Left-Invariant Extended Kalman Filter on a Lie group G. More...

#include <InvariantEKF.h>

Inheritance diagram for gtsam::InvariantEKF< G >:

Public Types
using	Base = LieGroupEKF< G >
	Base class type. More...

using	Covariance = typename Base::Covariance
	Covariance matrix type. Eigen::Matrix<double, Dim, Dim>. More...

using	Jacobian = typename Base::Jacobian
	Jacobian for group-specific operations like AdjointMap. Eigen::Matrix<double, Dim, Dim>. More...

using	TangentVector = typename Base::TangentVector

Public Types inherited from gtsam::LieGroupEKF< G >
using	Base = ManifoldEKF< G >
	Base class type. More...

using	Covariance = typename Base::Covariance

template<typename Dynamics >
using	enable_if_dynamics = std::enable_if_t< !std::is_convertible_v< Dynamics, TangentVector > &&std::is_invocable_r_v< TangentVector, Dynamics, const G &, OptionalJacobian< Dim, Dim > & > >

template<typename Control , typename Dynamics >
using	enable_if_full_dynamics = std::enable_if_t< std::is_invocable_r_v< TangentVector, Dynamics, const G &, const Control &, OptionalJacobian< Dim, Dim > & > >

using	Jacobian = typename Base::Jacobian
	Jacobian for group operations (Adjoint, Expmap derivatives, F). More...

using	TangentVector = typename Base::TangentVector

Public Types inherited from gtsam::ManifoldEKF< G >
using	Covariance = Eigen::Matrix< double, Dim, Dim >
	Covariance matrix type (P, Q). More...

using	Jacobian = Eigen::Matrix< double, Dim, Dim >
	State transition Jacobian type (F). More...

using	TangentVector = typename traits< G >::TangentVector
	Tangent vector type for the manifold M. More...

Public Member Functions
	InvariantEKF (const G &X0, const Covariance &P0)

void	predict (const G &U, const Covariance &Q)

void	predict (const TangentVector &u, double dt, const Covariance &Q)

Public Member Functions inherited from gtsam::LieGroupEKF< G >
	LieGroupEKF (const G &X0, const Covariance &P0)

template<typename Control , typename Dynamics , typename = enable_if_full_dynamics<Control, Dynamics>>
void	predict (Dynamics &&f, const Control &u, double dt, const Covariance &Q)

template<typename Dynamics , typename = enable_if_dynamics<Dynamics>>
void	predict (Dynamics &&f, double dt, const Covariance &Q)

template<typename Control , typename Dynamics , typename = enable_if_full_dynamics<Control, Dynamics>>
G	predictMean (Dynamics &&f, const Control &u, double dt, OptionalJacobian< Dim, Dim > A={}) const

template<typename Dynamics , typename = enable_if_dynamics<Dynamics>>
G	predictMean (Dynamics &&f, double dt, OptionalJacobian< Dim, Dim > A={}) const

Public Member Functions inherited from gtsam::ManifoldEKF< G >
const Covariance &	covariance () const

int	dimension () const

	ManifoldEKF (const G &X0, const Covariance &P0)

void	predict (const G &X_next, const Jacobian &F, const Covariance &Q)

const G &	state () const

void	update (const Measurement &prediction, const Eigen::Matrix< double, traits< Measurement >::dimension, Dim > &H, const Measurement &z, const Eigen::Matrix< double, traits< Measurement >::dimension, traits< Measurement >::dimension > &R)

void	update (MeasurementFunction &&h, const Measurement &z, const Eigen::Matrix< double, traits< Measurement >::dimension, traits< Measurement >::dimension > &R)

virtual	~ManifoldEKF ()=default

Additional Inherited Members
Static Public Attributes inherited from gtsam::LieGroupEKF< G >
static constexpr int	Dim = Base::Dim
	Compile-time dimension of G. More...

Static Public Attributes inherited from gtsam::ManifoldEKF< G >
static constexpr int	Dim
	Compile-time dimension of the manifold M. More...

Protected Attributes inherited from gtsam::ManifoldEKF< G >
int	n_
	Runtime tangent space dimension of M. More...

Covariance	P_
	Covariance (Eigen::Matrix<double, Dim, Dim>). More...

G	X_
	Manifold state estimate. More...

Detailed Description

template<typename G>
class gtsam::InvariantEKF< G >

Left-Invariant Extended Kalman Filter on a Lie group G.

Template Parameters

G	Lie group type (must satisfy LieGroup concept).

This filter inherits from LieGroupEKF but restricts the prediction interface to only the left-invariant prediction methods:

Prediction via group composition: predict(const G& U, const Covariance& Q)
Prediction via tangent control vector: predict(const TangentVector& u, double dt, const Covariance& Q)

The state-dependent prediction methods from LieGroupEKF are hidden. The update step remains the same as in ManifoldEKF/LieGroupEKF. For details on how static and dynamic dimensions are handled, please refer to the ManifoldEKF class documentation.

Definition at line 50 of file InvariantEKF.h.

Member Typedef Documentation

◆ Base

template<typename G >

using gtsam::InvariantEKF< G >::Base = LieGroupEKF<G>

Base class type.

Definition at line 52 of file InvariantEKF.h.

◆ Covariance

template<typename G >

using gtsam::InvariantEKF< G >::Covariance = typename Base::Covariance

Covariance matrix type. Eigen::Matrix<double, Dim, Dim>.

Definition at line 57 of file InvariantEKF.h.

◆ Jacobian

template<typename G >

using gtsam::InvariantEKF< G >::Jacobian = typename Base::Jacobian

Jacobian for group-specific operations like AdjointMap. Eigen::Matrix<double, Dim, Dim>.

Definition at line 55 of file InvariantEKF.h.

◆ TangentVector

template<typename G >

using gtsam::InvariantEKF< G >::TangentVector = typename Base::TangentVector

Tangent vector type

Definition at line 53 of file InvariantEKF.h.

Constructor & Destructor Documentation

◆ InvariantEKF()

template<typename G >

gtsam::InvariantEKF< G >::InvariantEKF	(	const G &	X0,
		const Covariance &	P0
	)

inline

Constructor: forwards to LieGroupEKF constructor.

Parameters

X0	Initial state on Lie group G.
P0	Initial covariance in the tangent space at X0.

Definition at line 65 of file InvariantEKF.h.

Member Function Documentation

◆ predict() [1/2]

template<typename G >

void gtsam::InvariantEKF< G >::predict	(	const G &	U,
		const Covariance &	Q
	)

inline

Predict step via group composition (Left-Invariant): X_{k+1} = X_k * U P_{k+1} = Ad_{U^{-1}} P_k Ad_{U^{-1}}^T + Q where Ad_{U^{-1}} is the Adjoint map of U^{-1}.

Parameters

U	Lie group element representing the motion increment.
Q	Process noise covariance.

Definition at line 79 of file InvariantEKF.h.

◆ predict() [2/2]

template<typename G >

void gtsam::InvariantEKF< G >::predict	(	const TangentVector &	u,
		double	dt,
		const Covariance &	Q
	)

inline

Predict step via tangent control vector: U = Expmap(u * dt) Then calls predict(U, Q).

Parameters

u	Tangent space control vector.
dt	Time interval.
Q	Process noise covariance matrix.

Definition at line 97 of file InvariantEKF.h.

The documentation for this class was generated from the following file:

InvariantEKF.h

Public Types

Public Member Functions

Additional Inherited Members

Detailed Description

template<typename G> class gtsam::InvariantEKF< G >

Member Typedef Documentation

◆ Base

◆ Covariance

◆ Jacobian

◆ TangentVector

Constructor & Destructor Documentation

◆ InvariantEKF()

Member Function Documentation

◆ predict() [1/2]

◆ predict() [2/2]

template<typename G>
class gtsam::InvariantEKF< G >