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deleted old test

release/4.3a0
lcarlone 2016-06-04 21:36:55 -04:00
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gtsam/navigation/tests/testImuFactorOld.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, Stephen Williams, Richard Roberts, Frank Dellaert
*/
#include <gtsam/navigation/ImuFactor.h>
#include <gtsam/navigation/ImuBias.h>
#include <gtsam/geometry/Pose3.h>
#include <gtsam/nonlinear/Values.h>
#include <gtsam/nonlinear/factorTesting.h>
#include <gtsam/linear/Sampler.h>
#include <gtsam/inference/Symbol.h>
#include <gtsam/base/TestableAssertions.h>
#include <gtsam/base/numericalDerivative.h>
#include <CppUnitLite/TestHarness.h>
#include <boost/bind.hpp>
#include <list>
using namespace std;
using namespace gtsam;
// Convenience for named keys
using symbol_shorthand::X;
using symbol_shorthand::V;
using symbol_shorthand::B;
#if 0
static const Vector3 kGravityAlongNavZDown(0, 0, 9.81);
static const Vector3 kZeroOmegaCoriolis(0, 0, 0);
static const Vector3 kNonZeroOmegaCoriolis(0, 0.1, 0.1);
static const imuBias::ConstantBias kZeroBiasHat, kZeroBias;
/* ************************************************************************* */
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 imuBias::ConstantBias& bias) {
return Rot3::Expmap(
factor.evaluateError(pose_i, vel_i, pose_j, vel_j, bias).head(3));
}
// Define covariance matrices
/* ************************************************************************* */
double accNoiseVar = 0.01;
double omegaNoiseVar = 0.03;
double intNoiseVar = 0.0001;
const Matrix3 kMeasuredAccCovariance = accNoiseVar * I_3x3;
const Matrix3 kMeasuredOmegaCovariance = omegaNoiseVar * I_3x3;
const Matrix3 kIntegrationErrorCovariance = intNoiseVar * I_3x3;
// Auxiliary functions to test preintegrated Jacobians
// delPdelBiasAcc_ delPdelBiasOmega_ delVdelBiasAcc_ delVdelBiasOmega_ delRdelBiasOmega_
/* ************************************************************************* */
PreintegratedImuMeasurements evaluatePreintegratedMeasurements(
const imuBias::ConstantBias& bias, const list<Vector3>& measuredAccs,
const list<Vector3>& measuredOmegas, const list<double>& deltaTs) {
PreintegratedImuMeasurements result(bias, kMeasuredAccCovariance,
kMeasuredOmegaCovariance, kIntegrationErrorCovariance);
list<Vector3>::const_iterator itAcc = measuredAccs.begin();
list<Vector3>::const_iterator itOmega = measuredOmegas.begin();
list<double>::const_iterator itDeltaT = deltaTs.begin();
for (; itAcc != measuredAccs.end(); ++itAcc, ++itOmega, ++itDeltaT) {
result.integrateMeasurement(*itAcc, *itOmega, *itDeltaT);
}
return result;
}
Vector3 evaluatePreintegratedMeasurementsPosition(
const imuBias::ConstantBias& bias, const list<Vector3>& measuredAccs,
const list<Vector3>& measuredOmegas, const list<double>& deltaTs) {
return evaluatePreintegratedMeasurements(bias, measuredAccs, measuredOmegas,
deltaTs).deltaPij();
}
Vector3 evaluatePreintegratedMeasurementsVelocity(
const imuBias::ConstantBias& bias, const list<Vector3>& measuredAccs,
const list<Vector3>& measuredOmegas, const list<double>& deltaTs) {
return evaluatePreintegratedMeasurements(bias, measuredAccs, measuredOmegas,
deltaTs).deltaVij();
}
Rot3 evaluatePreintegratedMeasurementsRotation(
const imuBias::ConstantBias& bias, const list<Vector3>& measuredAccs,
const list<Vector3>& measuredOmegas, const list<double>& deltaTs) {
return Rot3(
evaluatePreintegratedMeasurements(bias, measuredAccs, measuredOmegas,
deltaTs).deltaRij());
}
Rot3 evaluateRotation(const Vector3 measuredOmega, const Vector3 biasOmega,
const double deltaT) {
return Rot3::Expmap((measuredOmega - biasOmega) * deltaT);
}
Vector3 evaluateLogRotation(const Vector3 thetahat, const Vector3 deltatheta) {
return Rot3::Logmap(Rot3::Expmap(thetahat).compose(Rot3::Expmap(deltatheta)));
}
} // namespace
/* ************************************************************************* */
bool MonteCarlo(const PreintegratedImuMeasurements& pim,
const NavState& state, const imuBias::ConstantBias& bias, double dt,
const Pose3& body_P_sensor, const Vector3& measuredAcc,
const Vector3& measuredOmega, size_t N = 10,
size_t M = 1) {
// Get mean prediction from "ground truth" measurements
PreintegratedImuMeasurements pim1 = pim;
for (size_t k = 0; k < M; k++)
pim1.integrateMeasurement(measuredAcc, measuredOmega, dt, body_P_sensor);
NavState prediction = pim1.predict(state, bias);
Matrix9 actual = pim1.preintMeasCov();
// Do a Monte Carlo analysis to determine empirical density on the predicted state
Sampler sampleAccelerationNoise(Vector3::Constant(sqrt(accNoiseVar / dt)), 0);
Sampler sampleOmegaNoise(Vector3::Constant(sqrt(omegaNoiseVar / dt)), 10);
Matrix samples(9, N);
Vector9 sum = Vector9::Zero();
for (size_t i = 0; i < N; i++) {
PreintegratedImuMeasurements pim2 = pim;
for (size_t k = 0; k < M; k++) {
Vector3 perturbedAcc = measuredAcc + sampleAccelerationNoise.sample();
Vector3 perturbedOmega = measuredOmega + sampleOmegaNoise.sample();
pim2.integrateMeasurement(perturbedAcc, perturbedOmega, dt,
body_P_sensor);
}
NavState sampled = pim2.predict(state, bias);
Vector9 xi = sampled.localCoordinates(prediction);
samples.col(i) = xi;
sum += xi;
}
// Vector9 sampleMean = sum / N;
Matrix9 Q;
Q.setZero();
for (size_t i = 0; i < N; i++) {
Vector9 xi = samples.col(i);
// xi -= sampleMean;
Q += xi * xi.transpose() / (N - 1);
}
// Compare Monte-Carlo value with actual (computed) value
return assert_equal(Matrix(1000000*Q), 1000000*actual, 1);
}
/* ************************************************************************* */
TEST(ImuFactor, StraightLine) {
// Set up IMU measurements
static const double g = 10; // make gravity 10 to make this easy to check
static const double v = 50.0, a = 0.2, dt = 3.0;
const double dt22 = dt * dt / 2;
// 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
static const Rot3 nRb(Point3(0, 1, 0), Point3(1, 0, 0), Point3(0, 0, -1));
static const Point3 initial_position(10, 20, 0);
static const Vector3 initial_velocity(v, 0, 0);
static const NavState state1(nRb, initial_position, initial_velocity);
// set up acceleration in X direction, no angular velocity.
// Since body Z-axis is pointing down, accelerometer measures table exerting force in negative Z
Vector3 measuredAcc(a, 0, -g), measuredOmega(0, 0, 0);
// Create parameters assuming nav frame has Z up
boost::shared_ptr<PreintegratedImuMeasurements::Params> p =
PreintegratedImuMeasurements::Params::MakeSharedU(g);
p->accelerometerCovariance = kMeasuredAccCovariance;
p->gyroscopeCovariance = kMeasuredOmegaCovariance;
// Check G1 and G2 derivatives of pim.update
// Now, preintegrate for 3 seconds, in 10 steps
PreintegratedImuMeasurements pim(p, kZeroBiasHat);
for (size_t i = 0; i < 10; i++)
pim.integrateMeasurement(measuredAcc, measuredOmega, dt / 10);
// Matrix9 aG0; Matrix93 aG1,aG2;
// boost::function<NavState(const Vector3&, const Vector3&)> f =
// boost::bind(&ManifoldPreintegration::update, pim, _1, _2, dt/10,
// boost::none, boost::none, boost::none);
// pim.update(measuredAcc, measuredOmega, dt / 10, aG0, aG1, aG2);
// EXPECT(assert_equal(numericalDerivative21(f, measuredAcc, measuredOmega, 1e-7), aG1, 1e-7));
// EXPECT(assert_equal(numericalDerivative22(f, measuredAcc, measuredOmega, 1e-7), aG2, 1e-7));
// Do Monte-Carlo analysis
PreintegratedImuMeasurements pimMC(kZeroBiasHat, p->accelerometerCovariance,
p->gyroscopeCovariance, Z_3x3, true); // MonteCarlo does not sample integration noise
EXPECT(MonteCarlo(pimMC, state1, kZeroBias, dt/10, Pose3(), measuredAcc, measuredOmega));
// Check integrated quantities in body frame: gravity measured by IMU is integrated!
Vector3 b_deltaP(a * dt22, 0, -g * dt22);
Vector3 b_deltaV(a * dt, 0, -g * dt);
EXPECT(assert_equal(Rot3(), pim.deltaRij()));
EXPECT(assert_equal(b_deltaP, pim.deltaPij()));
EXPECT(assert_equal(b_deltaV, pim.deltaVij()));
// Check bias-corrected delta: also in body frame
Vector9 expectedBC;
expectedBC << Vector3(0, 0, 0), b_deltaP, b_deltaV;
EXPECT(assert_equal(expectedBC, pim.biasCorrectedDelta(kZeroBias)));
// Check prediction in nav, note we move along x in body, along y in nav
Point3 expected_position(10 + v * dt, 20 + a * dt22, 0);
Velocity3 expected_velocity(v, a * dt, 0);
NavState expected(nRb, expected_position, expected_velocity);
EXPECT(assert_equal(expected, pim.predict(state1, kZeroBias)));
}
/* ************************************************************************* */
TEST(ImuFactor, PreintegratedMeasurements) {
// Measurements
Vector3 measuredAcc(0.1, 0.0, 0.0);
Vector3 measuredOmega(M_PI / 100.0, 0.0, 0.0);
double deltaT = 0.5;
// Expected preintegrated values
Vector3 expectedDeltaP1;
expectedDeltaP1 << 0.5 * 0.1 * 0.5 * 0.5, 0, 0;
Vector3 expectedDeltaV1(0.05, 0.0, 0.0);
Rot3 expectedDeltaR1 = Rot3::RzRyRx(0.5 * M_PI / 100.0, 0.0, 0.0);
double expectedDeltaT1(0.5);
// Actual preintegrated values
PreintegratedImuMeasurements actual1(kZeroBiasHat, kMeasuredAccCovariance,
kMeasuredOmegaCovariance, kIntegrationErrorCovariance);
actual1.integrateMeasurement(measuredAcc, measuredOmega, deltaT);
EXPECT(assert_equal(Vector(expectedDeltaP1), Vector(actual1.deltaPij())));
EXPECT(assert_equal(Vector(expectedDeltaV1), Vector(actual1.deltaVij())));
EXPECT(assert_equal(expectedDeltaR1, Rot3(actual1.deltaRij())));
DOUBLES_EQUAL(expectedDeltaT1, actual1.deltaTij(), 1e-9);
// Integrate again
Vector3 expectedDeltaP2;
expectedDeltaP2 << 0.025 + expectedDeltaP1(0) + 0.5 * 0.1 * 0.5 * 0.5, 0, 0;
Vector3 expectedDeltaV2 = Vector3(0.05, 0.0, 0.0)
+ expectedDeltaR1.matrix() * measuredAcc * 0.5;
Rot3 expectedDeltaR2 = Rot3::RzRyRx(2.0 * 0.5 * M_PI / 100.0, 0.0, 0.0);
double expectedDeltaT2(1);
// Actual preintegrated values
PreintegratedImuMeasurements actual2 = actual1;
actual2.integrateMeasurement(measuredAcc, measuredOmega, deltaT);
EXPECT(assert_equal(Vector(expectedDeltaP2), Vector(actual2.deltaPij())));
EXPECT(assert_equal(Vector(expectedDeltaV2), Vector(actual2.deltaVij())));
EXPECT(assert_equal(expectedDeltaR2, Rot3(actual2.deltaRij())));
DOUBLES_EQUAL(expectedDeltaT2, actual2.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;
boost::shared_ptr<PreintegratedImuMeasurements::Params> p =
PreintegratedImuMeasurements::Params::MakeSharedD();
p->gyroscopeCovariance = kMeasuredOmegaCovariance;
p->omegaCoriolis = Vector3(0.02, 0.03, 0.04);
p->accelerometerCovariance = kMeasuredAccCovariance;
p->integrationCovariance = kIntegrationErrorCovariance;
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, imuBias::ConstantBias>(
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, imuBias::ConstantBias>(
boost::bind(&PreintegrationBase::predict, pim, state1, _1, boost::none,
boost::none), kZeroBias);
EXPECT(assert_equal(eH2, aH2));
return;
}
/* ************************************************************************* */
TEST(ImuFactor, ErrorAndJacobians) {
using namespace common;
PreintegratedImuMeasurements pim(kZeroBiasHat, kMeasuredAccCovariance,
kMeasuredOmegaCovariance, kIntegrationErrorCovariance);
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, kGravityAlongNavZDown,
kZeroOmegaCoriolis);
// 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-5));
// 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;
imuBias::ConstantBias 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;
imuBias::ConstantBias biasHat(Vector3(0.2, 0.0, 0.0), Vector3(0.0, 0.0, 0.1));
PreintegratedImuMeasurements pim(biasHat, kMeasuredAccCovariance,
kMeasuredOmegaCovariance, kIntegrationErrorCovariance);
pim.integrateMeasurement(measuredAcc, measuredOmega, deltaT);
// Make sure of biasCorrectedDelta
Matrix96 actualH;
pim.biasCorrectedDelta(bias, actualH);
Matrix expectedH = numericalDerivative11<Vector9, imuBias::ConstantBias>(
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, kGravityAlongNavZDown,
kNonZeroOmegaCoriolis);
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;
imuBias::ConstantBias 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;
PreintegratedImuMeasurements pim(
imuBias::ConstantBias(Vector3(0.2, 0.0, 0.0), Vector3(0.0, 0.0, 0.1)),
kMeasuredAccCovariance, kMeasuredOmegaCovariance,
kIntegrationErrorCovariance);
pim.integrateMeasurement(measuredAcc, measuredOmega, deltaT);
// Create factor
Pose3 bodyPsensor = Pose3();
bool use2ndOrderCoriolis = true;
ImuFactor factor(X(1), V(1), X(2), V(2), B(1), pim, kGravityAlongNavZDown,
kNonZeroOmegaCoriolis, bodyPsensor, use2ndOrderCoriolis);
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;
// Compute numerical derivatives
Matrix expectedDelRdelBiasOmega = numericalDerivative11<Rot3, Vector3>(
boost::bind(&evaluateRotation, measuredOmega, _1, deltaT),
Vector3(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);
// Compute numerical derivatives
Matrix expectedDelFdeltheta = numericalDerivative11<Vector, Vector3>(
boost::bind(&evaluateLogRotation, thetahat, _1), Vector3(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));
}
/* ************************************************************************* */
TEST(ImuFactor, FirstOrderPreIntegratedMeasurements) {
Pose3 body_P_sensor(Rot3::Expmap(Vector3(0, 0.1, 0.1)), Point3(1, 0, 1));
// Measurements
list<Vector3> measuredAccs, measuredOmegas;
list<double> deltaTs;
measuredAccs.push_back(Vector3(0.1, 0.0, 0.0));
measuredOmegas.push_back(Vector3(M_PI / 100.0, 0.0, 0.0));
deltaTs.push_back(0.01);
measuredAccs.push_back(Vector3(0.1, 0.0, 0.0));
measuredOmegas.push_back(Vector3(M_PI / 100.0, 0.0, 0.0));
deltaTs.push_back(0.01);
for (int i = 1; i < 100; i++) {
measuredAccs.push_back(Vector3(0.05, 0.09, 0.01));
measuredOmegas.push_back(
Vector3(M_PI / 100.0, M_PI / 300.0, 2 * M_PI / 100.0));
deltaTs.push_back(0.01);
}
// Actual preintegrated values
PreintegratedImuMeasurements preintegrated =
evaluatePreintegratedMeasurements(kZeroBias, measuredAccs, measuredOmegas,
deltaTs);
// Compute numerical derivatives
Matrix expectedDelPdelBias = numericalDerivative11<Vector,
imuBias::ConstantBias>(
boost::bind(&evaluatePreintegratedMeasurementsPosition, _1, measuredAccs,
measuredOmegas, deltaTs), kZeroBias);
Matrix expectedDelPdelBiasAcc = expectedDelPdelBias.leftCols(3);
Matrix expectedDelPdelBiasOmega = expectedDelPdelBias.rightCols(3);
Matrix expectedDelVdelBias = numericalDerivative11<Vector,
imuBias::ConstantBias>(
boost::bind(&evaluatePreintegratedMeasurementsVelocity, _1, measuredAccs,
measuredOmegas, deltaTs), kZeroBias);
Matrix expectedDelVdelBiasAcc = expectedDelVdelBias.leftCols(3);
Matrix expectedDelVdelBiasOmega = expectedDelVdelBias.rightCols(3);
Matrix expectedDelRdelBias =
numericalDerivative11<Rot3, imuBias::ConstantBias>(
boost::bind(&evaluatePreintegratedMeasurementsRotation, _1,
measuredAccs, measuredOmegas, deltaTs), kZeroBias);
Matrix expectedDelRdelBiasAcc = expectedDelRdelBias.leftCols(3);
Matrix expectedDelRdelBiasOmega = expectedDelRdelBias.rightCols(3);
// Compare Jacobians
EXPECT(assert_equal(expectedDelPdelBiasAcc, preintegrated.delPdelBiasAcc()));
EXPECT(
assert_equal(expectedDelPdelBiasOmega, preintegrated.delPdelBiasOmega()));
EXPECT(assert_equal(expectedDelVdelBiasAcc, preintegrated.delVdelBiasAcc()));
EXPECT(
assert_equal(expectedDelVdelBiasOmega, preintegrated.delVdelBiasOmega()));
EXPECT(assert_equal(expectedDelRdelBiasAcc, Matrix::Zero(3, 3)));
EXPECT(
assert_equal(expectedDelRdelBiasOmega, preintegrated.delRdelBiasOmega()));
}
/* ************************************************************************* */
TEST(ImuFactor, ErrorWithBiasesAndSensorBodyDisplacement) {
imuBias::ConstantBias bias(Vector3(0.2, 0, 0), Vector3(0, 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(Vector3(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(Vector3(0.5, 0.0, 0.0));
// 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 dt = 0.1;
Pose3 body_P_sensor(Rot3::Expmap(Vector3(0, 0.1, 0.1)), Point3(1, 0, 0));
imuBias::ConstantBias biasHat(Vector3(0.2, 0.0, 0.0), Vector3(0.0, 0.0, 0.0));
// Get mean prediction from "ground truth" measurements
PreintegratedImuMeasurements pim(biasHat, kMeasuredAccCovariance,
kMeasuredOmegaCovariance, Z_3x3, true); // MonteCarlo does not sample integration noise
EXPECT(MonteCarlo(pim, NavState(x1, v1), bias, dt, body_P_sensor,
measuredAcc, measuredOmega));
Matrix expected(9,9);
expected <<
0.0290780477, 4.63277848e-07, 9.23468723e-05, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, //
4.63277848e-07, 0.0290688208, 4.62505461e-06, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, //
9.23468723e-05, 4.62505461e-06, 0.0299907267, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, //
0.0, 0.0, 0.0, 0.0026, 0.0, 0.0, 0.005, 0.0, 0.0, //
0.0, 0.0, 0.0, 0.0, 0.0026, 0.0, 0.0, 0.005, 0.0, //
0.0, 0.0, 0.0, 0.0, 0.0, 0.0026, 0.0, 0.0, 0.005, //
0.0, 0.0, 0.0, 0.005, 0.0, 0.0, 0.01, 0.0, 0.0, //
0.0, 0.0, 0.0, 0.0, 0.005, 0.0, 0.0, 0.01, 0.0, //
0.0, 0.0, 0.0, 0.0, 0.0, 0.005, 0.0, 0.0, 0.01;
pim.integrateMeasurement(measuredAcc, measuredOmega, dt, body_P_sensor);
EXPECT(assert_equal(expected, pim.preintMeasCov(), 1e-6));
// Create factor
ImuFactor factor(X(1), V(1), X(2), V(2), B(1), pim, kGravityAlongNavZDown,
kNonZeroOmegaCoriolis);
// Predict
Pose3 actual_x2;
Vector3 actual_v2;
ImuFactor::Predict(x1, v1, actual_x2, actual_v2, bias, pim,
kGravityAlongNavZDown, kZeroOmegaCoriolis);
// Regression test with
Rot3 expectedR( //
0.456795409, -0.888128414, 0.0506544554, //
0.889548908, 0.45563417, -0.0331699173, //
0.00637924528, 0.0602114814, 0.998165258);
Point3 expectedT(5.30373101, 0.768972495, -49.9942188);
Vector3 expected_v2(0.107462014, -0.46205501, 0.0115624037);
Pose3 expected_x2(expectedR, expectedT);
EXPECT(assert_equal(expected_x2, actual_x2, 1e-7));
EXPECT(assert_equal(Vector(expected_v2), actual_v2, 1e-7));
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, PredictPositionAndVelocity) {
imuBias::ConstantBias 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, -9.81;
double deltaT = 0.001;
PreintegratedImuMeasurements pim(
imuBias::ConstantBias(Vector3(0.2, 0.0, 0.0), Vector3(0.0, 0.0, 0.0)),
kMeasuredAccCovariance, kMeasuredOmegaCovariance,
kIntegrationErrorCovariance, true);
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, kGravityAlongNavZDown,
kZeroOmegaCoriolis);
// Predict
Pose3 x1;
Vector3 v1(0, 0.0, 0.0);
PoseVelocityBias poseVelocity = pim.predict(x1, v1, bias,
kGravityAlongNavZDown, kZeroOmegaCoriolis);
Pose3 expectedPose(Rot3(), Point3(0, 0.5, 0));
Vector3 expectedVelocity;
expectedVelocity << 0, 1, 0;
EXPECT(assert_equal(expectedPose, poseVelocity.pose));
EXPECT(assert_equal(Vector(expectedVelocity), Vector(poseVelocity.velocity)));
}
/* ************************************************************************* */
TEST(ImuFactor, PredictRotation) {
imuBias::ConstantBias 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, -9.81;
double deltaT = 0.001;
PreintegratedImuMeasurements pim(
imuBias::ConstantBias(Vector3(0.2, 0.0, 0.0), Vector3(0.0, 0.0, 0.0)),
kMeasuredAccCovariance, kMeasuredOmegaCovariance,
kIntegrationErrorCovariance, true);
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, kGravityAlongNavZDown,
kZeroOmegaCoriolis);
// Predict
Pose3 x1, x2;
Vector3 v1 = Vector3(0, 0.0, 0.0);
Vector3 v2;
ImuFactor::Predict(x1, v1, x2, v2, bias, pim, kGravityAlongNavZDown,
kZeroOmegaCoriolis);
Pose3 expectedPose(Rot3().ypr(M_PI / 10, 0, 0), Point3(0, 0, 0));
Vector3 expectedVelocity;
expectedVelocity << 0, 0, 0;
EXPECT(assert_equal(expectedPose, x2));
EXPECT(assert_equal(Vector(expectedVelocity), Vector(v2)));
}
/* ************************************************************************* */
TEST(ImuFactor, PredictArbitrary) {
imuBias::ConstantBias biasHat(Vector3(0.2, 0.0, 0.0), Vector3(0.0, 0.0, 0.0));
// Measurements
Vector3 measuredOmega(M_PI / 10, M_PI / 10, M_PI / 10);
Vector3 measuredAcc(0.1, 0.2, -9.81);
double dt = 0.001;
ImuFactor::PreintegratedMeasurements pim(biasHat, kMeasuredAccCovariance,
kMeasuredOmegaCovariance, Z_3x3, true); // MonteCarlo does not sample integration noise
Pose3 x1;
Vector3 v1 = Vector3(0, 0, 0);
imuBias::ConstantBias bias(Vector3(0, 0, 0), Vector3(0, 0, 0));
EXPECT(MonteCarlo(pim, NavState(x1, v1), bias, 0.1, Pose3(),
measuredAcc, measuredOmega));
for (int i = 0; i < 1000; ++i)
pim.integrateMeasurement(measuredAcc, measuredOmega, dt);
Matrix expected(9,9);
expected << //
0.0299999995, 2.46739898e-10, 2.46739896e-10, -0.0144839494, 0.044978128, 0.0100471195, -0.0409843415, 0.134423822, 0.0383280513, //
2.46739898e-10, 0.0299999995, 2.46739902e-10, -0.0454268484, -0.0149428917, 0.00609093775, -0.13554868, -0.0471183681, 0.0247643646, //
2.46739896e-10, 2.46739902e-10, 0.0299999995, 0.00489577218, 0.00839301168, 0.000448720395, 0.00879031682, 0.0162199769, 0.00112485862, //
-0.0144839494, -0.0454268484, 0.00489577218, 0.142448905, 0.00345595825, -0.0225794125, 0.34774305, 0.0119449979, -0.075667905, //
0.044978128, -0.0149428917, 0.00839301168, 0.00345595825, 0.143318431, 0.0200549262, 0.0112877167, 0.351503176, 0.0629164907, //
0.0100471195, 0.00609093775, 0.000448720395, -0.0225794125, 0.0200549262, 0.0104041905, -0.0580647212, 0.051116506, 0.0285371399, //
-0.0409843415, -0.13554868, 0.00879031682, 0.34774305, 0.0112877167, -0.0580647212, 0.911721561, 0.0412249672, -0.205920425, //
0.134423822, -0.0471183681, 0.0162199769, 0.0119449979, 0.351503176, 0.051116506, 0.0412249672, 0.928013807, 0.169935105, //
0.0383280513, 0.0247643646, 0.00112485862, -0.075667905, 0.0629164907, 0.0285371399, -0.205920425, 0.169935105, 0.09407764;
EXPECT(assert_equal(expected, pim.preintMeasCov(), 1e-7));
// Create factor
ImuFactor factor(X(1), V(1), X(2), V(2), B(1), pim, kGravityAlongNavZDown,
kZeroOmegaCoriolis);
// Predict
Pose3 x2;
Vector3 v2;
ImuFactor::Predict(x1, v1, x2, v2, bias, pim, kGravityAlongNavZDown,
kZeroOmegaCoriolis);
// 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(-0.505517319, 0.569413747, 0.0861035711);
Vector3 expectedV(-1.59121524, 1.55353139, 0.3376838540);
Pose3 expectedPose(expectedR, expectedT);
EXPECT(assert_equal(expectedPose, x2, 1e-7));
EXPECT(assert_equal(Vector(expectedV), v2, 1e-7));
}
/* ************************************************************************* */
TEST(ImuFactor, bodyPSensorNoBias) {
imuBias::ConstantBias bias(Vector3(0, 0, 0), Vector3(0, 0.1, 0)); // Biases (acc, rot)
// Measurements
Vector3 n_gravity(0, 0, -9.81); // z-up nav frame
Vector3 omegaCoriolis(0, 0, 0);
// Sensor frame is z-down
// 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, -9.81);
double dt = 0.001;
// Rotate sensor (z-down) to body (same as navigation) i.e. z-up
Pose3 body_P_sensor(Rot3::ypr(0, 0, M_PI), Point3(0, 0, 0));
ImuFactor::PreintegratedMeasurements pim(bias, Z_3x3, Z_3x3, Z_3x3, true);
for (int i = 0; i < 1000; ++i)
pim.integrateMeasurement(s_accMeas, s_omegaMeas_ns, dt, body_P_sensor);
// Create factor
ImuFactor factor(X(1), V(1), X(2), V(2), B(1), pim, n_gravity, omegaCoriolis);
// Predict
Pose3 x1;
Vector3 v1(0, 0, 0);
PoseVelocityBias poseVelocity = pim.predict(x1, v1, bias, n_gravity,
omegaCoriolis);
Pose3 expectedPose(Rot3().ypr(-M_PI / 10, 0, 0), Point3(0, 0, 0));
EXPECT(assert_equal(expectedPose, poseVelocity.pose));
Vector3 expectedVelocity(0, 0, 0);
EXPECT(assert_equal(Vector(expectedVelocity), Vector(poseVelocity.velocity)));
}
/* ************************************************************************* */
#include <gtsam/nonlinear/NonlinearFactorGraph.h>
#include <gtsam/slam/BetweenFactor.h>
#include <gtsam/slam/PriorFactor.h>
#include <gtsam/nonlinear/LevenbergMarquardtOptimizer.h>
#include <gtsam/nonlinear/Marginals.h>
TEST(ImuFactor, bodyPSensorWithBias) {
using noiseModel::Diagonal;
typedef imuBias::ConstantBias Bias;
int numFactors = 80;
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
Vector3 n_gravity(0, 0, -9.81);
Vector3 omegaCoriolis(0, 0, 0);
// 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, -9.81);
Pose3 body_P_sensor(Rot3::ypr(0, 0, M_PI), Point3());
Matrix3 accCov = 1e-7 * I_3x3;
Matrix3 gyroCov = 1e-8 * I_3x3;
Matrix3 integrationCov = 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;
PriorFactor<Pose3> priorPose(X(0), Pose3(), priorNoisePose);
graph.add(priorPose);
values.insert(X(0), Pose3());
PriorFactor<Vector3> priorVel(V(0), zeroVel, priorNoiseVel);
graph.add(priorVel);
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)
PriorFactor<Bias> priorBiasFactor(B(0), priorBias, priorNoiseBias);
graph.add(priorBiasFactor);
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++) {
ImuFactor::PreintegratedMeasurements pim =
ImuFactor::PreintegratedMeasurements(zeroBias, accCov, gyroCov,
integrationCov, true);
for (int j = 0; j < 200; ++j)
pim.integrateMeasurement(measuredAcc, measuredOmega, deltaT,
body_P_sensor);
// Create factors
graph.add(
ImuFactor(X(i - 1), V(i - 1), X(i), V(i), B(i - 1), pim, n_gravity,
omegaCoriolis));
graph.add(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));
}
#endif
/* ************************************************************************* */
int main() {
TestResult tr;
return TestRegistry::runAllTests(tr);
}
/* ************************************************************************* */