# bdm::KalmanCh Class Reference

Kalman filter in square root form. More...

## 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:

`#include <kalman.h>`

List of all members.

## 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 .
virtual mpdf * | predictor () const
| Constructs conditional density of 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
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.

## Member Function Documentation

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

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

The following equality hold::

Thus this object evaluates only predictors! Not filtering densities.

Implements bdm::BM.

Reimplemented in bdm::EKFCh.

References bdm::chmat::_Ch(), bdm::Kalman< chmat >::_K, bdm::StateSpace< chmat >::A, bdm::StateSpace< chmat >::B, bdm_warning, bdm::StateSpace< chmat >::C, bdm::StateSpace< chmat >::D, bdm::StateSpace< chmat >::dimu, bdm::StateSpace< chmat >::dimx, bdm::StateSpace< chmat >::dimy, bdm::Kalman< chmat >::est, bdm::BM::evalll, bdm::eEF::evallog(), bdm::Kalman< chmat >::fy, bdm::BM::ll, and postA.

virtual double bdm::BM::logpred | ( | const vec & | dt | ) | const`[inline, virtual, inherited]`

Evaluates predictive log-likelihood of the given data record I.e. marginal likelihood of the data with the posterior integrated out.

Reimplemented in bdm::ARX, bdm::MixEF, and bdm::multiBM.

References bdm_error.

Referenced by bdm::BM::logpred_m().

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

- kalman.h
- kalman.cpp