gtsam/gtsam/navigation/AggregateImuReadings.cpp

331 lines
12 KiB
C++

/* ----------------------------------------------------------------------------
* 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 AggregateImuReadings.cpp
* @brief Integrates IMU readings on the NavState tangent space
* @author Frank Dellaert
*/
#include <gtsam/navigation/AggregateImuReadings.h>
#include <gtsam/navigation/functors.h>
#include <gtsam/nonlinear/ExpressionFactor.h>
#include <gtsam/nonlinear/NonlinearFactorGraph.h>
#include <gtsam/linear/GaussianBayesNet.h>
#include <gtsam/linear/GaussianFactorGraph.h>
#include <gtsam/inference/Symbol.h>
#include <boost/assign/std/list.hpp>
#include <cmath>
using namespace std;
using namespace boost::assign;
namespace gtsam {
using symbol_shorthand::T; // for theta
using symbol_shorthand::P; // for position
using symbol_shorthand::V; // for velocity
static const Symbol kBiasKey('B', 0);
AggregateImuReadings::AggregateImuReadings(const boost::shared_ptr<Params>& p,
const Bias& estimatedBias)
: p_(p),
accelerometerNoiseModel_(Diagonal(p->accelerometerCovariance)),
gyroscopeNoiseModel_(Diagonal(p->gyroscopeCovariance)),
estimatedBias_(estimatedBias),
k_(0),
deltaTij_(0.0) {
// Initialize values with zeros
static const Vector3 kZero(Vector3::Zero());
values.insert<Vector3>(T(0), kZero);
values.insert<Vector3>(P(0), kZero);
values.insert<Vector3>(V(0), kZero);
values.insert<Bias>(kBiasKey, estimatedBias_);
ttCov_.setZero();
tpCov_.setZero();
tvCov_.setZero();
ppCov_.setZero();
pvCov_.setZero();
vvCov_.setZero();
}
SharedDiagonal AggregateImuReadings::discreteAccelerometerNoiseModel(
double dt) const {
return noiseModel::Diagonal::Sigmas(accelerometerNoiseModel_->sigmas() /
std::sqrt(dt));
}
SharedDiagonal AggregateImuReadings::discreteGyroscopeNoiseModel(
double dt) const {
return noiseModel::Diagonal::Sigmas(gyroscopeNoiseModel_->sigmas() /
std::sqrt(dt));
}
void AggregateImuReadings::updateEstimate(const Vector3& measuredAcc,
const Vector3& measuredOmega,
double dt) {
// Get current estimates
const Vector3 theta = values.at<Vector3>(T(k_));
const Vector3 pos = values.at<Vector3>(P(k_));
const Vector3 vel = values.at<Vector3>(V(k_));
// Correct measurements
const Vector3 correctedAcc = measuredAcc - estimatedBias_.accelerometer();
const Vector3 correctedOmega = measuredOmega - estimatedBias_.gyroscope();
// Calculate exact mean propagation
Matrix3 dexp;
const Rot3 R = Rot3::Expmap(theta, dexp);
const Matrix3 F = dexp.inverse() * dt, H = R.matrix() * dt;
const Vector3 theta_plus = theta + F * correctedOmega;
const Vector3 pos_plus = pos + vel * dt + H * (0.5 * dt) * correctedAcc;
const Vector3 vel_plus = vel + H * correctedAcc;
// Propagate uncertainty
// TODO(frank): specialize to diagonal and upper triangular views
const Matrix3 w = gyroscopeNoiseModel_->covariance() / dt;
const Matrix3 a = accelerometerNoiseModel_->covariance() / dt;
const Matrix3 Avt = skewSymmetric(-correctedAcc * dt);
#define DEBUG_COVARIANCE
#ifdef DEBUG_COVARIANCE
// Slow covariance calculation for debugging
Matrix9 cov = zetaCov();
Matrix9 A;
A.setIdentity();
A.block<3, 3>(6, 0) = Avt;
A.block<3, 3>(3, 6) = I_3x3 * dt;
Matrix93 Ba, Bw;
Bw << F, Z_3x3, Z_3x3;
Ba << Z_3x3, H*(dt * 0.5), H;
cov = A * cov * A.transpose() + Bw * w * Bw.transpose() +
Ba * a * Ba.transpose();
assert_equal(cov, zetaCov(), 1e-2);
#endif
const Matrix3 HaH = H * a * H.transpose();
const Matrix3 temp = Avt * tvCov_ + tvCov_.transpose() * Avt.transpose();
tpCov_ += dt * tvCov_;
// H**2*a*dt**2/4 + dt*vp + dt*(dt*vv + pv)
ppCov_ += dt * (0.25 * dt * HaH + pvCov_ + pvCov_.transpose() + dt * vvCov_);
pvCov_ += dt * (0.5 * HaH + vvCov_ + temp);
tvCov_ += ttCov_ * Avt.transpose();
vvCov_ += HaH + Avt * ttCov_ * Avt.transpose() + temp;
ttCov_ += F * w * F.transpose();
#ifdef DEBUG_COVARIANCE
assert_equal(cov, zetaCov(), 1e-2);
#endif
// Add those values to estimate and linearize around them
values.insert<Vector3>(T(k_ + 1), theta_plus);
values.insert<Vector3>(P(k_ + 1), pos_plus);
values.insert<Vector3>(V(k_ + 1), vel_plus);
}
NonlinearFactorGraph AggregateImuReadings::createGraph(
const Vector3_& theta_, const Vector3_& pos_, const Vector3_& vel_,
const Vector3& measuredAcc, const Vector3& measuredOmega, double dt) const {
NonlinearFactorGraph graph;
Expression<Bias> bias_(kBiasKey);
Vector3_ theta_plus_(T(k_ + 1)), pos_plus_(P(k_ + 1)), vel_plus_(V(k_ + 1));
Vector3_ omega_(PredictAngularVelocity(dt), theta_, theta_plus_);
Vector3_ measuredOmega_(boost::bind(&Bias::correctGyroscope, _1, _2, _3, _4),
bias_, omega_);
auto gyroModel = discreteGyroscopeNoiseModel(dt);
graph.addExpressionFactor(gyroModel, measuredOmega, measuredOmega_);
Vector3_ averageVelocity_(averageVelocity, vel_, vel_plus_);
Vector3_ defect_(PositionDefect(dt), pos_, pos_plus_, averageVelocity_);
static const auto constrModel = noiseModel::Constrained::All(3);
static const Vector3 kZero(Vector3::Zero());
graph.addExpressionFactor(constrModel, kZero, defect_);
Vector3_ acc_(PredictAcceleration(dt), vel_, vel_plus_, theta_);
Vector3_ measuredAcc_(
boost::bind(&Bias::correctAccelerometer, _1, _2, _3, _4), bias_, acc_);
auto accModel = discreteAccelerometerNoiseModel(dt);
graph.addExpressionFactor(accModel, measuredAcc, measuredAcc_);
return graph;
}
AggregateImuReadings::SharedBayesNet AggregateImuReadings::initPosterior(
const Vector3& measuredAcc, const Vector3& measuredOmega, double dt) {
static const Vector3 kZero(Vector3::Zero());
static const Vector3_ zero_(kZero);
// We create a factor graph and then compute P(zeta|bias)
auto graph = createGraph(zero_, zero_, zero_, measuredAcc, measuredOmega, dt);
// Linearize using updated values (updateEstimate must have been called)
auto linear_graph = graph.linearize(values);
// eliminate all but biases
// NOTE(frank): After this, posterior_k_ contains P(zeta(1)|bias)
Ordering keys = list_of(T(k_ + 1))(P(k_ + 1))(V(k_ + 1));
return linear_graph->eliminatePartialSequential(keys, EliminateQR).first;
}
AggregateImuReadings::SharedBayesNet AggregateImuReadings::updatePosterior(
const Vector3& measuredAcc, const Vector3& measuredOmega, double dt) {
static const Vector3 kZero(Vector3::Zero());
static const auto constrModel = noiseModel::Constrained::All(3);
// We create a factor graph and then compute P(zeta|bias)
// TODO(frank): Expmap and ExpmapDerivative are called again :-(
auto graph = createGraph(Vector3_(T(k_)), Vector3_(P(k_)), Vector3_(V(k_)),
measuredAcc, measuredOmega, dt);
// Linearize using updated values (updateEstimate must have been called)
auto linear_graph = graph.linearize(values);
// add previous posterior
for (const auto& conditional : *posterior_k_)
linear_graph->add(boost::static_pointer_cast<GaussianFactor>(conditional));
// eliminate all but biases
// TODO(frank): does not seem to eliminate in order I want. What gives?
Ordering keys = list_of(T(k_))(P(k_))(V(k_))(T(k_ + 1))(P(k_ + 1))(V(k_ + 1));
SharedBayesNet bayesNet =
linear_graph->eliminatePartialSequential(keys, EliminateQR).first;
// The Bayes net now contains P(zeta(k)|zeta(k+1),bias) P(zeta(k+1)|bias)
// We marginalize zeta(k) by removing the conditionals on zeta(k)
// TODO(frank): could use erase(begin, begin+3) if order above was correct
SharedBayesNet marginal = boost::make_shared<GaussianBayesNet>();
for (const auto& conditional : *bayesNet) {
Symbol symbol(conditional->front());
if (symbol.index() > k_) marginal->push_back(conditional);
}
return marginal;
}
void AggregateImuReadings::integrateMeasurement(const Vector3& measuredAcc,
const Vector3& measuredOmega,
double dt) {
typedef map<Key, Matrix> Terms;
// Do exact mean propagation
updateEstimate(measuredAcc, measuredOmega, dt);
// Use factor graph machinery to linearize aroud exact propagation and
// calculate posterior density on the prediction
if (k_ == 0)
posterior_k_ = initPosterior(measuredAcc, measuredOmega, dt);
else
posterior_k_ = updatePosterior(measuredAcc, measuredOmega, dt);
// increment counter and time
k_ += 1;
deltaTij_ += dt;
}
Vector9 AggregateImuReadings::zeta() const {
Vector9 zeta;
zeta << values.at<Vector3>(T(k_)), values.at<Vector3>(P(k_)),
values.at<Vector3>(V(k_));
return zeta;
}
NavState AggregateImuReadings::predict(const NavState& state_i,
const Bias& bias_i,
OptionalJacobian<9, 9> H1,
OptionalJacobian<9, 6> H2) const {
// TODO(frank): handle bias
// Get current estimates
Vector3 theta = values.at<Vector3>(T(k_));
Vector3 pos = values.at<Vector3>(P(k_));
Vector3 vel = values.at<Vector3>(V(k_));
// Correct for initial velocity and gravity
#if 1
Rot3 Ri = state_i.attitude();
Matrix3 Rit = Ri.transpose();
Vector3 gt = deltaTij_ * p_->n_gravity;
pos += Rit * (state_i.velocity() * deltaTij_ + 0.5 * deltaTij_ * gt);
vel += Rit * gt;
#endif
// Convert local coordinates to manifold near state_i
Vector9 zeta;
zeta << theta, pos, vel;
return state_i.retract(zeta);
}
Matrix9 AggregateImuReadings::zetaCov() const {
Matrix9 cov;
cov << ttCov_, tpCov_, tvCov_, //
tpCov_.transpose(), ppCov_, pvCov_, //
tvCov_.transpose(), pvCov_.transpose(), vvCov_;
return cov;
}
SharedGaussian AggregateImuReadings::noiseModel() const {
Matrix9 cov;
cov << ttCov_, tpCov_, tvCov_, //
tpCov_.transpose(), ppCov_, pvCov_, //
tvCov_.transpose(), pvCov_.transpose(), vvCov_;
// Correct for application of retract, by calculating the retract derivative H
// We have inv(Rp'Rp) = H inv(Rz'Rz) H' => Rp = Rz * inv(H)
// From NavState::retract:
Matrix3 D_R_theta;
Vector3 theta = values.at<Vector3>(T(k_));
const Matrix3 iRj = Rot3::Expmap(theta, D_R_theta).matrix();
Matrix9 H;
H << D_R_theta, Z_3x3, Z_3x3, //
Z_3x3, iRj.transpose(), Z_3x3, //
Z_3x3, Z_3x3, iRj.transpose();
Matrix9 HcH = H * cov * H.transpose();
return noiseModel::Gaussian::Covariance(cov, false);
// // Get covariance on zeta from Bayes Net, which stores P(zeta|bias) as a
// // quadratic |R*zeta + S*bias -d|^2
// Matrix RS;
// Vector d;
// boost::tie(RS, d) = posterior_k_->matrix();
// // NOTEfrank): R'*R = inv(zetaCov)
//
// Matrix9 R = RS.block<9, 9>(0, 0);
// cout << "R'R" << endl;
// cout << (R.transpose() * R).inverse() << endl;
// cout << "cov" << endl;
// cout << cov << endl;
// // Rp = R * H.inverse(), implemented blockwise in-place below
// // TODO(frank): yet another application of expmap and expmap derivative
// // NOTE(frank): makes sense: a change in the j-frame has to be converted
// // to a change in the i-frame, byy rotating with iRj. Similarly, a change
// // in rotation nRj is mapped to a change in theta via the inverse dexp.
// R.block<9, 3>(0, 0) *= D_R_theta.inverse();
// R.block<9, 3>(0, 3) *= iRj;
// R.block<9, 3>(0, 6) *= iRj;
//
// // TODO(frank): think of a faster way - implement in noiseModel
// return noiseModel::Gaussian::SqrtInformation(R, false);
}
Matrix9 AggregateImuReadings::preintMeasCov() const {
return noiseModel()->covariance();
}
} // namespace gtsam