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Merged in feature/IMUenhanced (pull request #92) 

added missing Jacobian when 2ndOrderIntegration = true
release/4.3a0
Frank Dellaert 2015-02-10 16:37:05 +01:00
parent 5554c7af9b 3608429ae7
commit a5737fc8fb
4 changed files with 159 additions and 23 deletions
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14
gtsam/navigation/ImuFactor.cpp
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@ -94,13 +94,25 @@ void ImuFactor::PreintegratedMeasurements::integrateMeasurement(
preintMeasCov_.block<3,3>(3,3) += R_i * accelerometerCovariance() * R_i.transpose() * deltaT;
preintMeasCov_.block<3,3>(6,6) += D_Rincr_integratedOmega * gyroscopeCovariance() * D_Rincr_integratedOmega.transpose() * deltaT;
Matrix3 F_pos_noiseacc;
if(use2ndOrderIntegration()){
F_pos_noiseacc = 0.5 * R_i * deltaT * deltaT;
preintMeasCov_.block<3,3>(0,0) += (1/deltaT) * F_pos_noiseacc * accelerometerCovariance() * F_pos_noiseacc.transpose();
Matrix3 temp = F_pos_noiseacc * accelerometerCovariance() * R_i.transpose(); // already includes 1/deltaT
preintMeasCov_.block<3,3>(0,3) += temp;
preintMeasCov_.block<3,3>(3,0) += temp.transpose();
}
// F_test and G_test are given as output for testing purposes and are not needed by the factor
if(F_test){ // This in only for testing
(*F_test) << F;
}
if(G_test){ // This in only for testing & documentation, while the actual computation is done block-wise
if(!use2ndOrderIntegration())
F_pos_noiseacc = Z_3x3;
// intNoise accNoise omegaNoise
(*G_test) << I_3x3 * deltaT, Z_3x3, Z_3x3, // pos
(*G_test) << I_3x3 * deltaT, F_pos_noiseacc, Z_3x3, // pos
Z_3x3, R_i * deltaT, Z_3x3, // vel
Z_3x3, Z_3x3, D_Rincr_integratedOmega * deltaT; // angle
}

11
gtsam/navigation/PreintegrationBase.h
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@ -83,6 +83,7 @@ public:
integrationCovariance_(integrationErrorCovariance) {}
/// methods to access class variables
const bool use2ndOrderIntegration() const {return use2ndOrderIntegration_;}
const Vector3& deltaPij() const {return deltaPij_;}
const Vector3& deltaVij() const {return deltaVij_;}
const imuBias::ConstantBias& biasHat() const { return biasHat_;}
@ -149,8 +150,14 @@ public:
if(F){
Matrix3 F_vel_angles = - R_i * skewSymmetric(correctedAcc) * deltaT;
Matrix3 F_pos_angles;
if(use2ndOrderIntegration_)
F_pos_angles = 0.5 * F_vel_angles * deltaT;
else
F_pos_angles = Z_3x3;
// pos vel angle
*F << I_3x3, I_3x3 * deltaT, Z_3x3, // pos
*F << I_3x3, I_3x3 * deltaT, F_pos_angles, // pos
Z_3x3, I_3x3, F_vel_angles, // vel
Z_3x3, Z_3x3, F_angles_angles;// angle
}
@ -353,7 +360,7 @@ public:
// dfV/dPosej
Matrix::Zero(3,6),
// dfR/dPosej
D_fR_fRrot * ( I_3x3 ), Z_3x3;
D_fR_fRrot, Z_3x3;
}
if(H4) {
H4->resize(9,3);

2
gtsam/navigation/tests/testCombinedImuFactor.cpp
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@ -56,7 +56,7 @@ Vector updatePreintegratedMeasurementsTest(
if(!use2ndOrderIntegration){
deltaPij_new = deltaPij_old + deltaVij_old * deltaT;
}else{
deltaPij_new += deltaPij_old + deltaVij_old * deltaT + 0.5 * temp * deltaT;
deltaPij_new = deltaPij_old + deltaVij_old * deltaT + 0.5 * temp * deltaT;
}
Vector3 deltaVij_new = deltaVij_old + temp;
Rot3 deltaRij_new = deltaRij_old * Rot3::Expmap((correctedOmega-bias_old.gyroscope()) * deltaT);

149
gtsam/navigation/tests/testImuFactor.cpp
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@ -65,7 +65,7 @@ Vector updatePreintegratedPosVel(
if(!use2ndOrderIntegration_){
deltaPij_new = deltaPij_old + deltaVij_old * deltaT;
}else{
deltaPij_new += deltaPij_old + deltaVij_old * deltaT + 0.5 * temp * deltaT;
deltaPij_new = deltaPij_old + deltaVij_old * deltaT + 0.5 * temp * deltaT;
}
Vector3 deltaVij_new = deltaVij_old + temp;
@ -90,9 +90,9 @@ ImuFactor::PreintegratedMeasurements evaluatePreintegratedMeasurements(
const list<Vector3>& measuredAccs,
const list<Vector3>& measuredOmegas,
const list<double>& deltaTs,
const Vector3& initialRotationRate = Vector3(0.0,0.0,0.0) ){
const bool use2ndOrderIntegration = false){
ImuFactor::PreintegratedMeasurements result(bias, accNoiseVar * Matrix3::Identity(),
omegaNoiseVar *Matrix3::Identity(), intNoiseVar * Matrix3::Identity());
omegaNoiseVar *Matrix3::Identity(), intNoiseVar * Matrix3::Identity(),use2ndOrderIntegration);
list<Vector3>::const_iterator itAcc = measuredAccs.begin();
list<Vector3>::const_iterator itOmega = measuredOmegas.begin();
@ -107,8 +107,7 @@ Vector3 evaluatePreintegratedMeasurementsPosition(
const imuBias::ConstantBias& bias,
const list<Vector3>& measuredAccs,
const list<Vector3>& measuredOmegas,
const list<double>& deltaTs,
const Vector3& initialRotationRate = Vector3(0.0,0.0,0.0) ){
const list<double>& deltaTs){
return evaluatePreintegratedMeasurements(bias,
measuredAccs, measuredOmegas, deltaTs).deltaPij();
}
@ -117,8 +116,7 @@ Vector3 evaluatePreintegratedMeasurementsVelocity(
const imuBias::ConstantBias& bias,
const list<Vector3>& measuredAccs,
const list<Vector3>& measuredOmegas,
const list<double>& deltaTs,
const Vector3& initialRotationRate = Vector3(0.0,0.0,0.0) )
const list<double>& deltaTs)
{
return evaluatePreintegratedMeasurements(bias,
measuredAccs, measuredOmegas, deltaTs).deltaVij();
@ -128,10 +126,9 @@ Rot3 evaluatePreintegratedMeasurementsRotation(
const imuBias::ConstantBias& bias,
const list<Vector3>& measuredAccs,
const list<Vector3>& measuredOmegas,
const list<double>& deltaTs,
const Vector3& initialRotationRate = Vector3(0.0,0.0,0.0) ){
const list<double>& deltaTs){
return Rot3(evaluatePreintegratedMeasurements(bias,
measuredAccs, measuredOmegas, deltaTs, initialRotationRate).deltaRij());
measuredAccs, measuredOmegas, deltaTs).deltaRij());
}
Rot3 evaluateRotation(const Vector3 measuredOmega, const Vector3 biasOmega, const double deltaT){
@ -479,21 +476,21 @@ TEST( ImuFactor, FirstOrderPreIntegratedMeasurements )
// Actual preintegrated values
ImuFactor::PreintegratedMeasurements preintegrated =
evaluatePreintegratedMeasurements(bias, measuredAccs, measuredOmegas, deltaTs, Vector3(M_PI/100.0, 0.0, 0.0));
evaluatePreintegratedMeasurements(bias, measuredAccs, measuredOmegas, deltaTs);
// Compute numerical derivatives
Matrix expectedDelPdelBias = numericalDerivative11<Vector,imuBias::ConstantBias>(
boost::bind(&evaluatePreintegratedMeasurementsPosition, _1, measuredAccs, measuredOmegas, deltaTs, Vector3(M_PI/100.0, 0.0, 0.0)), bias);
boost::bind(&evaluatePreintegratedMeasurementsPosition, _1, measuredAccs, measuredOmegas, deltaTs), bias);
Matrix expectedDelPdelBiasAcc = expectedDelPdelBias.leftCols(3);
Matrix expectedDelPdelBiasOmega = expectedDelPdelBias.rightCols(3);
Matrix expectedDelVdelBias = numericalDerivative11<Vector,imuBias::ConstantBias>(
boost::bind(&evaluatePreintegratedMeasurementsVelocity, _1, measuredAccs, measuredOmegas, deltaTs, Vector3(M_PI/100.0, 0.0, 0.0)), bias);
boost::bind(&evaluatePreintegratedMeasurementsVelocity, _1, measuredAccs, measuredOmegas, deltaTs), bias);
Matrix expectedDelVdelBiasAcc = expectedDelVdelBias.leftCols(3);
Matrix expectedDelVdelBiasOmega = expectedDelVdelBias.rightCols(3);
Matrix expectedDelRdelBias = numericalDerivative11<Rot3,imuBias::ConstantBias>(
boost::bind(&evaluatePreintegratedMeasurementsRotation, _1, measuredAccs, measuredOmegas, deltaTs, Vector3(M_PI/100.0, 0.0, 0.0)), bias);
boost::bind(&evaluatePreintegratedMeasurementsRotation, _1, measuredAccs, measuredOmegas, deltaTs), bias);
Matrix expectedDelRdelBiasAcc = expectedDelRdelBias.leftCols(3);
Matrix expectedDelRdelBiasOmega = expectedDelRdelBias.rightCols(3);
@ -528,9 +525,10 @@ TEST( ImuFactor, JacobianPreintegratedCovariancePropagation )
measuredOmegas.push_back(Vector3(M_PI/100.0, M_PI/300.0, 2*M_PI/100.0));
deltaTs.push_back(0.01);
}
bool use2ndOrderIntegration = false;
// Actual preintegrated values
ImuFactor::PreintegratedMeasurements preintegrated =
evaluatePreintegratedMeasurements(bias, measuredAccs, measuredOmegas, deltaTs, Vector3(M_PI/100.0, 0.0, 0.0));
evaluatePreintegratedMeasurements(bias, measuredAccs, measuredOmegas, deltaTs, use2ndOrderIntegration);
// so far we only created a nontrivial linearization point for the preintegrated measurements
// Now we add a new measurement and ask for Jacobians
@ -547,7 +545,126 @@ TEST( ImuFactor, JacobianPreintegratedCovariancePropagation )
preintegrated.integrateMeasurement(newMeasuredAcc, newMeasuredOmega, newDeltaT,
body_P_sensor, Factual, Gactual);
bool use2ndOrderIntegration = false;
//////////////////////////////////////////////////////////////////////////////////////////////
// COMPUTE NUMERICAL DERIVATIVES FOR F
//////////////////////////////////////////////////////////////////////////////////////////////
// Compute expected f_pos_vel wrt positions
Matrix dfpv_dpos =
numericalDerivative11<Vector, Vector3>(boost::bind(&updatePreintegratedPosVel,
_1, deltaVij_old, deltaRij_old,
newMeasuredAcc, newMeasuredOmega, newDeltaT, use2ndOrderIntegration), deltaPij_old);
// Compute expected f_pos_vel wrt velocities
Matrix dfpv_dvel =
numericalDerivative11<Vector, Vector3>(boost::bind(&updatePreintegratedPosVel,
deltaPij_old, _1, deltaRij_old,
newMeasuredAcc, newMeasuredOmega, newDeltaT, use2ndOrderIntegration), deltaVij_old);
// Compute expected f_pos_vel wrt angles
Matrix dfpv_dangle =
numericalDerivative11<Vector, Rot3>(boost::bind(&updatePreintegratedPosVel,
deltaPij_old, deltaVij_old, _1,
newMeasuredAcc, newMeasuredOmega, newDeltaT, use2ndOrderIntegration), deltaRij_old);
Matrix FexpectedTop6(6,9); FexpectedTop6 << dfpv_dpos, dfpv_dvel, dfpv_dangle;
// Compute expected f_rot wrt angles
Matrix dfr_dangle =
numericalDerivative11<Rot3, Rot3>(boost::bind(&updatePreintegratedRot,
_1, newMeasuredOmega, newDeltaT), deltaRij_old);
Matrix FexpectedBottom3(3,9);
FexpectedBottom3 << Z_3x3, Z_3x3, dfr_dangle;
Matrix Fexpected(9,9); Fexpected << FexpectedTop6, FexpectedBottom3;
EXPECT(assert_equal(Fexpected, Factual));
//////////////////////////////////////////////////////////////////////////////////////////////
// COMPUTE NUMERICAL DERIVATIVES FOR G
//////////////////////////////////////////////////////////////////////////////////////////////
// Compute jacobian wrt integration noise
Matrix dgpv_dintNoise(6,3);
dgpv_dintNoise << I_3x3 * newDeltaT, Z_3x3;
// Compute jacobian wrt acc noise
Matrix dgpv_daccNoise =
numericalDerivative11<Vector, Vector3>(boost::bind(&updatePreintegratedPosVel,
deltaPij_old, deltaVij_old, deltaRij_old,
_1, newMeasuredOmega, newDeltaT, use2ndOrderIntegration), newMeasuredAcc);
// Compute expected F wrt gyro noise
Matrix dgpv_domegaNoise =
numericalDerivative11<Vector, Vector3>(boost::bind(&updatePreintegratedPosVel,
deltaPij_old, deltaVij_old, deltaRij_old,
newMeasuredAcc, _1, newDeltaT, use2ndOrderIntegration), newMeasuredOmega);
Matrix GexpectedTop6(6,9);
GexpectedTop6 << dgpv_dintNoise, dgpv_daccNoise, dgpv_domegaNoise;
// Compute expected f_rot wrt gyro noise
Matrix dgr_dangle =
numericalDerivative11<Rot3, Vector3>(boost::bind(&updatePreintegratedRot,
deltaRij_old, _1, newDeltaT), newMeasuredOmega);
Matrix GexpectedBottom3(3,9);
GexpectedBottom3 << Z_3x3, Z_3x3, dgr_dangle;
Matrix Gexpected(9,9); Gexpected << GexpectedTop6, GexpectedBottom3;
EXPECT(assert_equal(Gexpected, Gactual));
// Check covariance propagation
Matrix9 measurementCovariance;
measurementCovariance << intNoiseVar*I_3x3, Z_3x3, Z_3x3,
Z_3x3, accNoiseVar*I_3x3, Z_3x3,
Z_3x3, Z_3x3, omegaNoiseVar*I_3x3;
Matrix newPreintCovarianceExpected = Factual * oldPreintCovariance * Factual.transpose() +
(1/newDeltaT) * Gactual * measurementCovariance * Gactual.transpose();
Matrix newPreintCovarianceActual = preintegrated.preintMeasCov();
EXPECT(assert_equal(newPreintCovarianceExpected, newPreintCovarianceActual));
}
/* ************************************************************************* */
TEST( ImuFactor, JacobianPreintegratedCovariancePropagation_2ndOrderInt )
{
// Linearization point
imuBias::ConstantBias bias; ///< Current estimate of acceleration and rotation rate biases
Pose3 body_P_sensor = Pose3(); // (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);
}
bool use2ndOrderIntegration = true;
// Actual preintegrated values
ImuFactor::PreintegratedMeasurements preintegrated =
evaluatePreintegratedMeasurements(bias, measuredAccs, measuredOmegas, deltaTs, use2ndOrderIntegration);
// so far we only created a nontrivial linearization point for the preintegrated measurements
// Now we add a new measurement and ask for Jacobians
const Vector3 newMeasuredAcc = Vector3(0.1, 0.0, 0.0);
const Vector3 newMeasuredOmega = Vector3(M_PI/100.0, 0.0, 0.0);
const double newDeltaT = 0.01;
const Rot3 deltaRij_old = preintegrated.deltaRij(); // before adding new measurement
const Vector3 deltaVij_old = preintegrated.deltaVij(); // before adding new measurement
const Vector3 deltaPij_old = preintegrated.deltaPij(); // before adding new measurement
Matrix oldPreintCovariance = preintegrated.preintMeasCov();
Matrix Factual, Gactual;
preintegrated.integrateMeasurement(newMeasuredAcc, newMeasuredOmega, newDeltaT,
body_P_sensor, Factual, Gactual);
//////////////////////////////////////////////////////////////////////////////////////////////
// COMPUTE NUMERICAL DERIVATIVES FOR F