#include <vpKalmanFilter.h>

Inheritance diagram for vpKalmanFilter:

Public Member Functions
	vpKalmanFilter ()
	vpKalmanFilter (unsigned int n_signal)
	vpKalmanFilter (unsigned int size_state, unsigned int size_measure, unsigned int n_signal)
virtual	~vpKalmanFilter ()
void	setNumberOfSignal (unsigned int n_signal)
void	init (unsigned int size_state, unsigned int size_measure, unsigned int n_signal)
void	prediction ()
void	filtering (const vpColVector &z)
unsigned int	getStateSize ()
unsigned int	getMeasureSize ()
unsigned int	getNumberOfSignal ()
long	getIteration ()
void	verbose (bool on)

Public Attributes
vpColVector	Xest
vpColVector	Xpre
vpMatrix	F
vpMatrix	H
vpMatrix	R
vpMatrix	Q
double	dt
vpMatrix	Ppre
vpMatrix	Pest

Protected Attributes
long	iter
unsigned int	size_state
unsigned int	size_measure
unsigned int	nsignal
bool	verbose_mode
vpMatrix	W
vpMatrix	I

Detailed Description

This class provides a generic Kalman filtering algorithm along with some specific state model (constant velocity, constant acceleration) which are implemented in the vpLinearKalmanFilterInstantiation class.

The state evolution equation is given by:

$\‍[{\bf x}_k= {\bf F}_{k-1} {\bf x}_{k-1} + {\bf w}_{k-1} \\ \‍]$

where ${\bf x}_{k}$ is the unknown state at iteration $k$ .

The measurement equation is given by:

$\‍[{\bf z}_k = {\bf H} {\bf x}_k + {\bf r}_k \‍]$

where ${\bf z}_{k}$ is the measure (also named observation) at iteration $k$ .

The predicted state is obtained by:

$\‍[{\bf x}_{k|k-1} = {\bf F}_{k-1} {\bf x}_{k-1\mid k-1} \‍]$

$\‍[{\bf P}_{k \mid k-1} = {\bf F}_{k-1} {\bf P}_{k-1 \mid k-1} {\bf F}^T_{k-1} + {\bf Q}_k \‍]$

where

${\bf x}_{k|k-1}$ is the prediction of the state,
${\bf P}_{k \mid k-1}$ is the state prediction covariance matrix.

Filtering equation are:

$\‍[{\bf W}_k = {\bf P}_{k \mid k-1} {\bf H}^T \left[ {\bf H P}_{k \mid k-1} {\bf H}^T + {\bf R}_k \right]^{-1} \‍]$

$\‍[{\bf x}_{k \mid k} = {\bf x}_{k \mid k-1} + {\bf W}_k \left[ {\bf z}_k - {\bf H x}_{k \mid k-1} \right] \‍]$

$\‍[{\bf P}_{k \mid k} = \left({\bf I - W}_k {\bf H} \right) {\bf P}_{k \mid k-1} \‍]$

where ${\bf W}_k$ is the filter gain.

Notice that there is a recursion for the inverse covariance

$\‍[{\bf P}_{k \mid k}^{-1}= {\bf P}_{k \mid k-1}^{-1} + {\bf H}^T {\bf R}^{-1} {\bf H} \‍]$

where ${\bf P}_{k \mid k}^{-1}$ is the inverse of the covariance matrix.

ViSP provides different state evolution models implemented in the vpLinearKalmanFilterInstantiation class.

Definition at line 104 of file vpKalmanFilter.h.

Constructor & Destructor Documentation

◆ vpKalmanFilter() [1/3]

vpKalmanFilter::vpKalmanFilter ( )

Construct a default Kalman filter.

The verbose mode is disabled by default

Definition at line 88 of file vpKalmanFilter.cpp.

References dt, F, H, I, iter, nsignal, Pest, Ppre, Q, R, size_measure, size_state, verbose_mode, W, Xest, and Xpre.

◆ vpKalmanFilter() [2/3]

vpKalmanFilter::vpKalmanFilter ( unsigned int n_signal )

explicit

Construct a default Kalman filter by setting the number of signal to filter.

The verbose mode is disabled by default

Parameters

n_signal : Number of signal to filter.

Definition at line 101 of file vpKalmanFilter.cpp.

References dt, F, H, I, iter, nsignal, Pest, Ppre, Q, R, size_measure, size_state, verbose_mode, W, Xest, and Xpre.

◆ vpKalmanFilter() [3/3]

vpKalmanFilter::vpKalmanFilter	(	unsigned int	size_state_vector,
		unsigned int	size_measure_vector,
		unsigned int	n_signal )

Construct a Kalman filter.

The verbose mode is disabled by default

Parameters

size_state_vector	: Size of the state vector ${\bf x}_{(k)}$ for one signal.
size_measure_vector	: Size of the measure vector ${\bf z}_{(k)}$ for one signal.
n_signal	: Number of signal to filter.

Definition at line 120 of file vpKalmanFilter.cpp.

References dt, F, H, I, init(), iter, nsignal, Pest, Ppre, Q, R, size_measure, size_state, verbose_mode, W, Xest, and Xpre.

◆ ~vpKalmanFilter()

virtual vpKalmanFilter::~vpKalmanFilter ( )

inlinevirtual

Destructor that does noting.

Definition at line 128 of file vpKalmanFilter.h.

Member Function Documentation

◆ filtering()

void vpKalmanFilter::filtering ( const vpColVector & z )

Update the Kalman filter by applying the filtering equations and increment the filter iteration (vpKalmanFilter::iter).

Parameters

z	: Measure (or observation) ${\bf z}_k$ provided at iteration .

The filtering equation is given by:

$\‍[{\bf x}_{k \mid k} = {\bf x}_{k \mid k-1} + {\bf W}_k \left[ {\bf z}_k - {\bf H} {\bf x}_{k \mid k-1} \right] \‍]$

where ${\bf W_k}$ is the filter gain computed using the formula:

$\‍[{\bf W_k} = {\bf P}_{k \mid k-1} {\bf H}^T \left[ {\bf H P}_{k \mid k-1} {\bf H}^T + {\bf R}_k \right]^{-1} \‍]$

and where the updated covariance of the state is given by

$\‍[{\bf P}_{k \mid k} = \left({\bf I} - {\bf W}_k {\bf H} \right) {\bf P}_{k \mid k-1} \‍]$

or in a symmetric form

$\‍[{\bf P}_{k \mid k} = {\bf P}_{k \mid k-1} - {\bf W}_k {\bf S}_k {\bf W}^T_k \‍]$

with

$\‍[{\bf S}_k = {\bf H P}_{k \mid k-1} {\bf H}^T + {\bf R}_k \‍]$

Definition at line 200 of file vpKalmanFilter.cpp.

References H, vpMatrix::inverseByLU(), iter, Pest, Ppre, R, verbose_mode, W, Xest, and Xpre.

Referenced by vpLinearKalmanFilterInstantiation::filter().

◆ getIteration()

long vpKalmanFilter::getIteration ( )

inline

Return the iteration number.

Definition at line 153 of file vpKalmanFilter.h.

References iter.

◆ getMeasureSize()

unsigned int vpKalmanFilter::getMeasureSize ( )

inline

Return the size of the measure vector ${\bf z}_{(k)}$ for one signal.

Examples: testKalmanAcceleration.cpp.

Definition at line 145 of file vpKalmanFilter.h.

References size_measure.

◆ getNumberOfSignal()

unsigned int vpKalmanFilter::getNumberOfSignal ( )

inline

Return the number of signal to filter.

Definition at line 149 of file vpKalmanFilter.h.

References nsignal.

◆ getStateSize()

unsigned int vpKalmanFilter::getStateSize ( )

inline

Return the size of the state vector ${\bf x}_{(k)}$ for one signal.

Examples: servoAfma4Point2DCamVelocityKalman.cpp, servoViper850Point2DCamVelocityKalman.cpp, and testKalmanAcceleration.cpp.

Definition at line 141 of file vpKalmanFilter.h.

References size_state.

◆ init()

void vpKalmanFilter::init	(	unsigned int	size_state_vector,
		unsigned int	size_measure_vector,
		unsigned int	n_signal )

Initialize the Kalman filter.

Parameters

size_state_vector	: Size of the state vector ${\bf x}_{k}$ for one signal.
size_measure_vector	: Size of the measure vector ${\bf z}_{k}$ for one signal.
n_signal	: Number of signal to filter.

Definition at line 57 of file vpKalmanFilter.cpp.

References dt, F, H, I, iter, nsignal, Pest, Q, R, size_measure, size_state, Xest, and Xpre.

Referenced by vpLinearKalmanFilterInstantiation::initStateConstAccWithColoredNoise_MeasureVel(), vpLinearKalmanFilterInstantiation::initStateConstVel_MeasurePos(), vpLinearKalmanFilterInstantiation::initStateConstVelWithColoredNoise_MeasureVel(), and vpKalmanFilter().

◆ prediction()

void vpKalmanFilter::prediction ( )

Update the Kalman filter by applying the prediction equations.

The predicted state is given by

$\‍[{{\bf x}}_{k|k-1} = {\bf F}_{k-1} {\bf x}_{k-1\mid k-1} \‍]$

and the state prediction covariance by

$\‍[{\bf P}_{k \mid k-1} = {\bf F}_{k-1} {\bf P}_{k-1 \mid k-1} {\bf F}^T_{k-1} + {\bf Q}_k \‍]$

Definition at line 143 of file vpKalmanFilter.cpp.

References F, vpException::fatalError, nsignal, Pest, Ppre, Q, size_state, verbose_mode, Xest, and Xpre.

Referenced by vpLinearKalmanFilterInstantiation::filter().

◆ setNumberOfSignal()

void vpKalmanFilter::setNumberOfSignal ( unsigned int n_signal )

inline

Set the number of signal to filter.

Definition at line 132 of file vpKalmanFilter.h.

◆ verbose()

void vpKalmanFilter::verbose ( bool on )

inline

Sets the verbose mode.

Parameters

on	: If true, activates the verbose mode which consists in printing the Kalman filter internal values.

Examples: testKalmanAcceleration.cpp, and testKalmanVelocity.cpp.

Definition at line 159 of file vpKalmanFilter.h.

References verbose_mode.

Member Data Documentation

◆ dt

double vpKalmanFilter::dt

Sampling time $\Delta t$ in second between two successive iterations. Only used in some specific state models implemented in vpLinearKalmanFilterInstantiation.

Definition at line 187 of file vpKalmanFilter.h.

Referenced by vpLinearKalmanFilterInstantiation::filter(), init(), vpLinearKalmanFilterInstantiation::initStateConstAccWithColoredNoise_MeasureVel(), vpLinearKalmanFilterInstantiation::initStateConstVel_MeasurePos(), vpKalmanFilter(), vpKalmanFilter(), and vpKalmanFilter().

◆ F

vpMatrix vpKalmanFilter::F

Transition matrix ${\bf F}$ that describes the evolution of the state.

Definition at line 175 of file vpKalmanFilter.h.

Referenced by init(), vpLinearKalmanFilterInstantiation::initStateConstAccWithColoredNoise_MeasureVel(), vpLinearKalmanFilterInstantiation::initStateConstVel_MeasurePos(), vpLinearKalmanFilterInstantiation::initStateConstVelWithColoredNoise_MeasureVel(), prediction(), vpKalmanFilter(), vpKalmanFilter(), and vpKalmanFilter().

◆ H

vpMatrix vpKalmanFilter::H

Matrix ${\bf H}$ that describes the evolution of the measurements.

Definition at line 178 of file vpKalmanFilter.h.

Referenced by filtering(), init(), vpLinearKalmanFilterInstantiation::initStateConstAccWithColoredNoise_MeasureVel(), vpLinearKalmanFilterInstantiation::initStateConstVel_MeasurePos(), vpLinearKalmanFilterInstantiation::initStateConstVelWithColoredNoise_MeasureVel(), vpKalmanFilter(), vpKalmanFilter(), and vpKalmanFilter().

◆ I

vpMatrix vpKalmanFilter::I

protected

Identity matrix $\bf I$ .

Definition at line 212 of file vpKalmanFilter.h.

Referenced by init(), vpKalmanFilter(), vpKalmanFilter(), and vpKalmanFilter().

◆ iter

long vpKalmanFilter::iter

protected

Filter step or iteration. When set to zero, initialize the filter.

Definition at line 110 of file vpKalmanFilter.h.

Referenced by vpLinearKalmanFilterInstantiation::filter(), filtering(), getIteration(), init(), vpLinearKalmanFilterInstantiation::initStateConstAccWithColoredNoise_MeasureVel(), vpLinearKalmanFilterInstantiation::initStateConstVel_MeasurePos(), vpLinearKalmanFilterInstantiation::initStateConstVelWithColoredNoise_MeasureVel(), vpKalmanFilter(), vpKalmanFilter(), and vpKalmanFilter().

◆ nsignal

unsigned int vpKalmanFilter::nsignal

protected

Number of signal to filter.

Definition at line 117 of file vpKalmanFilter.h.

Referenced by vpLinearKalmanFilterInstantiation::filter(), getNumberOfSignal(), init(), vpLinearKalmanFilterInstantiation::initStateConstAccWithColoredNoise_MeasureVel(), prediction(), vpKalmanFilter(), vpKalmanFilter(), and vpKalmanFilter().

◆ Pest

vpMatrix vpKalmanFilter::Pest

The updated covariance of the state ${\bf P}_{k \mid k}$ where ${\bf P}_{k \mid k} = \left({\bf I - W}_k {\bf H} \right) {\bf P}_{k \mid k-1}$ .

Definition at line 201 of file vpKalmanFilter.h.

Referenced by filtering(), init(), vpLinearKalmanFilterInstantiation::initStateConstAccWithColoredNoise_MeasureVel(), vpLinearKalmanFilterInstantiation::initStateConstVel_MeasurePos(), vpLinearKalmanFilterInstantiation::initStateConstVelWithColoredNoise_MeasureVel(), prediction(), vpKalmanFilter(), vpKalmanFilter(), and vpKalmanFilter().

◆ Ppre

vpMatrix vpKalmanFilter::Ppre

The state prediction covariance ${\bf P}_{k \mid k-1}$ where ${\bf P}_{k \mid k-1} = {\bf F}_{k-1} {\bf P}_{k-1 \mid k-1} {\bf F}^T_{k-1} + {\bf Q}_k$ .

Definition at line 194 of file vpKalmanFilter.h.

Referenced by filtering(), prediction(), vpKalmanFilter(), vpKalmanFilter(), and vpKalmanFilter().

◆ Q

vpMatrix vpKalmanFilter::Q

Process noise covariance matrix ${\bf Q}$ .

Definition at line 183 of file vpKalmanFilter.h.

Referenced by init(), vpLinearKalmanFilterInstantiation::initStateConstAccWithColoredNoise_MeasureVel(), vpLinearKalmanFilterInstantiation::initStateConstVel_MeasurePos(), vpLinearKalmanFilterInstantiation::initStateConstVelWithColoredNoise_MeasureVel(), prediction(), vpKalmanFilter(), vpKalmanFilter(), and vpKalmanFilter().

◆ R

vpMatrix vpKalmanFilter::R

Measurement noise covariance matrix ${\bf R}$ .

Definition at line 181 of file vpKalmanFilter.h.

Referenced by filtering(), init(), vpLinearKalmanFilterInstantiation::initStateConstAccWithColoredNoise_MeasureVel(), vpLinearKalmanFilterInstantiation::initStateConstVel_MeasurePos(), vpLinearKalmanFilterInstantiation::initStateConstVelWithColoredNoise_MeasureVel(), vpKalmanFilter(), vpKalmanFilter(), and vpKalmanFilter().

◆ size_measure

unsigned int vpKalmanFilter::size_measure

protected

Size of the measure vector ${\bf z}_k$ .

Definition at line 115 of file vpKalmanFilter.h.

Referenced by vpLinearKalmanFilterInstantiation::filter(), getMeasureSize(), init(), vpLinearKalmanFilterInstantiation::initStateConstAccWithColoredNoise_MeasureVel(), vpLinearKalmanFilterInstantiation::initStateConstVel_MeasurePos(), vpLinearKalmanFilterInstantiation::initStateConstVelWithColoredNoise_MeasureVel(), vpLinearKalmanFilterInstantiation::setStateModel(), vpKalmanFilter(), vpKalmanFilter(), and vpKalmanFilter().

◆ size_state

unsigned int vpKalmanFilter::size_state

protected

Size of the state vector ${\bf x}_k$ .

Definition at line 113 of file vpKalmanFilter.h.

Referenced by vpLinearKalmanFilterInstantiation::filter(), getStateSize(), init(), vpLinearKalmanFilterInstantiation::initStateConstAccWithColoredNoise_MeasureVel(), vpLinearKalmanFilterInstantiation::initStateConstVel_MeasurePos(), vpLinearKalmanFilterInstantiation::initStateConstVelWithColoredNoise_MeasureVel(), prediction(), vpLinearKalmanFilterInstantiation::setStateModel(), vpKalmanFilter(), vpKalmanFilter(), and vpKalmanFilter().

◆ verbose_mode

bool vpKalmanFilter::verbose_mode

protected

When set to true, print the content of internal variables during filtering() and prediction().

Definition at line 121 of file vpKalmanFilter.h.

Referenced by filtering(), prediction(), verbose(), vpKalmanFilter(), vpKalmanFilter(), and vpKalmanFilter().

◆ W

vpMatrix vpKalmanFilter::W

protected

Filter gain ${\bf W}_k$ where ${\bf W}_k = {\bf P}_{k \mid k-1} {\bf H}^T \left[ {\bf H P}_{k \mid k-1} {\bf H}^T + {\bf R}_k \right]^{-1}$ .

Definition at line 209 of file vpKalmanFilter.h.

Referenced by filtering(), vpKalmanFilter(), vpKalmanFilter(), and vpKalmanFilter().

◆ Xest

vpColVector vpKalmanFilter::Xest

The updated state estimate ${\bf x}_{k \mid k}$ where ${\bf x}_{k \mid k} = {\bf x}_{k \mid k-1} + {\bf W}_k \left[ {\bf z}_k - {\bf H x}_{k \mid k-1} \right]$ .