Kalman< STA_MAP, OBS_MAP > Class Template Reference

Kalman filter. More...

Public Types
using	TProcess = Hierarchical< Markov< Gaussian, STA_MAP, Gaussian >, Memoryless< Gaussian, OBS_MAP >>
	Type of process object. More...
using	TCompeleteState = std::tuple< arma::vec, arma::mat >
	Type of the posterior state \((\hat{\mathbf{x}}, \hat{\mathbf{P}})\). More...

Public Member Functions
	Kalman (const TProcess &process)
	Construct a Kalman filter. More...
template<class... TArgs>
void	predict (const TArgs &...args)
	Prediction. More...
template<class... TArgs>
TCompeleteState	correct (const arma::vec &measurement, const TArgs &...args)
	Correction. More...
TCompeleteState	initialize ()
	Initialization. More...
Public Member Functions inherited from RecursiveBayesianBase< Kalman< STA_MAP, OBS_MAP > >
decltype(auto)	step (const TMeasurement &measurement, const TArgs &...args)
decltype(auto)	filter (const std::vector< TMeasurement > &measurements, const std::vector< TControl > &controls=std::vector< std::tuple<>>())

Detailed Description

template<class STA_MAP, class OBS_MAP>
class ssmkit::filter::Kalman< STA_MAP, OBS_MAP >

Kalman filter.

Definition at line 30 of file kalman.hpp.

Member Typedef Documentation

using TProcess = Hierarchical<Markov<Gaussian, STA_MAP, Gaussian>, Memoryless<Gaussian, OBS_MAP>>

Type of process object.

Definition at line 37 of file kalman.hpp.

using TCompeleteState = std::tuple<arma::vec, arma::mat>

Type of the posterior state \((\hat{\mathbf{x}}, \hat{\mathbf{P}})\).

Definition at line 40 of file kalman.hpp.

Constructor & Destructor Documentation

Kalman ( const TProcess &  process )

inline

Construct a Kalman filter.

Construct a Kalman filter with parameters taken from process argument.

Definition at line 67 of file kalman.hpp.

Member Function Documentation

void predict ( const TArgs &...  args )

inline

Prediction.

Performs the prediction step.

\begin{equation}\hat{\mathbf{x}}_{t|t-1} = \mathbf{F}\hat{\mathbf{x}}_{t-1|t-1}+u_d(y^d_1, \cdots, y^d_{N_d}) \end{equation}

\begin{equation}\mathbf{P}_{t|t-1} = \mathbf{F}\mathbf{P}_{t-1|t-1}\mathbf{F}^T+\mathbf{Q}\end{equation}

Parameters

args...

Control variables \(y^d_1, \cdots, y^d_{N_d}\) of the dynamic process, if any.

Definition at line 94 of file kalman.hpp.

TCompeleteState correct ( const arma::vec &  measurement, const TArgs &...  args  )

inline

Correction.

Performs correction step.

\begin{equation}\tilde{\mathbf{z}}_t=\mathbf{z}_t-\mathbf{H}\hat{\mathbf{x}}_{t|t-1}-u_m(y^m_1, \cdots, y^m_{N_m})\end{equation}

\begin{equation}\mathbf {S}_t=\mathbf{H}\mathbf{P}_{t|t-1}\mathbf{H}^T+\mathbf{R} \end{equation}

\begin{equation}\mathbf{K}_t=\mathbf{P}_{t|t-1}\mathbf{H}^T\mathbf{S}_t^{-1} \end{equation}

\begin{equation}\hat{\mathbf{x}}_{t|t}=\hat{\mathbf{x}}_{t|t-1}+\mathbf{K}_{t}\tilde{\mathbf{z}}_t \end{equation}

\begin{equation}\mathbf{P}_{t|t}=(I-\mathbf{K}_t\mathbf{H})\mathbf{P}_{t|t-1}\end{equation}

Parameters

measurement	Measurement vector \(\mathbf{z}_t\).
args...	Control variables \(y^m_1, \cdots, y^m_{N_m}\) of the measurement process, if any.

Returns

Estimated state \((\hat{\mathbf{x}}_{t|t}, \mathbf{P}_{t|t})\)

Definition at line 118 of file kalman.hpp.

TCompeleteState initialize ( )

inline

Initialization.

Returns

Initial state \((\hat{\mathbf{x}}_{0|0}, \mathbf{P}_{0|0})\)

Definition at line 137 of file kalman.hpp.

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

• src/ssmkit/filter/kalman.hpp