Kalman::KFilter< T, BEG, OQ, OVR, DBG > Class Template Reference

Generic Linear Kalman Filter template base class. More...

#include <kfilter.hpp>

Inheritance diagram for Kalman::KFilter< T, BEG, OQ, OVR, DBG >:

Public Member Functions
virtual	~KFilter ()=0
	Virtual destructor.
Protected Member Functions
virtual void	makeB ()
	Virtual creator of B.
virtual void	makeBaseB ()
	Virtual pre-creator of B.
Protected Attributes
Matrix	B
	Input matrix.
Private Member Functions
virtual void	makeMeasure ()
	Measurement function overridden to be linear.
virtual void	makeProcess ()
	Process function overridden to be linear.
virtual void	sizeUpdate ()
	Matrix and vector resizing function, overridden to take B into account.
Private Attributes
Vector	x__
	Temporary vector.

Detailed Description

template<typename T, K_UINT_32 BEG, bool OQ = false, bool OVR = false, bool DBG = true>
class Kalman::KFilter< T, BEG, OQ, OVR, DBG >

Generic Linear Kalman Filter template base class.

Usage: This class is derived from EKFilter. You should really read all the documentation of EKFilter before reading this.
This class implements a Variable-Dimension Linear Kalman Filter based on the EKFilter template class.

Notation

Assume a state vector $ x $

(to estimate) and a linear process function $ f $

(to model) that describes the evolution of this state through time, that is :

$x_k = f \left( x_{k-1}, u_{k-1}, w_{k-1} \right) = //! A x_{k-1} + B u_{k-1} + W w_{k-1}$

where

is the (known) input vector fed to the process and $ w $

is the (unknown) process noise vector due to uncertainty and process modeling errors. Further suppose that the (known) process noise covariance matrix is :

$Q = E \left( w w^T \right)$

Now, let's assume a (known) measurement vector $ z $

, which depends on the current state $ x $

in the form of a linear function $ h $

(to model) :

$z_k = h \left( x_k, v_k \right) = //! H x_k + V v_k$

where

is the (unknown) measurement noise vector with a (known) covariance matrix :

$R = E \left( v v^T \right)$

Suppose that we have an estimate of the previous state $\hat{x}_{k-1}$ , called a corrected state or an a posteriori state estimate. We can build a predicted state (also called an a priori state estimate) by using $ f $

:

$\tilde{x}_k = f \left( \hat{x}_{k-1}, u_{k-1}, 0 \right) = //! A \hat{x}_{k-1} + B u_{k-1}$

since the input is known and the process noise, unknown. With this predicted state, we can get a predicted measurement vector by using $ h $

:

$\tilde{z}_k = h \left( \tilde{x}_k, 0 \right) = //! H \tilde{x}_k$

since the measurement noise is unknown.

Note:: In this class, makeProcess() and makeMeasure() have already been overridden, and cannot be ovverridden again. However, there is a new matrix to create : B. This means there are two new virtual functions that can be overridden : makeBaseB() and makeB().

See also:: EKFilter

Definition at line 82 of file kfilter.hpp.