root/bdm/estim/libKF.h @ 51

/*!
  \file
  \brief Bayesian Filtering for linear Gaussian models (Kalman Filter) and extensions
  \author Vaclav Smidl.

  -----------------------------------
  BDM++ - C++ library for Bayesian Decision Making under Uncertainty

  Using IT++ for numerical operations
  -----------------------------------
*/

#ifndef KF_H
#define KF_H

#include <itpp/itbase.h>
#include "../stat/libFN.h"
#include "../stat/libEF.h"
#include "../math/chmat.h"

using namespace itpp;

/*!
* \brief Basic Kalman filter with full matrices (education purpose only)! Will be deleted soon!
*/

class KalmanFull {
        int dimx, dimy, dimu;
        mat A, B, C, D, R, Q;

        //cache
        mat _Pp, _Ry, _iRy, _K;
public:
        //posterior
        //! Mean value of the posterior density
        vec mu;
        //! Variance of the posterior density
        mat P;

        bool evalll;
        double ll;
public:
        //! Full constructor
        KalmanFull ( mat A, mat B, mat C, mat D, mat R, mat Q, mat P0, vec mu0 );
        //! Here dt = [yt;ut] of appropriate dimensions
        void bayes ( const vec &dt );
        //! print elements of KF
        friend std::ostream &operator<< ( std::ostream &os, const KalmanFull &kf );

};


/*!
* \brief Kalman filter with covariance matrices in square root form.

Parameter evolution model:\f[ x_t = A x_{t-1} + B u_t + Q^{1/2} e_t \f] 
Observation model: \f[ y_t = C x_{t-1} + C u_t + Q^{1/2} w_t. \f]
Where $e_t$ and $w_t$ are independent vectors Normal(0,1)-distributed disturbances. 
*/
template<class sq_T>

class Kalman : public BM {
protected:
        //! Indetifier of output rv
        RV rvy;
        //! Indetifier of exogeneous rv
        RV rvu;
        //! cache of rv.count()
        int dimx;
        //! cache of rvy.count()
        int dimy;
        //! cache of rvu.count()
        int dimu;
        //! Matrix A
        mat A;
        //! Matrix B
        mat B; 
        //! Matrix C
        mat C;
        //! Matrix D
        mat D;
        //! Matrix Q in square-root form
        sq_T Q;
        //! Matrix R in square-root form
        sq_T R;

        //!posterior density on $x_t$
        enorm<sq_T> est;
        //!preditive density on $y_t$
        enorm<sq_T> fy;

        //! placeholder for Kalman gain
        mat _K;
        //! cache of fy.mu
        vec* _yp;
        //! cache of fy.R
        sq_T* _Ry;
        //! cache of fy.iR
        sq_T* _iRy;
        //!cache of est.mu
        vec* _mu;
        //!cache of est.R
        sq_T* _P;
        //!cache of est.iR
        sq_T* _iP;

public:
        //! Default constructor
        Kalman ( RV rvx0, RV rvy0, RV rvu0 );
        //! Copy constructor
        Kalman ( const Kalman<sq_T> &K0 );
        //! Set parameters with check of relevance
        void set_parameters ( const mat &A0,const mat &B0,const mat &C0,const mat &D0,const sq_T &R0,const sq_T &Q0 );
        //! Set estimate values, used e.g. in initialization.
        void set_est ( const vec &mu0, const sq_T &P0 ) {
                sq_T pom(dimy);
                est.set_parameters ( mu0,P0 );
                P0.mult_sym(C,pom);
                fy.set_parameters ( C*mu0, pom );
        };

        //! Here dt = [yt;ut] of appropriate dimensions
        void bayes ( const vec &dt );
        //!access function
        epdf& _epdf() {return est;}
        //!access function
        mat& __K() {return _K;}
        //!access function
        vec _dP() {return _P->getD();}
};

/*! \brief Kalman filter in square root form
*/
class KalmanCh : public Kalman<chmat>{
protected:
//! pre array (triangular matrix)
mat preA;
//! post array (triangular matrix)
mat postA;

public:
        //! Default constructor
        KalmanCh ( RV rvx0, RV rvy0, RV rvu0 ):Kalman<chmat>(rvx0,rvy0,rvu0),preA(dimy+dimx+dimx,dimy+dimx),postA(dimy+dimx,dimy+dimx){};
        //! Set parameters with check of relevance
        void set_parameters ( const mat &A0,const mat &B0,const mat &C0,const mat &D0,const chmat &R0,const chmat &Q0 );
        void set_est ( const vec &mu0, const chmat &P0 ) {
                est.set_parameters ( mu0,P0 );
        };
        
        
        /*!\brief  Here dt = [yt;ut] of appropriate dimensions
        
        The following equality hold::\f[
\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]\f]

Thus this objevt evaluates only predictors! Not filtering densities.
        */
        void bayes ( const vec &dt );
};

/*!
\brief Extended Kalman Filter

An approximation of the exact Bayesian filter with Gaussian noices and non-linear evolutions of their mean.
*/
template<class sq_T>
class EKF : public Kalman<fsqmat> {
        //! Internal Model f(x,u)
        diffbifn* pfxu;
        //! Observation Model h(x,u)
        diffbifn* phxu;
public:
        //! Default constructor
        EKF ( RV rvx, RV rvy, RV rvu );
        //! Set nonlinear functions for mean values and covariance matrices.
        void set_parameters ( diffbifn* pfxu, diffbifn* phxu, const sq_T Q0, const sq_T R0 );
        //! Here dt = [yt;ut] of appropriate dimensions
        void bayes ( const vec &dt );
};

/*!
\brief Extended Kalman Filter in Square roor

An approximation of the exact Bayesian filter with Gaussian noices and non-linear evolutions of their mean.
*/

class EKFCh : public KalmanCh {
        //! Internal Model f(x,u)
        diffbifn* pfxu;
        //! Observation Model h(x,u)
        diffbifn* phxu;
public:
        //! Default constructor
        EKFCh ( RV rvx, RV rvy, RV rvu );
        //! Set nonlinear functions for mean values and covariance matrices.
        void set_parameters ( diffbifn* pfxu, diffbifn* phxu, const chmat Q0, const chmat R0 );
        //! Here dt = [yt;ut] of appropriate dimensions
        void bayes ( const vec &dt );
};

/*!
\brief Kalman Filter with conditional diagonal matrices R and Q.
*/

class KFcondQR : public Kalman<ldmat>, public BMcond {
//protected:
public:
        //!Default constructor
        KFcondQR ( RV rvx, RV rvy, RV rvu, RV rvRQ ) : Kalman<ldmat> ( rvx, rvy,rvu ),BMcond ( rvRQ ) {};

        void condition ( const vec &RQ );
};

/*!
\brief Kalman Filter with conditional diagonal matrices R and Q.
*/

class KFcondR : public Kalman<ldmat>, public BMcond {
//protected:
public:
        //!Default constructor
        KFcondR ( RV rvx, RV rvy, RV rvu, RV rvR ) : Kalman<ldmat> ( rvx, rvy,rvu ),BMcond ( rvR ) {};

        void condition ( const vec &R );
};

//////// INstance

template<class sq_T>
Kalman<sq_T>::Kalman ( const Kalman<sq_T> &K0 ) : BM ( K0.rv ),rvy ( K0.rvy ),rvu ( K0.rvu ),
                dimx ( rv.count() ), dimy ( rvy.count() ),dimu ( rvu.count() ),
                A ( dimx,dimx ), B ( dimx,dimu ), C ( dimy,dimx ), D ( dimy,dimu ),
                Q(dimx), R(dimy),
                est ( rv ), fy ( rvy ) {

        this->set_parameters ( K0.A, K0.B, K0.C, K0.D, K0.R, K0.Q );

//establish pointers
        _mu = est._mu();
        est._R ( _P,_iP );

//fy
        _yp = fy._mu();
        fy._R ( _Ry,_iRy );

// copy values in pointers
        *_mu = *K0._mu;
        *_P = *K0._P;
        *_iP = *K0._iP;
        *_yp = *K0._yp;
        *_iRy = *K0._iRy;
        *_Ry = *K0._Ry;

}

template<class sq_T>
Kalman<sq_T>::Kalman ( RV rvx, RV rvy0, RV rvu0 ) : BM ( rvx ),rvy ( rvy0 ),rvu ( rvu0 ),
                dimx ( rvx.count() ), dimy ( rvy.count() ),dimu ( rvu.count() ),
                A ( dimx,dimx ), B ( dimx,dimu ), C ( dimy,dimx ), D ( dimy,dimu ),
                Q(dimx), R (dimy),
                est ( rvx ), fy ( rvy ) {
//assign cache
//est
        _mu = est._mu();
        est._R ( _P,_iP );

//fy
        _yp = fy._mu();
        fy._R ( _Ry,_iRy );
};

template<class sq_T>
void Kalman<sq_T>::set_parameters ( const mat &A0,const  mat &B0, const mat &C0, const mat &D0, const sq_T &R0, const sq_T &Q0 ) {
        it_assert_debug ( A0.cols() ==dimx, "Kalman: A is not square" );
        it_assert_debug ( B0.rows() ==dimx, "Kalman: B is not compatible" );
        it_assert_debug ( C0.cols() ==dimx, "Kalman: C is not square" );
        it_assert_debug ( ( D0.rows() ==dimy ) || ( D0.cols() ==dimu ), "Kalman: D is not compatible" );
        it_assert_debug ( ( R0.cols() ==dimy ) || ( R0.rows() ==dimy ), "Kalman: R is not compatible" );
        it_assert_debug ( ( Q0.cols() ==dimx ) || ( Q0.rows() ==dimx ), "Kalman: Q is not compatible" );

        A = A0;
        B = B0;
        C = C0;
        D = D0;
        R = R0;
        Q = Q0;
}

template<class sq_T>
void Kalman<sq_T>::bayes ( const vec &dt ) {
        it_assert_debug ( dt.length() == ( dimy+dimu ),"KalmanFull::bayes wrong size of dt" );

        vec u = dt.get ( dimy,dimy+dimu-1 );
        vec y = dt.get ( 0,dimy-1 );
        //Time update
        *_mu = A* ( *_mu ) + B*u;
        //P  = A*P*A.transpose() + Q; in sq_T
        _P->mult_sym ( A );
        ( *_P ) +=Q;

        //Data update
        //_Ry = C*P*C.transpose() + R; in sq_T
        _P->mult_sym ( C, *_Ry );
        ( *_Ry ) +=R;

        mat Pfull = _P->to_mat();

        _Ry->inv ( *_iRy ); // result is in _iRy;
        fy._cached ( true );
        _K = Pfull*C.transpose() * ( _iRy->to_mat() );

        sq_T pom ( ( int ) Pfull.rows() );
        _iRy->mult_sym_t ( C*Pfull,pom );
        ( *_P ) -= pom; // P = P -PC'iRy*CP;
        ( *_yp ) = C* ( *_mu ) +D*u; //y prediction
        ( *_mu ) += _K* ( y- ( *_yp ) );


        if ( evalll==true ) { //likelihood of observation y
                ll=fy.evalpdflog ( y );
        }

//cout << "y: " << y-(*_yp) <<" R: " << _Ry->to_mat() << " iR: " << _iRy->to_mat() << " ll: " << ll <<endl;

};

//TODO why not const pointer??

template<class sq_T>
EKF<sq_T>::EKF ( RV rvx0, RV rvy0, RV rvu0 ) : Kalman<sq_T> ( rvx0,rvy0,rvu0 ) {}

template<class sq_T>
void EKF<sq_T>::set_parameters ( diffbifn* pfxu0,  diffbifn* phxu0,const sq_T Q0,const sq_T R0 ) {
        pfxu = pfxu0;
        phxu = phxu0;

        //initialize matrices A C, later, these will be only updated!
        pfxu->dfdx_cond ( *_mu,zeros ( dimu ),A,true );
//      pfxu->dfdu_cond ( *_mu,zeros ( dimu ),B,true );
        B.clear();
        phxu->dfdx_cond ( *_mu,zeros ( dimu ),C,true );
//      phxu->dfdu_cond ( *_mu,zeros ( dimu ),D,true );
        D.clear();

        R = R0;
        Q = Q0;
}

template<class sq_T>
void EKF<sq_T>::bayes ( const vec &dt ) {
        it_assert_debug ( dt.length() == ( dimy+dimu ),"KalmanFull::bayes wrong size of dt" );

        vec u = dt.get ( dimy,dimy+dimu-1 );
        vec y = dt.get ( 0,dimy-1 );
        //Time update
        *_mu = pfxu->eval ( *_mu, u );
        pfxu->dfdx_cond ( *_mu,u,A,false ); //update A by a derivative of fx

        //P  = A*P*A.transpose() + Q; in sq_T
        _P->mult_sym ( A );
        ( *_P ) +=Q;

        //Data update
        phxu->dfdx_cond ( *_mu,u,C,false ); //update C by a derivative hx
        //_Ry = C*P*C.transpose() + R; in sq_T
        _P->mult_sym ( C, *_Ry );
        ( *_Ry ) +=R;

        mat Pfull = _P->to_mat();

        _Ry->inv ( *_iRy ); // result is in _iRy;
        fy._cached ( true );
        _K = Pfull*C.transpose() * ( _iRy->to_mat() );

        sq_T pom ( ( int ) Pfull.rows() );
        _iRy->mult_sym_t ( C*Pfull,pom );
        ( *_P ) -= pom; // P = P -PC'iRy*CP;
        *_yp = phxu->eval ( *_mu,u ); //y prediction
        ( *_mu ) += _K* ( y-*_yp );

        if ( evalll==true ) {ll+=fy.evalpdflog ( y );}
};


#endif // KF_H