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Massive refactor: matrices only!

release/4.3a0
Frank Dellaert 2016-01-03 00:30:45 -08:00
parent a5c955a44c
commit 07693337af
3 changed files with 90 additions and 243 deletions
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253
gtsam/navigation/AggregateImuReadings.cpp
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@ -16,28 +16,12 @@
*/ */
#include <gtsam/navigation/AggregateImuReadings.h> #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> #include <cmath>
using namespace std; using namespace std;
using namespace boost::assign;
namespace gtsam { 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, AggregateImuReadings::AggregateImuReadings(const boost::shared_ptr<Params>& p,
const Bias& estimatedBias) const Bias& estimatedBias)
: p_(p), : p_(p),
@ -46,18 +30,8 @@ AggregateImuReadings::AggregateImuReadings(const boost::shared_ptr<Params>& p,
estimatedBias_(estimatedBias), estimatedBias_(estimatedBias),
k_(0), k_(0),
deltaTij_(0.0) { deltaTij_(0.0) {
// Initialize values with zeros zeta_.setZero();
static const Vector3 kZero(Vector3::Zero()); cov_.setZero();
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( SharedDiagonal AggregateImuReadings::discreteAccelerometerNoiseModel(
@ -72,230 +46,101 @@ SharedDiagonal AggregateImuReadings::discreteGyroscopeNoiseModel(
std::sqrt(dt)); std::sqrt(dt));
} }
void AggregateImuReadings::updateEstimate(const Vector3& measuredAcc, // Tangent space sugar.
const Vector3& measuredOmega, namespace sugar {
double dt) { typedef const Vector9 constV9;
// Get current estimates static Eigen::Block<Vector9, 3, 1> dR(Vector9& v) { return v.segment<3>(0); }
const Vector3 theta = values.at<Vector3>(T(k_)); static Eigen::Block<Vector9, 3, 1> dP(Vector9& v) { return v.segment<3>(3); }
const Vector3 pos = values.at<Vector3>(P(k_)); static Eigen::Block<Vector9, 3, 1> dV(Vector9& v) { return v.segment<3>(6); }
const Vector3 vel = values.at<Vector3>(V(k_)); static Eigen::Block<constV9, 3, 1> dR(constV9& v) { return v.segment<3>(0); }
static Eigen::Block<constV9, 3, 1> dP(constV9& v) { return v.segment<3>(3); }
static Eigen::Block<constV9, 3, 1> dV(constV9& v) { return v.segment<3>(6); }
}
// Correct measurements Vector9 AggregateImuReadings::UpdateEstimate(
const Vector3 correctedAcc = measuredAcc - estimatedBias_.accelerometer(); const Vector9& zeta, const Vector3& correctedAcc,
const Vector3 correctedOmega = measuredOmega - estimatedBias_.gyroscope(); const Vector3& correctedOmega, double dt, OptionalJacobian<9, 9> A,
OptionalJacobian<9, 3> Ba, OptionalJacobian<9, 3> Bw) {
using namespace sugar;
// Calculate exact mean propagation // Calculate exact mean propagation
Matrix3 dexp; Matrix3 dexp;
const Rot3 R = Rot3::Expmap(theta, dexp); const Rot3 R = Rot3::Expmap(dR(zeta), dexp);
const Matrix3 F = dexp.inverse() * dt, H = R.matrix() * dt; 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 Vector9 zeta_plus;
// TODO(frank): specialize to diagonal and upper triangular views dR(zeta_plus) = dR(zeta) + F * correctedOmega;
const Matrix3 w = gyroscopeNoiseModel_->covariance() / dt; dP(zeta_plus) = dP(zeta) + dV(zeta) * dt + H * (0.5 * dt) * correctedAcc;
const Matrix3 a = accelerometerNoiseModel_->covariance() / dt; dV(zeta_plus) = dV(zeta) + H * correctedAcc;
const Matrix3 Avt = skewSymmetric(-correctedAcc * dt);
#define DEBUG_COVARIANCE if (A) {
#ifdef DEBUG_COVARIANCE const Matrix3 Avt = skewSymmetric(-correctedAcc * dt);
// Slow covariance calculation for debugging A->setIdentity();
Matrix9 cov = zetaCov(); A->block<3, 3>(6, 0) = Avt;
Matrix9 A; A->block<3, 3>(3, 6) = I_3x3 * dt;
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);
} }
if (Ba) *Ba << Z_3x3, H*(dt * 0.5), H;
if (Bw) *Bw << F, Z_3x3, Z_3x3;
return marginal; return zeta_plus;
} }
void AggregateImuReadings::integrateMeasurement(const Vector3& measuredAcc, void AggregateImuReadings::integrateMeasurement(const Vector3& measuredAcc,
const Vector3& measuredOmega, const Vector3& measuredOmega,
double dt) { double dt) {
typedef map<Key, Matrix> Terms; // Correct measurements
const Vector3 correctedAcc = measuredAcc - estimatedBias_.accelerometer();
const Vector3 correctedOmega = measuredOmega - estimatedBias_.gyroscope();
// Do exact mean propagation // Do exact mean propagation
updateEstimate(measuredAcc, measuredOmega, dt); Matrix9 A;
Matrix93 Ba, Bw;
zeta_ = UpdateEstimate(zeta_, correctedAcc, correctedOmega, dt, A, Ba, Bw);
// Use factor graph machinery to linearize aroud exact propagation and // propagate uncertainty
// calculate posterior density on the prediction // TODO(frank): specialize to diagonal and upper triangular views
if (k_ == 0) const Matrix3 w = gyroscopeNoiseModel_->covariance() / dt;
posterior_k_ = initPosterior(measuredAcc, measuredOmega, dt); const Matrix3 a = accelerometerNoiseModel_->covariance() / dt;
else cov_ = A * cov_ * A.transpose() + Bw * w * Bw.transpose() +
posterior_k_ = updatePosterior(measuredAcc, measuredOmega, dt); Ba * a * Ba.transpose();
// increment counter and time // increment counter and time
k_ += 1; k_ += 1;
deltaTij_ += dt; 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, NavState AggregateImuReadings::predict(const NavState& state_i,
const Bias& bias_i, const Bias& bias_i,
OptionalJacobian<9, 9> H1, OptionalJacobian<9, 9> H1,
OptionalJacobian<9, 6> H2) const { OptionalJacobian<9, 6> H2) const {
// TODO(frank): handle bias using namespace sugar;
Vector9 zeta = zeta_;
// 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 // Correct for initial velocity and gravity
#if 1 #if 1
Rot3 Ri = state_i.attitude(); Rot3 Ri = state_i.attitude();
Matrix3 Rit = Ri.transpose(); Matrix3 Rit = Ri.transpose();
Vector3 gt = deltaTij_ * p_->n_gravity; Vector3 gt = deltaTij_ * p_->n_gravity;
pos += Rit * (state_i.velocity() * deltaTij_ + 0.5 * deltaTij_ * gt); dP(zeta) += Rit * (state_i.velocity() * deltaTij_ + 0.5 * deltaTij_ * gt);
vel += Rit * gt; dV(zeta) += Rit * gt;
#endif #endif
// Convert local coordinates to manifold near state_i
Vector9 zeta;
zeta << theta, pos, vel;
return state_i.retract(zeta); 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 { 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 // 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) // We have inv(Rp'Rp) = H inv(Rz'Rz) H' => Rp = Rz * inv(H)
// From NavState::retract: // From NavState::retract:
Matrix3 D_R_theta; Matrix3 D_R_theta;
Vector3 theta = values.at<Vector3>(T(k_)); const Matrix3 iRj = Rot3::Expmap(theta(), D_R_theta).matrix();
const Matrix3 iRj = Rot3::Expmap(theta, D_R_theta).matrix();
Matrix9 H; Matrix9 H;
H << D_R_theta, Z_3x3, Z_3x3, // H << D_R_theta, Z_3x3, Z_3x3, //
Z_3x3, iRj.transpose(), Z_3x3, // Z_3x3, iRj.transpose(), Z_3x3, //
Z_3x3, Z_3x3, iRj.transpose(); Z_3x3, Z_3x3, iRj.transpose();
Matrix9 HcH = H * cov * H.transpose(); Matrix9 HcH = H * cov_ * H.transpose();
return noiseModel::Gaussian::Covariance(cov, false); return noiseModel::Gaussian::Covariance(cov_, false);
// // Get covariance on zeta from Bayes Net, which stores P(zeta|bias) as a // // Get covariance on zeta from Bayes Net, which stores P(zeta|bias) as a
// // quadratic |R*zeta + S*bias -d|^2 // // quadratic |R*zeta + S*bias -d|^2

51
gtsam/navigation/AggregateImuReadings.h
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@ -22,11 +22,6 @@
namespace gtsam { namespace gtsam {
class NonlinearFactorGraph;
template <typename T>
class Expression;
typedef Expression<Vector3> Vector3_;
// Convert covariance to diagonal noise model, if possible, otherwise throw // Convert covariance to diagonal noise model, if possible, otherwise throw
static noiseModel::Diagonal::shared_ptr Diagonal(const Matrix& covariance) { static noiseModel::Diagonal::shared_ptr Diagonal(const Matrix& covariance) {
bool smart = true; bool smart = true;
@ -37,8 +32,6 @@ static noiseModel::Diagonal::shared_ptr Diagonal(const Matrix& covariance) {
return diagonal; return diagonal;
} }
class GaussianBayesNet;
/** /**
* Class that integrates state estimate on the manifold. * Class that integrates state estimate on the manifold.
* We integrate zeta = [theta, position, velocity] * We integrate zeta = [theta, position, velocity]
@ -48,7 +41,6 @@ class AggregateImuReadings {
public: public:
typedef imuBias::ConstantBias Bias; typedef imuBias::ConstantBias Bias;
typedef ImuFactor::PreintegratedMeasurements::Params Params; typedef ImuFactor::PreintegratedMeasurements::Params Params;
typedef boost::shared_ptr<GaussianBayesNet> SharedBayesNet;
private: private:
const boost::shared_ptr<Params> p_; const boost::shared_ptr<Params> p_;
@ -58,22 +50,17 @@ class AggregateImuReadings {
size_t k_; ///< index/count of measurements integrated size_t k_; ///< index/count of measurements integrated
double deltaTij_; ///< sum of time increments double deltaTij_; ///< sum of time increments
/// posterior on current iterate, stored as a Bayes net
/// P(delta_zeta|estimatedBias_delta):
SharedBayesNet posterior_k_;
/// Current estimate of zeta_k /// Current estimate of zeta_k
Values values; Vector9 zeta_;
Matrix9 cov_;
/// Covariances
Matrix3 ttCov_, tpCov_, tvCov_, //
ppCov_, pvCov_, //
vvCov_;
public: public:
AggregateImuReadings(const boost::shared_ptr<Params>& p, AggregateImuReadings(const boost::shared_ptr<Params>& p,
const Bias& estimatedBias = Bias()); const Bias& estimatedBias = Bias());
const Vector9& zeta() const { return zeta_; }
const Matrix9& zetaCov() const { return cov_; }
// We obtain discrete-time noise models by dividing the continuous-time // We obtain discrete-time noise models by dividing the continuous-time
// covariances by dt: // covariances by dt:
@ -89,8 +76,6 @@ class AggregateImuReadings {
void integrateMeasurement(const Vector3& measuredAcc, void integrateMeasurement(const Vector3& measuredAcc,
const Vector3& measuredOmega, double dt); const Vector3& measuredOmega, double dt);
Vector9 zeta() const;
/// Predict state at time j /// Predict state at time j
NavState predict(const NavState& state_i, const Bias& estimatedBias_i, NavState predict(const NavState& state_i, const Bias& estimatedBias_i,
OptionalJacobian<9, 9> H1 = boost::none, OptionalJacobian<9, 9> H1 = boost::none,
@ -102,25 +87,13 @@ class AggregateImuReadings {
/// @deprecated: Explicitly calculate covariance /// @deprecated: Explicitly calculate covariance
Matrix9 preintMeasCov() const; Matrix9 preintMeasCov() const;
private: Vector3 theta() const { return zeta_.head<3>(); }
Matrix9 zetaCov() const; static Vector9 UpdateEstimate(const Vector9& zeta,
const Vector3& correctedAcc,
void updateEstimate(const Vector3& measuredAcc, const Vector3& measuredOmega, const Vector3& correctedOmega, double dt,
double dt); OptionalJacobian<9, 9> A,
OptionalJacobian<9, 3> Ba,
NonlinearFactorGraph createGraph(const Vector3_& theta_, OptionalJacobian<9, 3> Bw);
const Vector3_& pose_, const Vector3_& vel_,
const Vector3& measuredAcc,
const Vector3& measuredOmega,
double dt) const;
// initialize posterior with first (corrected) IMU measurement
SharedBayesNet initPosterior(const Vector3& measuredAcc,
const Vector3& measuredOmega, double dt);
// integrate
SharedBayesNet updatePosterior(const Vector3& measuredAcc,
const Vector3& measuredOmega, double dt);
}; };
} // namespace gtsam } // namespace gtsam

29
gtsam/navigation/tests/testAggregateImuReadings.cpp
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@ -27,6 +27,18 @@ using namespace gtsam;
static const double kDt = 0.1; static const double kDt = 0.1;
static const double kGyroSigma = 0.02;
static const double kAccelSigma = 0.1;
// Create default parameters with Z-down and above noise parameters
static boost::shared_ptr<AggregateImuReadings::Params> defaultParams() {
auto p = PreintegratedImuMeasurements::Params::MakeSharedD(10);
p->gyroscopeCovariance = kGyroSigma * kGyroSigma * I_3x3;
p->accelerometerCovariance = kAccelSigma * kAccelSigma * I_3x3;
p->integrationCovariance = 0.0000001 * I_3x3;
return p;
}
/* ************************************************************************* */ /* ************************************************************************* */
TEST(AggregateImuReadings, CorrectWithExpmapDerivative1) { TEST(AggregateImuReadings, CorrectWithExpmapDerivative1) {
Matrix aH1, aH2; Matrix aH1, aH2;
@ -157,6 +169,23 @@ TEST(AggregateImuReadings, PredictAcceleration2) {
EXPECT(assert_equal(numericalDerivative33(f, vel, vel_plus, theta), aH3)); EXPECT(assert_equal(numericalDerivative33(f, vel, vel_plus, theta), aH3));
} }
/* ************************************************************************* */
TEST(AggregateImuReadings, UpdateEstimate) {
AggregateImuReadings pim(defaultParams());
Matrix9 aH1;
Matrix93 aH2, aH3;
boost::function<Vector9(const Vector9&, const Vector3&, const Vector3&)> f =
boost::bind(&AggregateImuReadings::UpdateEstimate, _1, _2, _3, kDt,
boost::none, boost::none, boost::none);
Vector9 zeta;
zeta << 0.1, 0.2, 0.3, 0.1, 0.2, 0.3, 0.1, 0.2, 0.3;
const Vector3 acc(0.1, 0.2, 0.3), omega(0.1, 0.2, 0.3);
pim.UpdateEstimate(zeta, acc, omega, kDt, aH1, aH2, aH3);
EXPECT(assert_equal(numericalDerivative31(f, zeta, acc, omega), aH1));
EXPECT(assert_equal(numericalDerivative32(f, zeta, acc, omega), aH2));
EXPECT(assert_equal(numericalDerivative33(f, zeta, acc, omega), aH3));
}
/* ************************************************************************* */ /* ************************************************************************* */
int main() { int main() {
TestResult tr; TestResult tr;