bdm::KalmanCh Class Reference

Kalman filter in square root form. More...

#include <kalman.h>

Public Member Functions
BM *	_copy_ () const
	copy constructor
void	set_parameters (const mat &A0, const mat &B0, const mat &C0, const mat &D0, const chmat &Q0, const chmat &R0)
	set parameters for adapt from Kalman
void	initialize ()
	initialize internal parametetrs
void	bayes (const vec &dt)
	Here dt = [yt;ut] of appropriate dimensions.
void	from_setting (const Setting &set)
	load basic elements of Kalman from structure
void	set_statistics (const vec &mu0, const mat &P0)
void	set_statistics (const vec &mu0, const chmat &P0)
const enorm< chmat > &	posterior () const
	posterior
shared_ptr< epdf >	shared_posterior ()
	shared posterior
void	validate ()
virtual string	to_string ()
	This method returns a basic info about the current instance.
virtual void	to_setting (Setting &set) const
	This method save all the instance properties into the Setting structure.
int	_dimx ()
	access function
int	_dimy ()
	access function
int	_dimu ()
	access function
const mat &	_A () const
	access function
const mat &	_B () const
	access function
const mat &	_C () const
	access function
const mat &	_D () const
	access function
const chmat &	_Q () const
	access function
const chmat &	_R () const
	access function
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 conditional density of 1-step ahead predictor $f(d_{t+1} \|d_{t+h-1}, \ldots d_{t})$ .
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
RV	yrv
	id of output
RV	urv
	id of input
mat	_K
	Kalman gain.
shared_ptr< enorm< chmat > >	est
	posterior
enorm< chmat >	fy
	marginal on data f(y\|y)
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.
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.
Internal storage - needs initialize()
pre array (triangular matrix)
mat	preA
mat	postA
	post array (triangular matrix)
Extension to conditional BM
This extension is useful e.g. in Marginalized Particle Filter (bdm::MPF). Alternatively, it can be used for automated connection to DS when the condition is observed
const RV &	_rvc () const
	access function
virtual void	condition (const vec &val)
	Substitute `val` for `rvc`.
RV	rvc
	Name of extension variable.
Logging of results

virtual void	set_options (const string &opt)
	Set boolean options from a string, recognized are: "logbounds,logll".
virtual void	log_add (logger &L, const string &name="")
	Add all logged variables to a logger.
virtual void	logit (logger &L)
ivec	LIDs
	IDs of storages in loggers 4:[1=mean,2=lb,3=ub,4=ll].
ivec	LFlags
	Flags for logging - same size as LIDs, each entry correspond to the same in LIDs.

Detailed Description

Kalman filter in square root form.

Trivial example:

#include "estim/kalman.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;
}

Complete constructor:

Member Function Documentation

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

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

The following equality hold::

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