657 lines
30 KiB
C++
657 lines
30 KiB
C++
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/* ----------------------------------------------------------------------------
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* GTSAM Copyright 2010, Georgia Tech Research Corporation,
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* Atlanta, Georgia 30332-0415
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* All Rights Reserved
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* Authors: Frank Dellaert, et al. (see THANKS for the full author list)
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* See LICENSE for the license information
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* -------------------------------------------------------------------------- */
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/**
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* @file EquivInertialNavFactor_GlobalVel.h
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* @author Vadim Indelman, Stephen Williams
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* @brief Equivalent inertial navigation factor (velocity in the global frame).
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* @date Sep. 26, 2012
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**/
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#pragma once
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#include <gtsam/nonlinear/NonlinearFactor.h>
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#include <gtsam/linear/NoiseModel.h>
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#include <gtsam/geometry/Rot3.h>
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#include <gtsam/base/LieVector.h>
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#include <gtsam/base/Matrix.h>
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// Using numerical derivative to calculate d(Pose3::Expmap)/dw
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#include <gtsam/base/numericalDerivative.h>
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#include <boost/optional.hpp>
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#include <ostream>
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namespace gtsam {
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/*
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* NOTES:
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* =====
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* Concept: Based on [Lupton12tro]
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* - Pre-integrate IMU measurements using the static function PreIntegrateIMUObservations.
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* Pre-integrated quantities are expressed in the body system of t0 - the first time instant (in which pre-integration began).
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* All sensor-to-body transformations are performed here.
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* - If required, calculate inertial solution by calling the static functions: predictPose_inertial, predictVelocity_inertial.
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* - When the time is right, incorporate pre-integrated IMU data by creating an EquivInertialNavFactor_GlobalVel factor, which will
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* relate between navigation variables at the two time instances (t0 and current time).
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*
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* Other notes:
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* - The global frame (NED or ENU) is defined by the user by specifying the gravity vector in this frame.
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* - The IMU frame is implicitly defined by the user via the rotation matrix between global and imu frames.
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* - Camera and IMU frames are identical
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* - The user should specify a continuous equivalent noise covariance, which can be calculated using
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* the static function CalcEquivalentNoiseCov based on the IMU gyro and acc measurement noise covariance
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* matrices and the process\modeling covariance matrix. The IneritalNavFactor converts this into a
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* discrete form using the supplied delta_t between sub-sequential measurements.
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* - Earth-rate correction:
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* + Currently the user should supply R_ECEF_to_G, which is the rotation from ECEF to the global
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* frame (Local-Level system: ENU or NED, see above).
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* + R_ECEF_to_G can be calculated by approximated values of latitude and longitude of the system.
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* + Currently it is assumed that a relatively small distance is traveled w.r.t. to initial pose, since R_ECEF_to_G is constant.
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* Otherwise, R_ECEF_to_G should be updated each time using the current lat-lon.
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*
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* - Frame Notation:
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* Quantities are written as {Frame of Representation/Destination Frame}_{Quantity Type}_{Quatity Description/Origination Frame}
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* So, the rotational velocity of the sensor written in the body frame is: body_omega_sensor
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* And the transformation from the body frame to the world frame would be: world_P_body
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* This allows visual chaining. For example, converting the sensed angular velocity of the IMU
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* (angular velocity of the sensor in the sensor frame) into the world frame can be performed as:
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* world_R_body * body_R_sensor * sensor_omega_sensor = world_omega_sensor
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*
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*
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* - Common Quantity Types
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* P : pose/3d transformation
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* R : rotation
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* omega : angular velocity
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* t : translation
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* v : velocity
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* a : acceleration
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*
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* - Common Frames
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* sensor : the coordinate system attached to the sensor origin
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* body : the coordinate system attached to body/inertial frame.
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* Unless an optional frame transformation is provided, the
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* sensor frame and the body frame will be identical
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* world : the global/world coordinate frame. This is assumed to be
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* a tangent plane to the earth's surface somewhere near the
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* vehicle
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*/
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template<class POSE, class VELOCITY, class IMUBIAS>
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class EquivInertialNavFactor_GlobalVel : public NoiseModelFactor5<POSE, VELOCITY, IMUBIAS, POSE, VELOCITY> {
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private:
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typedef EquivInertialNavFactor_GlobalVel<POSE, VELOCITY, IMUBIAS> This;
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typedef NoiseModelFactor5<POSE, VELOCITY, IMUBIAS, POSE, VELOCITY> Base;
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Vector delta_pos_in_t0_;
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Vector delta_vel_in_t0_;
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Vector3 delta_angles_;
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double dt12_;
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Vector world_g_;
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Vector world_rho_;
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Vector world_omega_earth_;
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Matrix Jacobian_wrt_t0_Overall_;
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boost::optional<IMUBIAS> Bias_initial_; // Bias used when pre-integrating IMU measurements
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boost::optional<POSE> body_P_sensor_; // The pose of the sensor in the body frame
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public:
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// shorthand for a smart pointer to a factor
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typedef typename boost::shared_ptr<EquivInertialNavFactor_GlobalVel> shared_ptr;
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/** default constructor - only use for serialization */
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EquivInertialNavFactor_GlobalVel() {}
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/** Constructor */
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EquivInertialNavFactor_GlobalVel(const Key& Pose1, const Key& Vel1, const Key& IMUBias1, const Key& Pose2, const Key& Vel2,
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const Vector& delta_pos_in_t0, const Vector& delta_vel_in_t0, const Vector3& delta_angles,
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double dt12, const Vector world_g, const Vector world_rho,
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const Vector& world_omega_earth, const noiseModel::Gaussian::shared_ptr& model_equivalent,
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const Matrix& Jacobian_wrt_t0_Overall,
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boost::optional<IMUBIAS> Bias_initial = boost::none, boost::optional<POSE> body_P_sensor = boost::none) :
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Base(model_equivalent, Pose1, Vel1, IMUBias1, Pose2, Vel2),
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delta_pos_in_t0_(delta_pos_in_t0), delta_vel_in_t0_(delta_vel_in_t0), delta_angles_(delta_angles),
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dt12_(dt12), world_g_(world_g), world_rho_(world_rho), world_omega_earth_(world_omega_earth), Jacobian_wrt_t0_Overall_(Jacobian_wrt_t0_Overall),
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Bias_initial_(Bias_initial), body_P_sensor_(body_P_sensor) { }
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virtual ~EquivInertialNavFactor_GlobalVel() {}
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/** implement functions needed for Testable */
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/** print */
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virtual void print(const std::string& s = "EquivInertialNavFactor_GlobalVel", const KeyFormatter& keyFormatter = DefaultKeyFormatter) const {
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std::cout << s << "("
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<< keyFormatter(this->key1()) << ","
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<< keyFormatter(this->key2()) << ","
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<< keyFormatter(this->key3()) << ","
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<< keyFormatter(this->key4()) << ","
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<< keyFormatter(this->key5()) << "\n";
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std::cout << "delta_pos_in_t0: " << this->delta_pos_in_t0_.transpose() << std::endl;
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std::cout << "delta_vel_in_t0: " << this->delta_vel_in_t0_.transpose() << std::endl;
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std::cout << "delta_angles: " << this->delta_angles_ << std::endl;
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std::cout << "dt12: " << this->dt12_ << std::endl;
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std::cout << "gravity (in world frame): " << this->world_g_.transpose() << std::endl;
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std::cout << "craft rate (in world frame): " << this->world_rho_.transpose() << std::endl;
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std::cout << "earth's rotation (in world frame): " << this->world_omega_earth_.transpose() << std::endl;
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if(this->body_P_sensor_)
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this->body_P_sensor_->print(" sensor pose in body frame: ");
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this->noiseModel_->print(" noise model");
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}
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/** equals */
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virtual bool equals(const NonlinearFactor& expected, double tol=1e-9) const {
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const This *e = dynamic_cast<const This*> (&expected);
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return e != NULL && Base::equals(*e, tol)
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&& (delta_pos_in_t0_ - e->delta_pos_in_t0_).norm() < tol
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&& (delta_vel_in_t0_ - e->delta_vel_in_t0_).norm() < tol
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&& (delta_angles_ - e->delta_angles_).norm() < tol
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&& (dt12_ - e->dt12_) < tol
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&& (world_g_ - e->world_g_).norm() < tol
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&& (world_rho_ - e->world_rho_).norm() < tol
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&& (world_omega_earth_ - e->world_omega_earth_).norm() < tol
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&& ((!body_P_sensor_ && !e->body_P_sensor_) || (body_P_sensor_ && e->body_P_sensor_ && body_P_sensor_->equals(*e->body_P_sensor_)));
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}
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POSE predictPose(const POSE& Pose1, const VELOCITY& Vel1, const IMUBIAS& Bias1) const {
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// Correct delta_pos_in_t0_ using (Bias1 - Bias_t0)
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Vector delta_BiasAcc = Bias1.accelerometer();
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Vector delta_BiasGyro = Bias1.gyroscope();
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if (Bias_initial_){
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delta_BiasAcc -= Bias_initial_->accelerometer();
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delta_BiasGyro -= Bias_initial_->gyroscope();
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}
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Matrix J_Pos_wrt_BiasAcc = Jacobian_wrt_t0_Overall_.block(4,9,3,3);
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Matrix J_Pos_wrt_BiasGyro = Jacobian_wrt_t0_Overall_.block(4,12,3,3);
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Matrix J_angles_wrt_BiasGyro = Jacobian_wrt_t0_Overall_.block(0,12,3,3);
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/* Position term */
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Vector delta_pos_in_t0_corrected = delta_pos_in_t0_ + J_Pos_wrt_BiasAcc*delta_BiasAcc + J_Pos_wrt_BiasGyro*delta_BiasGyro;
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/* Rotation term */
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Vector delta_angles_corrected = delta_angles_ + J_angles_wrt_BiasGyro*delta_BiasGyro;
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// Another alternative:
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// Vector delta_angles_corrected = Rot3::Logmap( Rot3::Expmap(delta_angles_)*Rot3::Expmap(J_angles_wrt_BiasGyro*delta_BiasGyro) );
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return predictPose_inertial(Pose1, Vel1,
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delta_pos_in_t0_corrected, delta_angles_corrected,
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dt12_, world_g_, world_rho_, world_omega_earth_);
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}
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static inline POSE predictPose_inertial(const POSE& Pose1, const VELOCITY& Vel1,
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const Vector& delta_pos_in_t0, const Vector3& delta_angles,
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const double dt12, const Vector& world_g, const Vector& world_rho, const Vector& world_omega_earth){
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const POSE& world_P1_body = Pose1;
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const VELOCITY& world_V1_body = Vel1;
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/* Position term */
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Vector body_deltaPos_body = delta_pos_in_t0;
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Vector world_deltaPos_pls_body = world_P1_body.rotation().matrix() * body_deltaPos_body;
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Vector world_deltaPos_body = world_V1_body * dt12 + 0.5*world_g*dt12*dt12 + world_deltaPos_pls_body;
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// Incorporate earth-related terms. Note - these are assumed to be constant between t1 and t2.
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world_deltaPos_body -= 2*skewSymmetric(world_rho + world_omega_earth)*world_V1_body * dt12*dt12;
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/* TODO: the term dt12*dt12 in 0.5*world_g*dt12*dt12 is not entirely correct:
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* the gravity should be canceled from the accelerometer measurements, bust since position
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* is added with a delta velocity from a previous term, the actual delta time is more complicated.
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* Need to figure out this in the future - currently because of this issue we'll get some more error
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* in Z axis.
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*/
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/* Rotation term */
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Vector body_deltaAngles_body = delta_angles;
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// Convert earth-related terms into the body frame
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Matrix body_R_world(world_P1_body.rotation().inverse().matrix());
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Vector body_rho = body_R_world * world_rho;
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Vector body_omega_earth = body_R_world * world_omega_earth;
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// Incorporate earth-related terms. Note - these are assumed to be constant between t1 and t2.
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body_deltaAngles_body -= (body_rho + body_omega_earth)*dt12;
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return POSE(Pose1.rotation() * POSE::Rotation::Expmap(body_deltaAngles_body), Pose1.translation() + typename POSE::Translation(world_deltaPos_body));
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}
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VELOCITY predictVelocity(const POSE& Pose1, const VELOCITY& Vel1, const IMUBIAS& Bias1) const {
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// Correct delta_vel_in_t0_ using (Bias1 - Bias_t0)
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Vector delta_BiasAcc = Bias1.accelerometer();
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Vector delta_BiasGyro = Bias1.gyroscope();
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if (Bias_initial_){
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delta_BiasAcc -= Bias_initial_->accelerometer();
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delta_BiasGyro -= Bias_initial_->gyroscope();
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}
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Matrix J_Vel_wrt_BiasAcc = Jacobian_wrt_t0_Overall_.block(6,9,3,3);
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Matrix J_Vel_wrt_BiasGyro = Jacobian_wrt_t0_Overall_.block(6,12,3,3);
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Vector delta_vel_in_t0_corrected = delta_vel_in_t0_ + J_Vel_wrt_BiasAcc*delta_BiasAcc + J_Vel_wrt_BiasGyro*delta_BiasGyro;
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return predictVelocity_inertial(Pose1, Vel1,
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delta_vel_in_t0_corrected,
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dt12_, world_g_, world_rho_, world_omega_earth_);
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}
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static inline VELOCITY predictVelocity_inertial(const POSE& Pose1, const VELOCITY& Vel1,
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const Vector& delta_vel_in_t0,
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const double dt12, const Vector& world_g, const Vector& world_rho, const Vector& world_omega_earth) {
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const POSE& world_P1_body = Pose1;
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const VELOCITY& world_V1_body = Vel1;
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Vector body_deltaVel_body = delta_vel_in_t0;
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Vector world_deltaVel_body = world_P1_body.rotation().matrix() * body_deltaVel_body;
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VELOCITY VelDelta( world_deltaVel_body + world_g * dt12 );
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// Incorporate earth-related terms. Note - these are assumed to be constant between t1 and t2.
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VelDelta -= 2*skewSymmetric(world_rho + world_omega_earth)*world_V1_body * dt12;
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// Predict
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return Vel1.compose( VelDelta );
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}
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void predict(const POSE& Pose1, const VELOCITY& Vel1, const IMUBIAS& Bias1, POSE& Pose2, VELOCITY& Vel2) const {
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Pose2 = predictPose(Pose1, Vel1, Bias1);
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Vel2 = predictVelocity(Pose1, Vel1, Bias1);
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}
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POSE evaluatePoseError(const POSE& Pose1, const VELOCITY& Vel1, const IMUBIAS& Bias1, const POSE& Pose2, const VELOCITY& Vel2) const {
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// Predict
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POSE Pose2Pred = predictPose(Pose1, Vel1, Bias1);
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// Calculate error
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return Pose2.between(Pose2Pred);
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}
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VELOCITY evaluateVelocityError(const POSE& Pose1, const VELOCITY& Vel1, const IMUBIAS& Bias1, const POSE& Pose2, const VELOCITY& Vel2) const {
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// Predict
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VELOCITY Vel2Pred = predictVelocity(Pose1, Vel1, Bias1);
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// Calculate error
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return Vel2.between(Vel2Pred);
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}
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Vector evaluateError(const POSE& Pose1, const VELOCITY& Vel1, const IMUBIAS& Bias1, const POSE& Pose2, const VELOCITY& Vel2,
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boost::optional<Matrix&> H1 = boost::none,
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boost::optional<Matrix&> H2 = boost::none,
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boost::optional<Matrix&> H3 = boost::none,
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boost::optional<Matrix&> H4 = boost::none,
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boost::optional<Matrix&> H5 = boost::none) const {
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// TODO: Write analytical derivative calculations
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// Jacobian w.r.t. Pose1
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if (H1){
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Matrix H1_Pose = numericalDerivative11<POSE, POSE>(boost::bind(&EquivInertialNavFactor_GlobalVel::evaluatePoseError, this, _1, Vel1, Bias1, Pose2, Vel2), Pose1);
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Matrix H1_Vel = numericalDerivative11<VELOCITY, POSE>(boost::bind(&EquivInertialNavFactor_GlobalVel::evaluateVelocityError, this, _1, Vel1, Bias1, Pose2, Vel2), Pose1);
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*H1 = stack(2, &H1_Pose, &H1_Vel);
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}
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// Jacobian w.r.t. Vel1
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if (H2){
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Matrix H2_Pose = numericalDerivative11<POSE, VELOCITY>(boost::bind(&EquivInertialNavFactor_GlobalVel::evaluatePoseError, this, Pose1, _1, Bias1, Pose2, Vel2), Vel1);
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Matrix H2_Vel = numericalDerivative11<VELOCITY, VELOCITY>(boost::bind(&EquivInertialNavFactor_GlobalVel::evaluateVelocityError, this, Pose1, _1, Bias1, Pose2, Vel2), Vel1);
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*H2 = stack(2, &H2_Pose, &H2_Vel);
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}
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// Jacobian w.r.t. IMUBias1
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if (H3){
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Matrix H3_Pose = numericalDerivative11<POSE, IMUBIAS>(boost::bind(&EquivInertialNavFactor_GlobalVel::evaluatePoseError, this, Pose1, Vel1, _1, Pose2, Vel2), Bias1);
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Matrix H3_Vel = numericalDerivative11<VELOCITY, IMUBIAS>(boost::bind(&EquivInertialNavFactor_GlobalVel::evaluateVelocityError, this, Pose1, Vel1, _1, Pose2, Vel2), Bias1);
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*H3 = stack(2, &H3_Pose, &H3_Vel);
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}
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// Jacobian w.r.t. Pose2
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if (H4){
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Matrix H4_Pose = numericalDerivative11<POSE, POSE>(boost::bind(&EquivInertialNavFactor_GlobalVel::evaluatePoseError, this, Pose1, Vel1, Bias1, _1, Vel2), Pose2);
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Matrix H4_Vel = numericalDerivative11<VELOCITY, POSE>(boost::bind(&EquivInertialNavFactor_GlobalVel::evaluateVelocityError, this, Pose1, Vel1, Bias1, _1, Vel2), Pose2);
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*H4 = stack(2, &H4_Pose, &H4_Vel);
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}
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// Jacobian w.r.t. Vel2
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if (H5){
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Matrix H5_Pose = numericalDerivative11<POSE, VELOCITY>(boost::bind(&EquivInertialNavFactor_GlobalVel::evaluatePoseError, this, Pose1, Vel1, Bias1, Pose2, _1), Vel2);
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Matrix H5_Vel = numericalDerivative11<VELOCITY, VELOCITY>(boost::bind(&EquivInertialNavFactor_GlobalVel::evaluateVelocityError, this, Pose1, Vel1, Bias1, Pose2, _1), Vel2);
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*H5 = stack(2, &H5_Pose, &H5_Vel);
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}
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Vector ErrPoseVector(POSE::Logmap(evaluatePoseError(Pose1, Vel1, Bias1, Pose2, Vel2)));
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Vector ErrVelVector(VELOCITY::Logmap(evaluateVelocityError(Pose1, Vel1, Bias1, Pose2, Vel2)));
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return concatVectors(2, &ErrPoseVector, &ErrVelVector);
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}
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static inline POSE PredictPoseFromPreIntegration(const POSE& Pose1, const VELOCITY& Vel1, const IMUBIAS& Bias1,
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const Vector& delta_pos_in_t0, const Vector3& delta_angles,
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double dt12, const Vector world_g, const Vector world_rho,
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const Vector& world_omega_earth, const Matrix& Jacobian_wrt_t0_Overall,
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const boost::optional<IMUBIAS>& Bias_initial = boost::none) {
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// Correct delta_pos_in_t0_ using (Bias1 - Bias_t0)
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Vector delta_BiasAcc = Bias1.accelerometer();
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Vector delta_BiasGyro = Bias1.gyroscope();
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if (Bias_initial){
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delta_BiasAcc -= Bias_initial->accelerometer();
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delta_BiasGyro -= Bias_initial->gyroscope();
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}
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Matrix J_Pos_wrt_BiasAcc = Jacobian_wrt_t0_Overall.block(4,9,3,3);
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Matrix J_Pos_wrt_BiasGyro = Jacobian_wrt_t0_Overall.block(4,12,3,3);
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Matrix J_angles_wrt_BiasGyro = Jacobian_wrt_t0_Overall.block(0,12,3,3);
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/* Position term */
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Vector delta_pos_in_t0_corrected = delta_pos_in_t0 + J_Pos_wrt_BiasAcc*delta_BiasAcc + J_Pos_wrt_BiasGyro*delta_BiasGyro;
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/* Rotation term */
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Vector delta_angles_corrected = delta_angles + J_angles_wrt_BiasGyro*delta_BiasGyro;
|
|
// Another alternative:
|
|
// Vector delta_angles_corrected = Rot3::Logmap( Rot3::Expmap(delta_angles_)*Rot3::Expmap(J_angles_wrt_BiasGyro*delta_BiasGyro) );
|
|
|
|
return predictPose_inertial(Pose1, Vel1, delta_pos_in_t0_corrected, delta_angles_corrected, dt12, world_g, world_rho, world_omega_earth);
|
|
}
|
|
|
|
static inline VELOCITY PredictVelocityFromPreIntegration(const POSE& Pose1, const VELOCITY& Vel1, const IMUBIAS& Bias1,
|
|
const Vector& delta_vel_in_t0, double dt12, const Vector world_g, const Vector world_rho,
|
|
const Vector& world_omega_earth, const Matrix& Jacobian_wrt_t0_Overall,
|
|
const boost::optional<IMUBIAS>& Bias_initial = boost::none) {
|
|
|
|
// Correct delta_vel_in_t0_ using (Bias1 - Bias_t0)
|
|
Vector delta_BiasAcc = Bias1.accelerometer();
|
|
Vector delta_BiasGyro = Bias1.gyroscope();
|
|
if (Bias_initial){
|
|
delta_BiasAcc -= Bias_initial->accelerometer();
|
|
delta_BiasGyro -= Bias_initial->gyroscope();
|
|
}
|
|
|
|
Matrix J_Vel_wrt_BiasAcc = Jacobian_wrt_t0_Overall.block(6,9,3,3);
|
|
Matrix J_Vel_wrt_BiasGyro = Jacobian_wrt_t0_Overall.block(6,12,3,3);
|
|
|
|
Vector delta_vel_in_t0_corrected = delta_vel_in_t0 + J_Vel_wrt_BiasAcc*delta_BiasAcc + J_Vel_wrt_BiasGyro*delta_BiasGyro;
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|
|
|
return predictVelocity_inertial(Pose1, Vel1, delta_vel_in_t0_corrected, dt12, world_g, world_rho, world_omega_earth);
|
|
}
|
|
|
|
static inline void PredictFromPreIntegration(const POSE& Pose1, const VELOCITY& Vel1, const IMUBIAS& Bias1, POSE& Pose2, VELOCITY& Vel2,
|
|
const Vector& delta_pos_in_t0, const Vector& delta_vel_in_t0, const Vector3& delta_angles,
|
|
double dt12, const Vector world_g, const Vector world_rho,
|
|
const Vector& world_omega_earth, const Matrix& Jacobian_wrt_t0_Overall,
|
|
const boost::optional<IMUBIAS>& Bias_initial = boost::none) {
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|
|
|
Pose2 = PredictPoseFromPreIntegration(Pose1, Vel1, Bias1, delta_pos_in_t0, delta_angles, dt12, world_g, world_rho, world_omega_earth, Jacobian_wrt_t0_Overall, Bias_initial);
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|
Vel2 = PredictVelocityFromPreIntegration(Pose1, Vel1, Bias1, delta_vel_in_t0, dt12, world_g, world_rho, world_omega_earth, Jacobian_wrt_t0_Overall, Bias_initial);
|
|
}
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static inline void PreIntegrateIMUObservations(const Vector& msr_acc_t, const Vector& msr_gyro_t, const double msr_dt,
|
|
Vector& delta_pos_in_t0, Vector3& delta_angles, Vector& delta_vel_in_t0, double& delta_t,
|
|
const noiseModel::Gaussian::shared_ptr& model_continuous_overall,
|
|
Matrix& EquivCov_Overall, Matrix& Jacobian_wrt_t0_Overall, const IMUBIAS Bias_t0 = IMUBIAS(),
|
|
boost::optional<POSE> p_body_P_sensor = boost::none){
|
|
// Note: all delta terms refer to an IMU\sensor system at t0
|
|
// Note: Earth-related terms are not accounted here but are incorporated in predict functions.
|
|
|
|
POSE body_P_sensor = POSE();
|
|
bool flag_use_body_P_sensor = false;
|
|
if (p_body_P_sensor){
|
|
body_P_sensor = *p_body_P_sensor;
|
|
flag_use_body_P_sensor = true;
|
|
}
|
|
|
|
delta_pos_in_t0 = PreIntegrateIMUObservations_delta_pos(msr_dt, delta_pos_in_t0, delta_vel_in_t0);
|
|
delta_vel_in_t0 = PreIntegrateIMUObservations_delta_vel(msr_gyro_t, msr_acc_t, msr_dt, delta_angles, delta_vel_in_t0, flag_use_body_P_sensor, body_P_sensor, Bias_t0);
|
|
delta_angles = PreIntegrateIMUObservations_delta_angles(msr_gyro_t, msr_dt, delta_angles, flag_use_body_P_sensor, body_P_sensor, Bias_t0);
|
|
|
|
delta_t += msr_dt;
|
|
|
|
// Update EquivCov_Overall
|
|
Matrix Z_3x3 = zeros(3,3);
|
|
Matrix I_3x3 = eye(3,3);
|
|
|
|
Matrix H_pos_pos = numericalDerivative11<LieVector, LieVector>(boost::bind(&PreIntegrateIMUObservations_delta_pos, msr_dt, _1, delta_vel_in_t0), delta_pos_in_t0);
|
|
Matrix H_pos_vel = numericalDerivative11<LieVector, LieVector>(boost::bind(&PreIntegrateIMUObservations_delta_pos, msr_dt, delta_pos_in_t0, _1), delta_vel_in_t0);
|
|
Matrix H_pos_angles = Z_3x3;
|
|
Matrix H_pos_bias = collect(2, &Z_3x3, &Z_3x3);
|
|
|
|
Matrix H_vel_vel = numericalDerivative11<LieVector, LieVector>(boost::bind(&PreIntegrateIMUObservations_delta_vel, msr_gyro_t, msr_acc_t, msr_dt, delta_angles, _1, flag_use_body_P_sensor, body_P_sensor, Bias_t0), delta_vel_in_t0);
|
|
Matrix H_vel_angles = numericalDerivative11<LieVector, LieVector>(boost::bind(&PreIntegrateIMUObservations_delta_vel, msr_gyro_t, msr_acc_t, msr_dt, _1, delta_vel_in_t0, flag_use_body_P_sensor, body_P_sensor, Bias_t0), delta_angles);
|
|
Matrix H_vel_bias = numericalDerivative11<LieVector, IMUBIAS>(boost::bind(&PreIntegrateIMUObservations_delta_vel, msr_gyro_t, msr_acc_t, msr_dt, delta_angles, delta_vel_in_t0, flag_use_body_P_sensor, body_P_sensor, _1), Bias_t0);
|
|
Matrix H_vel_pos = Z_3x3;
|
|
|
|
Matrix H_angles_angles = numericalDerivative11<LieVector, LieVector>(boost::bind(&PreIntegrateIMUObservations_delta_angles, msr_gyro_t, msr_dt, _1, flag_use_body_P_sensor, body_P_sensor, Bias_t0), delta_angles);
|
|
Matrix H_angles_bias = numericalDerivative11<LieVector, IMUBIAS>(boost::bind(&PreIntegrateIMUObservations_delta_angles, msr_gyro_t, msr_dt, delta_angles, flag_use_body_P_sensor, body_P_sensor, _1), Bias_t0);
|
|
Matrix H_angles_pos = Z_3x3;
|
|
Matrix H_angles_vel = Z_3x3;
|
|
|
|
Matrix F_angles = collect(4, &H_angles_angles, &H_angles_pos, &H_angles_vel, &H_angles_bias);
|
|
Matrix F_pos = collect(4, &H_pos_angles, &H_pos_pos, &H_pos_vel, &H_pos_bias);
|
|
Matrix F_vel = collect(4, &H_vel_angles, &H_vel_pos, &H_vel_vel, &H_vel_bias);
|
|
Matrix F_bias_a = collect(5, &Z_3x3, &Z_3x3, &Z_3x3, &I_3x3, &Z_3x3);
|
|
Matrix F_bias_g = collect(5, &Z_3x3, &Z_3x3, &Z_3x3, &Z_3x3, &I_3x3);
|
|
Matrix F = stack(5, &F_angles, &F_pos, &F_vel, &F_bias_a, &F_bias_g);
|
|
|
|
noiseModel::Gaussian::shared_ptr model_discrete_curr = calc_descrete_noise_model(model_continuous_overall, msr_dt );
|
|
Matrix Q_d = inverse(model_discrete_curr->R().transpose() * model_discrete_curr->R() );
|
|
|
|
EquivCov_Overall = F * EquivCov_Overall * F.transpose() + Q_d;
|
|
|
|
// Update Jacobian_wrt_t0_Overall
|
|
Jacobian_wrt_t0_Overall = F * Jacobian_wrt_t0_Overall;
|
|
}
|
|
|
|
static inline Vector PreIntegrateIMUObservations_delta_pos(const double msr_dt,
|
|
const Vector& delta_pos_in_t0, const Vector& delta_vel_in_t0){
|
|
|
|
// Note: all delta terms refer to an IMU\sensor system at t0
|
|
// Note: delta_vel_in_t0 is already in body frame, so no need to use the body_P_sensor transformation here.
|
|
|
|
return delta_pos_in_t0 + delta_vel_in_t0 * msr_dt;
|
|
}
|
|
|
|
|
|
|
|
static inline Vector PreIntegrateIMUObservations_delta_vel(const Vector& msr_gyro_t, const Vector& msr_acc_t, const double msr_dt,
|
|
const Vector3& delta_angles, const Vector& delta_vel_in_t0, const bool flag_use_body_P_sensor, const POSE& body_P_sensor,
|
|
IMUBIAS Bias_t0 = IMUBIAS()){
|
|
|
|
// Note: all delta terms refer to an IMU\sensor system at t0
|
|
|
|
// Calculate the corrected measurements using the Bias object
|
|
Vector AccCorrected = Bias_t0.correctAccelerometer(msr_acc_t);
|
|
Vector body_t_a_body;
|
|
if (flag_use_body_P_sensor){
|
|
Matrix body_R_sensor = body_P_sensor.rotation().matrix();
|
|
|
|
Vector GyroCorrected(Bias_t0.correctGyroscope(msr_gyro_t));
|
|
|
|
Vector body_omega_body = body_R_sensor * GyroCorrected;
|
|
Matrix body_omega_body__cross = skewSymmetric(body_omega_body);
|
|
|
|
body_t_a_body = body_R_sensor * AccCorrected - body_omega_body__cross * body_omega_body__cross * body_P_sensor.translation().vector();
|
|
} else{
|
|
body_t_a_body = AccCorrected;
|
|
}
|
|
|
|
Rot3 R_t_to_t0 = Rot3::Expmap(delta_angles);
|
|
|
|
return delta_vel_in_t0 + R_t_to_t0.matrix() * body_t_a_body * msr_dt;
|
|
}
|
|
|
|
|
|
static inline Vector PreIntegrateIMUObservations_delta_angles(const Vector& msr_gyro_t, const double msr_dt,
|
|
const Vector3& delta_angles, const bool flag_use_body_P_sensor, const POSE& body_P_sensor,
|
|
IMUBIAS Bias_t0 = IMUBIAS()){
|
|
|
|
// Note: all delta terms refer to an IMU\sensor system at t0
|
|
|
|
// Calculate the corrected measurements using the Bias object
|
|
Vector GyroCorrected = Bias_t0.correctGyroscope(msr_gyro_t);
|
|
|
|
Vector body_t_omega_body;
|
|
if (flag_use_body_P_sensor){
|
|
body_t_omega_body = body_P_sensor.rotation().matrix() * GyroCorrected;
|
|
} else {
|
|
body_t_omega_body = GyroCorrected;
|
|
}
|
|
|
|
Rot3 R_t_to_t0 = Rot3::Expmap(delta_angles);
|
|
|
|
R_t_to_t0 = R_t_to_t0 * Rot3::Expmap( body_t_omega_body*msr_dt );
|
|
return Rot3::Logmap(R_t_to_t0);
|
|
}
|
|
|
|
|
|
static inline noiseModel::Gaussian::shared_ptr CalcEquivalentNoiseCov(const noiseModel::Gaussian::shared_ptr& gaussian_acc, const noiseModel::Gaussian::shared_ptr& gaussian_gyro,
|
|
const noiseModel::Gaussian::shared_ptr& gaussian_process){
|
|
|
|
Matrix cov_acc = inverse( gaussian_acc->R().transpose() * gaussian_acc->R() );
|
|
Matrix cov_gyro = inverse( gaussian_gyro->R().transpose() * gaussian_gyro->R() );
|
|
Matrix cov_process = inverse( gaussian_process->R().transpose() * gaussian_process->R() );
|
|
|
|
cov_process.block(0,0, 3,3) += cov_gyro;
|
|
cov_process.block(6,6, 3,3) += cov_acc;
|
|
|
|
return noiseModel::Gaussian::Covariance(cov_process);
|
|
}
|
|
|
|
static inline void CalcEquivalentNoiseCov_DifferentParts(const noiseModel::Gaussian::shared_ptr& gaussian_acc, const noiseModel::Gaussian::shared_ptr& gaussian_gyro,
|
|
const noiseModel::Gaussian::shared_ptr& gaussian_process,
|
|
Matrix& cov_acc, Matrix& cov_gyro, Matrix& cov_process_without_acc_gyro){
|
|
|
|
cov_acc = inverse( gaussian_acc->R().transpose() * gaussian_acc->R() );
|
|
cov_gyro = inverse( gaussian_gyro->R().transpose() * gaussian_gyro->R() );
|
|
cov_process_without_acc_gyro = inverse( gaussian_process->R().transpose() * gaussian_process->R() );
|
|
}
|
|
|
|
static inline void Calc_g_rho_omega_earth_NED(const Vector& Pos_NED, const Vector& Vel_NED, const Vector& LatLonHeight_IC, const Vector& Pos_NED_Initial,
|
|
Vector& g_NED, Vector& rho_NED, Vector& omega_earth_NED) {
|
|
|
|
Matrix ENU_to_NED = Matrix_(3, 3,
|
|
0.0, 1.0, 0.0,
|
|
1.0, 0.0, 0.0,
|
|
0.0, 0.0, -1.0);
|
|
|
|
Matrix NED_to_ENU = Matrix_(3, 3,
|
|
0.0, 1.0, 0.0,
|
|
1.0, 0.0, 0.0,
|
|
0.0, 0.0, -1.0);
|
|
|
|
// Convert incoming parameters to ENU
|
|
Vector Pos_ENU = NED_to_ENU * Pos_NED;
|
|
Vector Vel_ENU = NED_to_ENU * Vel_NED;
|
|
Vector Pos_ENU_Initial = NED_to_ENU * Pos_NED_Initial;
|
|
|
|
// Call ENU version
|
|
Vector g_ENU;
|
|
Vector rho_ENU;
|
|
Vector omega_earth_ENU;
|
|
Calc_g_rho_omega_earth_ENU(Pos_ENU, Vel_ENU, LatLonHeight_IC, Pos_ENU_Initial, g_ENU, rho_ENU, omega_earth_ENU);
|
|
|
|
// Convert output to NED
|
|
g_NED = ENU_to_NED * g_ENU;
|
|
rho_NED = ENU_to_NED * rho_ENU;
|
|
omega_earth_NED = ENU_to_NED * omega_earth_ENU;
|
|
}
|
|
|
|
static inline void Calc_g_rho_omega_earth_ENU(const Vector& Pos_ENU, const Vector& Vel_ENU, const Vector& LatLonHeight_IC, const Vector& Pos_ENU_Initial,
|
|
Vector& g_ENU, Vector& rho_ENU, Vector& omega_earth_ENU){
|
|
double R0 = 6.378388e6;
|
|
double e = 1/297;
|
|
double Re( R0*( 1-e*(sin( LatLonHeight_IC(0) ))*(sin( LatLonHeight_IC(0) )) ) );
|
|
|
|
// Calculate current lat, lon
|
|
Vector delta_Pos_ENU(Pos_ENU - Pos_ENU_Initial);
|
|
double delta_lat(delta_Pos_ENU(1)/Re);
|
|
double delta_lon(delta_Pos_ENU(0)/(Re*cos(LatLonHeight_IC(0))));
|
|
double lat_new(LatLonHeight_IC(0) + delta_lat);
|
|
double lon_new(LatLonHeight_IC(1) + delta_lon);
|
|
|
|
// Rotation of lon about z axis
|
|
Rot3 C1(cos(lon_new), sin(lon_new), 0.0,
|
|
-sin(lon_new), cos(lon_new), 0.0,
|
|
0.0, 0.0, 1.0);
|
|
|
|
// Rotation of lat about y axis
|
|
Rot3 C2(cos(lat_new), 0.0, sin(lat_new),
|
|
0.0, 1.0, 0.0,
|
|
-sin(lat_new), 0.0, cos(lat_new));
|
|
|
|
Rot3 UEN_to_ENU(0, 1, 0,
|
|
0, 0, 1,
|
|
1, 0, 0);
|
|
|
|
Rot3 R_ECEF_to_ENU( UEN_to_ENU * C2 * C1 );
|
|
|
|
Vector omega_earth_ECEF(Vector_(3, 0.0, 0.0, 7.292115e-5));
|
|
omega_earth_ENU = R_ECEF_to_ENU.matrix() * omega_earth_ECEF;
|
|
|
|
// Calculating g
|
|
double height(LatLonHeight_IC(2));
|
|
double EQUA_RADIUS = 6378137.0; // equatorial radius of the earth; WGS-84
|
|
double ECCENTRICITY = 0.0818191908426; // eccentricity of the earth ellipsoid
|
|
double e2( pow(ECCENTRICITY,2) );
|
|
double den( 1-e2*pow(sin(lat_new),2) );
|
|
double Rm( (EQUA_RADIUS*(1-e2))/( pow(den,(3/2)) ) );
|
|
double Rp( EQUA_RADIUS/( sqrt(den) ) );
|
|
double Ro( sqrt(Rp*Rm) ); // mean earth radius of curvature
|
|
double g0( 9.780318*( 1 + 5.3024e-3 * pow(sin(lat_new),2) - 5.9e-6 * pow(sin(2*lat_new),2) ) );
|
|
double g_calc( g0/( pow(1 + height/Ro, 2) ) );
|
|
g_ENU = Vector_(3, 0.0, 0.0, -g_calc);
|
|
|
|
|
|
// Calculate rho
|
|
double Ve( Vel_ENU(0) );
|
|
double Vn( Vel_ENU(1) );
|
|
double rho_E = -Vn/(Rm + height);
|
|
double rho_N = Ve/(Rp + height);
|
|
double rho_U = Ve*tan(lat_new)/(Rp + height);
|
|
rho_ENU = Vector_(3, rho_E, rho_N, rho_U);
|
|
}
|
|
|
|
static inline noiseModel::Gaussian::shared_ptr calc_descrete_noise_model(const noiseModel::Gaussian::shared_ptr& model, double delta_t){
|
|
/* Q_d (approx)= Q * delta_t */
|
|
/* In practice, square root of the information matrix is represented, so that:
|
|
* R_d (approx)= R / sqrt(delta_t)
|
|
* */
|
|
return noiseModel::Gaussian::SqrtInformation(model->R()/sqrt(delta_t));
|
|
}
|
|
private:
|
|
|
|
/** Serialization function */
|
|
friend class boost::serialization::access;
|
|
template<class ARCHIVE>
|
|
void serialize(ARCHIVE & ar, const unsigned int version) {
|
|
ar & boost::serialization::make_nvp("NonlinearFactor2",
|
|
boost::serialization::base_object<Base>(*this));
|
|
}
|
|
|
|
|
|
|
|
}; // \class EquivInertialNavFactor_GlobalVel
|
|
|
|
} /// namespace gtsam
|