KalmanFilter.hpp File Reference

Generalized Kalman Filter class. More...

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Classes
class	NAV::KalmanFilter
	Generalized Kalman Filter class. More...

Functions
template<typename Derived >
Derived::PlainObject	NAV::transitionMatrix_Phi_exp (const Eigen::MatrixBase< Derived > &F, typename Derived::Scalar tau_s)
	Calculates the state transition matrix 𝚽 using the exponential matrix.
template<typename Derived >
Derived::PlainObject	NAV::transitionMatrix_Phi_Taylor (const Eigen::MatrixBase< Derived > &F, double tau_s, size_t order)
	Calculates the state transition matrix 𝚽 limited to specified order in 𝐅𝜏ₛ

Detailed Description

Generalized Kalman Filter class.

Author

T. Topp (topp@.nosp@m.ins..nosp@m.uni-s.nosp@m.tutt.nosp@m.gart..nosp@m.de)

Date

2020-11-25

Function Documentation

transitionMatrix_Phi_exp()

template<typename Derived >

Derived::PlainObject NAV::transitionMatrix_Phi_exp	(	const Eigen::MatrixBase< Derived > &	F,
		typename Derived::Scalar	tau_s )

Calculates the state transition matrix 𝚽 using the exponential matrix.

Parameters

[in]	F	System Matrix
[in]	tau_s	time interval in [s]

Note

See [17] Groves, ch. 3.2.3, eq. 3.33, p. 97

Attention

The cost of the computation is approximately 20n^3 for matrices of size n. The number 20 depends weakly on the norm of the matrix.

transitionMatrix_Phi_Taylor()

template<typename Derived >

Derived::PlainObject NAV::transitionMatrix_Phi_Taylor	(	const Eigen::MatrixBase< Derived > &	F,
		double	tau_s,
		size_t	order )

Calculates the state transition matrix 𝚽 limited to specified order in 𝐅𝜏ₛ

Parameters

[in]	F	System Matrix
[in]	tau_s	time interval in [s]
[in]	order	The order of the Taylor polynom to calculate

Note

See [17] Groves, ch. 3.2.3, eq. 3.34, p. 98