bdm::KalmanCh Class Reference

#include <libKF.h>

Inheritance diagram for bdm::KalmanCh:

Detailed Description

Kalman filter in square root form.

Trivial example:

#include <estim/libKF.h>
using namespace bdm;
        
// estimation of AR(0) model
int main() {
        //dimensions
        int dx=3, dy=3, du=1;
        // matrices
        mat A = eye(dx);
        mat B = zeros(dx,du);
        mat C = eye(dx);
        mat D = zeros(dy,du);
        mat Q = eye(dx);
        mat R = 0.1*eye(dy);
        //prior
        mat P0 = 100*eye(dx);
        vec mu0 = zeros(dx);
        // Estimator
        KalmanCh KF;
        KF.set_parameters(A,B,C,D,/*covariances*/ Q,R);
        KF.set_statistics(mu0,P0);
        // Estimation loop
        for (int i=0;i<100;i++){
                KF.bayes(randn(dx+du));
        }
        //print results
        cout << "Posterior estimate of x is: "  << endl;
        cout << "mean: "<< KF.posterior().mean()<< endl;
        cout << "variance: "<< KF.posterior().variance()<< endl;
}


Public Member Functions
	KalmanCh ()
	Default constructor.
void	set_parameters (const mat &A0, const mat &B0, const mat &C0, const mat &D0, const chmat &Q0, const chmat &R0)
	Set parameters with check of relevance.
void	set_statistics (const vec &mu0, const chmat &P0)
void	bayes (const vec &dt)
	Here dt = [yt;ut] of appropriate dimensions.
void	set_est (const vec &mu0, const chmat &P0)
	Set estimate values, used e.g. in initialization.
const epdf &	posterior () const
	access function
const enorm< chmat > *	_e () const
mat &	__K ()
	access function
vec	_dP ()
	access function
Constructors
virtual BM *	_copy_ ()
Mathematical operations
virtual void	bayesB (const mat &Dt)
	Batch Bayes rule (columns of Dt are observations).
virtual double	logpred (const vec &dt) const
vec	logpred_m (const mat &dt) const
	Matrix version of logpred.
virtual epdf *	epredictor () const
	Constructs a predictive density $f(d_{t+1} \|d_{t}, \ldots d_{0})$ .
virtual mpdf *	predictor () const
	Constructs a conditional density 1-step ahead predictor.
Access to attributes
const RV &	_drv () const
void	set_drv (const RV &rv)
void	set_rv (const RV &rv)
double	_ll () const
void	set_evalll (bool evl0)
Protected Attributes
mat	preA
	pre array (triangular matrix)
mat	postA
	post array (triangular matrix)
RV	rvy
	Indetifier of output rv.
RV	rvu
	Indetifier of exogeneous rv.
int	dimx
	cache of rv.count()
int	dimy
	cache of rvy.count()
int	dimu
	cache of rvu.count()
mat	A
	Matrix A.
mat	B
	Matrix B.
mat	C
	Matrix C.
mat	D
	Matrix D.
chmat	Q
	Matrix Q in square-root form.
chmat	R
	Matrix R in square-root form.
enorm< chmat >	est
	posterior density on $x_t$
enorm< chmat >	fy
	preditive density on $y_t$
mat	_K
	placeholder for Kalman gain
vec &	_yp
	cache of fy.mu
chmat &	_Ry
	cache of fy.R
vec &	_mu
	cache of est.mu
chmat &	_P
	cache of est.R
RV	drv
	Random variable of the data (optional).
double	ll
	Logarithm of marginalized data likelihood.
bool	evalll
	If true, the filter will compute likelihood of the data record and store it in `ll` . Set to false if you want to save computational time.

Member Function Documentation

void bdm::KalmanCh::bayes ( const vec & dt ) [virtual]

Here dt = [yt;ut] of appropriate dimensions.

The following equality hold::

$\left[\begin{array}{cc} R^{0.5}\\ P_{t|t-1}^{0.5}C' & P_{t|t-1}^{0.5}CA'\\ & Q^{0.5}\end{array}\right]<\mathrm{orth.oper.}>=\left[\begin{array}{cc} R_{y}^{0.5} & KA'\\ & P_{t+1|t}^{0.5}\\ \\\end{array}\right]$