPECT(assert_equal(expectedDelFdeltheta, actualDelFdeltheta));
}
/* ************************************************************************* */
TEST(ImuFactor, fistOrderExponential) {
// Linearization point
Vector3 biasOmega(0, 0, 0); // Current estimate of rotation rate bias
// Measurements
Vector3 measuredOmega(0.1, 0, 0);
double deltaT = 1.0;
// change w.r.t. linearization point
double alpha = 0.0;
Vector3 deltabiasOmega;
deltabiasOmega << alpha, alpha, alpha;
const Matrix3 Jr = Rot3::ExpmapDerivative(
(measuredOmega - biasOmega) * deltaT);
Matrix3 delRdelBiasOmega = -Jr * deltaT; // the delta bias appears with the minus sign
const Matrix expectedRot = Rot3::Expmap(
(measuredOmega - biasOmega - deltabiasOmega) * deltaT).matrix();
const Matrix3 hatRot =
Rot3::Expmap((measuredOmega - biasOmega) * deltaT).matrix();
const Matrix3 actualRot = hatRot
* Rot3::Expmap(delRdelBiasOmega * deltabiasOmega).matrix();
// hatRot * (I_3x3 + skewSymmetric(delRdelBiasOmega * deltabiasOmega));
// This is a first order expansion so the equality is only an approximation
EXPECT(assert_equal(expectedRot, actualRot));
}
/* ************************************************************************* */
Vector3 correctedAcc(const PreintegratedImuMeasurements& pim,
const Vector3& measuredAcc, const Vector3& measuredOmega) {
Vector3 correctedAcc = pim.biasHat().correctAccelerometer(measuredAcc);
Vector3 correctedOmega = pim.biasHat().correctGyroscope(measuredOmega);
return pim.correctMeasurementsBySensorPose(correctedAcc, correctedOmega).first;
}
TEST(ImuFactor, ErrorWithBiasesAndSensorBodyDisplacement) {
const Rot3 nRb = Rot3::Expmap(Vector3(0, 0, M_PI / 4.0));
const Point3 p1(5.0, 1.0, -50.0);
const Vector3 v1(0.5, 0.0, 0.0);
const Vector3 a = nRb * Vector3(0.2, 0.0, 0.0);
const AcceleratingScenario scenario(nRb, p1, v1, a,
Vector3(0, 0, M_PI / 10.0 + 0.3));
auto p = testing::Params();
p->body_P_sensor = Pose3(Rot3::Expmap(Vector3(0, M_PI / 2, 0)),
Point3(0.1, 0.05, 0.01));
p->omegaCoriolis = kNonZeroOmegaCoriolis;
Bias biasHat(Vector3(0.2, 0.0, 0.0), Vector3(0.0, 0.0, 0.0));
const double T = 3.0; // seconds
ScenarioRunner runner(scenario, p, T / 10);
// PreintegratedImuMeasurements pim = runner.integrate(T);
// EXPECT(assert_equal(scenario.pose(T), runner.predict(pim).pose, 1e-9));
//
// Matrix6 estimatedCov = runner.estimatePoseCovariance(T);
// EXPECT(assert_equal(estimatedCov, runner.poseCovariance(pim), 0.1));
//
///////////////////////////////////////////////////////////////////////////////////////////
Pose3 x1(nRb, p1);
// Measurements
Vector3 measuredOmega = runner.actualAngularVelocity(0);
Vector3 measuredAcc = runner.actualSpecificForce(0);
// Get mean prediction from "ground truth" measurements
const Vector3 accNoiseVar2(0.01, 0.02, 0.03);
const Vector3 omegaNoiseVar2(0.03, 0.01, 0.02);
PreintegratedImuMeasurements pim(p, biasHat);
// Check updatedDeltaXij derivatives
Matrix3 D_correctedAcc_measuredOmega = Z_3x3;
pim.correctMeasurementsBySensorPose(measuredAcc, measuredOmega,
boost::none, D_correctedAcc_measuredOmega, boost::none);
Matrix3 expectedD = numericalDerivative11<Vector3, Vector3>(
boost::bind(correctedAcc, pim, measuredAcc, _1), measuredOmega, 1e-6);
EXPECT(assert_equal(expectedD, D_correctedAcc_measuredOmega, 1e-5));
double dt = 0.1;
// TODO(frank): revive derivative tests
// Matrix93 G1, G2;
// Vector9 preint =
// pim.updatedDeltaXij(measuredAcc, measuredOmega, dt, boost::none, G1, G2);
//
// Matrix93 expectedG1 = numericalDerivative21<NavState, Vector3, Vector3>(
// boost::bind(&PreintegratedImuMeasurements::updatedDeltaXij, pim, _1, _2,
// dt, boost::none, boost::none, boost::none), measuredAcc,
// measuredOmega, 1e-6);
// EXPECT(assert_equal(expectedG1, G1, 1e-5));
//
// Matrix93 expectedG2 = numericalDerivative22<NavState, Vector3, Vector3>(
// boost::bind(&PreintegratedImuMeasurements::updatedDeltaXij, pim, _1, _2,
// dt, boost::none, boost::none, boost::none), measuredAcc,
// measuredOmega, 1e-6);
// EXPECT(assert_equal(expectedG2, G2, 1e-5));
Bias bias(Vector3(0.2, 0, 0), Vector3(0, 0, 0.3)); // Biases (acc, rot)
// integrate at least twice to get position information
// otherwise factor cov noise from preint_cov is not positive definite
pim.integrateMeasurement(measuredAcc, measuredOmega, dt);
pim.integrateMeasurement(measuredAcc, measuredOmega, dt);
// Create factor
ImuFactor factor(X(1), V(1), X(2), V(2), B(1), pim);
Pose3 x2(Rot3::Expmap(Vector3(0, 0, M_PI / 4.0 + M_PI / 10.0)),
Point3(5.5, 1.0, -50.0));
Vector3 v2(Vector3(0.5, 0.0, 0.0));
Values values;
values.insert(X(1), x1);
values.insert(V(1), v1);
values.insert(X(2), x2);
values.insert(V(2), v2);
values.insert(B(1), bias);
// Make sure linearization is correct
double diffDelta = 1e-8;
EXPECT_CORRECT_FACTOR_JACOBIANS(factor, values, diffDelta, 1e-3);
}
/* ************************************************************************* */
TEST(ImuFactor, PredictPositionAndVelocity) {
gttic(PredictPositionAndVelocity);
Bias bias(Vector3(0, 0, 0), Vector3(0, 0, 0)); // Biases (acc, rot)
// Measurements
Vector3 measuredOmega;
measuredOmega << 0, 0, 0; // M_PI/10.0+0.3;
Vector3 measuredAcc;
measuredAcc << 0, 1, -kGravity;
double deltaT = 0.001;
PreintegratedImuMeasurements pim(testing::Params(),
Bias(Vector3(0.2, 0.0, 0.0), Vector3(0.0, 0.0, 0.0)));
for (int i = 0; i < 1000; ++i)
pim.integrateMeasurement(measuredAcc, measuredOmega, deltaT);
// Create factor
ImuFactor factor(X(1), V(1), X(2), V(2), B(1), pim);
// Predict
Pose3 x1;
Vector3 v1(0, 0.0, 0.0);
NavState actual = pim.predict(NavState(x1, v1), bias);
NavState expected(Rot3(), Point3(0, 0.5, 0), Vector3(0, 1, 0));
EXPECT(assert_equal(expected, actual));
}
/* ************************************************************************* */
TEST(ImuFactor, PredictRotation) {
gttic(PredictRotation);
Bias bias(Vector3(0, 0, 0), Vector3(0, 0, 0)); // Biases (acc, rot)
// Measurements
Vector3 measuredOmega;
measuredOmega << 0, 0, M_PI / 10; // M_PI/10.0+0.3;
Vector3 measuredAcc;
measuredAcc << 0, 0, -kGravity;
double deltaT = 0.001;
PreintegratedImuMeasurements pim(testing::Params(),
Bias(Vector3(0.2, 0.0, 0.0), Vector3(0.0, 0.0, 0.0)));
for (int i = 0; i < 1000; ++i)
pim.integrateMeasurement(measuredAcc, measuredOmega, deltaT);
// Create factor
ImuFactor factor(X(1), V(1), X(2), V(2), B(1), pim);
// Predict
NavState actual = pim.predict(NavState(), bias);
NavState expected(Rot3::Ypr(M_PI / 10, 0, 0), Point3(0,0,0), Z_3x1);
EXPECT(assert_equal(expected, actual));
}
/* ************************************************************************* */
TEST(ImuFactor, PredictArbitrary) {
gttic(PredictArbitrary);
Pose3 x1;
const Vector3 v1(0, 0, 0);
const AcceleratingScenario scenario(x1.rotation(), x1.translation(), v1,
Vector3(0.1, 0.2, 0), Vector3(M_PI / 10, M_PI / 10, M_PI / 10));
const double T = 3.0; // seconds
ScenarioRunner runner(scenario, testing::Params(), T / 10);
//
// PreintegratedImuMeasurements pim = runner.integrate(T);
// EXPECT(assert_equal(scenario.pose(T), runner.predict(pim).pose, 1e-9));
//
// Matrix6 estimatedCov = runner.estimatePoseCovariance(T);
// EXPECT(assert_equal(estimatedCov, runner.poseCovariance(pim), 0.1));
//////////////////////////////////////////////////////////////////////////////////
Bias biasHat(Vector3(0.2, 0.0, 0.0), Vector3(0.0, 0.0, 0.0));
// Measurements
Vector3 measuredOmega = runner.actualAngularVelocity(0);
Vector3 measuredAcc = runner.actualSpecificForce(0);
auto p = testing::Params();
p->integrationCovariance = Z_3x3; // MonteCarlo does not sample integration noise
PreintegratedImuMeasurements pim(p, biasHat);
Bias bias(Vector3(0, 0, 0), Vector3(0, 0, 0));
// EXPECT(MonteCarlo(pim, NavState(x1, v1), bias, 0.1, boost::none, measuredAcc, measuredOmega,
// Vector3::Constant(accNoiseVar), Vector3::Constant(omegaNoiseVar), 100000));
double dt = 0.001;
for (int i = 0; i < 1000; ++i)
pim.integrateMeasurement(measuredAcc, measuredOmega, dt);
// Create factor
ImuFactor factor(X(1), V(1), X(2), V(2), B(1), pim);
// Predict
NavState actual = pim.predict(NavState(x1, v1), bias);
// Regression test for Imu Refactor
Rot3 expectedR( //
+0.903715275, -0.250741668, 0.347026393, //
+0.347026393, 0.903715275, -0.250741668, //
-0.250741668, 0.347026393, 0.903715275);
Point3 expectedT(-0.516077031, 0.57842919, 0.0876478403);
Vector3 expectedV(-1.62337767, 1.57954409, 0.343833571);
NavState expected(expectedR, expectedT, expectedV);
EXPECT(assert_equal(expected, actual, 1e-7));
}
/* ************************************************************************* */
TEST(ImuFactor, bodyPSensorNoBias) {
gttic(bodyPSensorNoBias);
Bias bias(Vector3(0, 0, 0), Vector3(0, 0.1, 0)); // Biases (acc, rot)
// Rotate sensor (z-down) to body (same as navigation) i.e. z-up
auto p = testing::Params();
p->n_gravity = Vector3(0, 0, -kGravity); // z-up nav frame
p->body_P_sensor = Pose3(Rot3::Ypr(0, 0, M_PI), Point3(0, 0, 0));
// Measurements
// Gyroscope measurement is the angular velocity of sensor w.r.t nav frame in sensor frame
Vector3 s_omegaMeas_ns(0, 0.1, M_PI / 10);
// Acc measurement is acceleration of sensor in the sensor frame, when stationary,
// table exerts an equal and opposite force w.r.t gravity
Vector3 s_accMeas(0, 0, -kGravity);
double dt = 0.001;
PreintegratedImuMeasurements pim(p, bias);
for (int i = 0; i < 1000; ++i)
pim.integrateMeasurement(s_accMeas, s_omegaMeas_ns, dt);
// Create factor
ImuFactor factor(X(1), V(1), X(2), V(2), B(1), pim);
// Predict
NavState actual = pim.predict(NavState(), bias);
Pose3 expectedPose(Rot3::Ypr(-M_PI / 10, 0, 0), Point3(0, 0, 0));
EXPECT(assert_equal(expectedPose, actual.pose()));
Vector3 expectedVelocity(0, 0, 0);
EXPECT(assert_equal(Vector(expectedVelocity), Vector(actual.velocity())));
}
/* ************************************************************************* */
#include <gtsam/nonlinear/NonlinearFactorGraph.h>
#include <gtsam/slam/BetweenFactor.h>
#include <gtsam/nonlinear/LevenbergMarquardtOptimizer.h>
#include <gtsam/nonlinear/Marginals.h>
TEST(ImuFactor, bodyPSensorWithBias) {
gttic(bodyPSensorWithBias);
using noiseModel::Diagonal;
typedef Bias Bias;
int numFactors = 10;
Vector6 noiseBetweenBiasSigma;
noiseBetweenBiasSigma << Vector3(2.0e-5, 2.0e-5, 2.0e-5), Vector3(3.0e-6,
3.0e-6, 3.0e-6);
SharedDiagonal biasNoiseModel = Diagonal::Sigmas(noiseBetweenBiasSigma);
// Measurements
// Sensor frame is z-down
// Gyroscope measurement is the angular velocity of sensor w.r.t nav frame in sensor frame
Vector3 measuredOmega(0, 0.01, 0);
// Acc measurement is acceleration of sensor in the sensor frame, when stationary,
// table exerts an equal and opposite force w.r.t gravity
Vector3 measuredAcc(0, 0, -kGravity);
auto p = testing::Params();
p->n_gravity = Vector3(0, 0, -kGravity);
p->body_P_sensor = Pose3(Rot3::Ypr(0, 0, M_PI), Point3(0,0,0));
p->accelerometerCovariance = 1e-7 * I_3x3;
p->gyroscopeCovariance = 1e-8 * I_3x3;
p->integrationCovariance = 1e-9 * I_3x3;
double deltaT = 0.005;
// Specify noise values on priors
Vector6 priorNoisePoseSigmas(
(Vector(6) << 0.001, 0.001, 0.001, 0.01, 0.01, 0.01).finished());
Vector3 priorNoiseVelSigmas((Vector(3) << 0.1, 0.1, 0.1).finished());
Vector6 priorNoiseBiasSigmas(
(Vector(6) << 0.1, 0.1, 0.1, 0.5e-1, 0.5e-1, 0.5e-1).finished());
SharedDiagonal priorNoisePose = Diagonal::Sigmas(priorNoisePoseSigmas);
SharedDiagonal priorNoiseVel = Diagonal::Sigmas(priorNoiseVelSigmas);
SharedDiagonal priorNoiseBias = Diagonal::Sigmas(priorNoiseBiasSigmas);
Vector3 zeroVel(0, 0, 0);
// Create a factor graph with priors on initial pose, vlocity and bias
NonlinearFactorGraph graph;
Values values;
graph.addPrior<>(X(0), Pose3(), priorNoisePose);
values.insert(X(0), Pose3());
graph.addPrior<>(V(0), zeroVel, priorNoiseVel);
values.insert(V(0), zeroVel);
// The key to this test is that we specify the bias, in the sensor frame, as known a priori
// We also create factors below that encode our assumption that this bias is constant over time
// In theory, after optimization, we should recover that same bias estimate
Bias priorBias(Vector3(0, 0, 0), Vector3(0, 0.01, 0)); // Biases (acc, rot)
graph.addPrior<>(B(0), priorBias, priorNoiseBias);
values.insert(B(0), priorBias);
// Now add IMU factors and bias noise models
Bias zeroBias(Vector3(0, 0, 0), Vector3(0, 0, 0));
for (int i = 1; i < numFactors; i++) {
PreintegratedImuMeasurements pim = PreintegratedImuMeasurements(p,
priorBias);
for (int j = 0; j < 200; ++j)
pim.integrateMeasurement(measuredAcc, measuredOmega, deltaT);
// Create factors
graph.emplace_shared<ImuFactor>(X(i - 1), V(i - 1), X(i), V(i), B(i - 1), pim);
graph.emplace_shared<BetweenFactor<Bias> >(B(i - 1), B(i), zeroBias, biasNoiseModel);
values.insert(X(i), Pose3());
values.insert(V(i), zeroVel);
values.insert(B(i), priorBias);
}
// Finally, optimize, and get bias at last time step
Values results = LevenbergMarquardtOptimizer(graph, values).optimize();
Bias biasActual = results.at<Bias>(B(numFactors - 1));
// And compare it with expected value (our prior)
Bias biasExpected(Vector3(0, 0, 0), Vector3(0, 0.01, 0));
EXPECT(assert_equal(biasExpected, biasActual, 1e-3));
}
/* ************************************************************************* */
#ifdef GTSAM_TANGENT_PREINTEGRATION
static const double kVelocity = 2.0, kAngularVelocity = M_PI / 6;
struct ImuFactorMergeTest {
boost::shared_ptr<PreintegrationParams> p_;
const ConstantTwistScenario forward_, loop_;
ImuFactorMergeTest()
: p_(PreintegrationParams::MakeSharedU(kGravity)),
forward_(kZero, Vector3(kVelocity, 0, 0)),
loop_(Vector3(0, -kAngularVelocity, 0), Vector3(kVelocity, 0, 0)) {
// arbitrary noise values
p_->gyroscopeCovariance = I_3x3 * 0.01;
p_->accelerometerCovariance = I_3x3 * 0.02;
p_->accelerometerCovariance = I_3x3 * 0.03;
}
int TestScenario(TestResult& result_, const std::string& name_,
const Scenario& scenario,
const Bias& bias01,
const Bias& bias12, double tol) {
// Test merge by creating a 01, 12, and 02 PreintegratedRotation,
// then checking the merge of 01-12 matches 02.
PreintegratedImuMeasurements pim01(p_, bias01);
PreintegratedImuMeasurements pim12(p_, bias12);
PreintegratedImuMeasurements pim02_expected(p_, bias01);
double deltaT = 0.01;
ScenarioRunner runner(scenario, p_, deltaT);
// TODO(frank) can this loop just go into runner ?
for (int i = 0; i < 100; i++) {
double t = i * deltaT;
// integrate the measurements appropriately
Vector3 accel_meas = runner.actualSpecificForce(t);
Vector3 omega_meas = runner.actualAngularVelocity(t);
pim02_expected.integrateMeasurement(accel_meas, omega_meas, deltaT);
if (i < 50) {
pim01.integrateMeasurement(accel_meas, omega_meas, deltaT);
} else {
pim12.integrateMeasurement(accel_meas, omega_meas, deltaT);
}
}
auto actual_pim02 = ImuFactor::Merge(pim01, pim12);
EXPECT(assert_equal(pim02_expected.preintegrated(),
actual_pim02.preintegrated(), tol));
EXPECT(assert_equal(pim02_expected, actual_pim02, tol));
ImuFactor::shared_ptr factor01 =
boost::make_shared<ImuFactor>(X(0), V(0), X(1), V(1), B(0), pim01);
ImuFactor::shared_ptr factor12 =
boost::make_shared<ImuFactor>(X(1), V(1), X(2), V(2), B(0), pim12);
ImuFactor::shared_ptr factor02_expected = boost::make_shared<ImuFactor>(
X(0), V(0), X(2), V(2), B(0), pim02_expected);
ImuFactor::shared_ptr factor02_merged = ImuFactor::Merge(factor01, factor12);
EXPECT(assert_equal(*factor02_expected, *factor02_merged, tol));
return result_.getFailureCount();
}
void TestScenarios(TestResult& result_, const std::string& name_,
const Bias& bias01,
const Bias& bias12, double tol) {
for (auto scenario : {forward_, loop_})
TestScenario(result_, name_, scenario, bias01, bias12, tol);
}
};
/* ************************************************************************* */
// Test case with zero biases
TEST(ImuFactor, MergeZeroBias) {
ImuFactorMergeTest mergeTest;
mergeTest.TestScenarios(result_, name_, kZeroBias, kZeroBias, 1e-4);
}
// Test case with identical biases: we expect an exact answer.
TEST(ImuFactor, MergeConstantBias) {
ImuFactorMergeTest mergeTest;
Bias bias(Vector3(0.03, -0.02, 0.01), Vector3(-0.01, 0.02, -0.03));
mergeTest.TestScenarios(result_, name_, bias, bias, 1e-4);
}
// Test case with different biases where we expect there to be some variation.
TEST(ImuFactor, MergeChangingBias) {
ImuFactorMergeTest mergeTest;
mergeTest.TestScenarios(result_, name_,
Bias(Vector3(0.03, -0.02, 0.01), Vector3(-0.01, 0.02, -0.03)),
Bias(Vector3(0.01, 0.02, 0.03), Vector3(0.03, -0.02, 0.01)), 1e-1);
}
// Test case with non-zero coriolis
TEST(ImuFactor, MergeWithCoriolis) {
ImuFactorMergeTest mergeTest;
mergeTest.p_->omegaCoriolis = Vector3(0.1, 0.2, -0.1);
mergeTest.TestScenarios(result_, name_, kZeroBias, kZeroBias, 1e-4);
}
#endif
/* ************************************************************************* */
// Same values as pre-integration test but now testing covariance
TEST(ImuFactor, CheckCovariance) {
gttic(CheckCovariance);
// Measurements
Vector3 measuredAcc(0.1, 0.0, 0.0);
Vector3 measuredOmega(M_PI / 100.0, 0.0, 0.0);
double deltaT = 0.5;
PreintegratedImuMeasurements actual(testing::Params());
actual.integrateMeasurement(measuredAcc, measuredOmega, deltaT);
Matrix9 expected;
expected << 1.0577e-08, 0, 0, 0, 0, 0, 0, 0, 0, //
0, 1.0577e-08, 0, 0, 0, 0, 0, 0, 0, //
0, 0, 1.0577e-08, 0, 0, 0, 0, 0, 0, //
0, 0, 0, 5.00868e-05, 0, 0, 3.47222e-07, 0, 0, //
0, 0, 0, 0, 5.00868e-05, 0, 0, 3.47222e-07, 0, //
0, 0, 0, 0, 0, 5.00868e-05, 0, 0, 3.47222e-07, //
0, 0, 0, 3.47222e-07, 0, 0, 1.38889e-06, 0, 0, //
0, 0, 0, 0, 3.47222e-07, 0, 0, 1.38889e-06, 0, //
0, 0, 0, 0, 0, 3.47222e-07, 0, 0, 1.38889e-06;
EXPECT(assert_equal(expected, actual.preintMeasCov()));
}
/* ************************************************************************* */
int main() {
TestResult tr;
auto result = TestRegistry::runAllTests(tr);
#ifdef ENABLE_TIMING
tictoc_print_();
#endif
return result;
}
/* ************************************************************************* */
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