root/bdm/estim/libKF.h @ 283

/*!
  \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 "../stat/libFN.h"
#include "../stat/libEF.h"
#include "../math/chmat.h"

namespace bdm {

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

class KalmanFull {
protected:
        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 );
        //! For EKFfull;
        KalmanFull() {};
};


/*!
* \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 est.mu
        vec& _mu;
        //!cache of est.R
        sq_T& _P;

public:
        //! Default constructor
        Kalman ( );
        //! 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 &Q0,const sq_T &R0 );
        //! 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
        const epdf& posterior() const {return est;}
        const enorm<sq_T>* _e() const {return &est;}
        //!access function
        mat& __K() {return _K;}
        //!access function
        vec _dP() {return _P->getD();}
};

/*! \brief Kalman filter in square root form

Trivial example:
\include kalman_simple.cpp

*/
class KalmanCh : public Kalman<chmat> {
protected:
//! pre array (triangular matrix)
        mat preA;
//! post array (triangular matrix)
        mat postA;

public:
        //! copy constructor
        BM* _copy_() const {
                KalmanCh* K=new KalmanCh;
                K->set_parameters ( A,B,C,D,Q,R );
                K->set_statistics ( _mu,_P );
                return K;
        }
        //! Set parameters with check of relevance
        void set_parameters ( const mat &A0,const mat &B0,const mat &C0,const mat &D0,const chmat &Q0,const chmat &R0 );
        void set_statistics ( 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 object evaluates only predictors! Not filtering densities.
        */
        void bayes ( const vec &dt );
};

/*!
\brief Extended Kalman Filter in full matrices

An approximation of the exact Bayesian filter with Gaussian noices and non-linear evolutions of their mean.
*/
class EKFfull : public KalmanFull, public BM {

        //! Internal Model f(x,u)
        diffbifn* pfxu;
        //! Observation Model h(x,u)
        diffbifn* phxu;

        enorm<fsqmat> E;
public:
        //! Default constructor
        EKFfull ( );
        //! Set nonlinear functions for mean values and covariance matrices.
        void set_parameters ( diffbifn* pfxu, diffbifn* phxu, const mat Q0, const mat R0 );
        //! Here dt = [yt;ut] of appropriate dimensions
        void bayes ( const vec &dt );
        //! set estimates
        void set_est ( vec mu0, mat P0 ) {mu=mu0;P=P0;};
        //!dummy!
        const epdf& posterior() const{return E;};
        const enorm<fsqmat>* _e() const{return &E;};
        const mat _R() {return P;}
};

/*!
\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 );
        //! copy constructor
        EKF<sq_T>* _copy_() const { return new EKF<sq_T>(this); }
        //! 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 root

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

class EKFCh : public KalmanCh {
protected:
        //! Internal Model f(x,u)
        diffbifn* pfxu;
        //! Observation Model h(x,u)
        diffbifn* phxu;
public:
        //! copy constructor duplicated - calls different set_parameters
        BM* _copy_() const {
                EKFCh* E=new EKFCh;
                E->set_parameters ( pfxu,phxu,Q,R );
                E->set_statistics ( _mu,_P );
                return E;
        }
        //! 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> {
//protected:
public:
        void condition ( const vec &QR ) {
                it_assert_debug ( QR.length() == ( dimx+dimy ),"KFcondRQ: conditioning by incompatible vector" );

                Q.setD ( QR ( 0, dimx-1 ) );
                R.setD ( QR ( dimx, -1 ) );
        };
};

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

class KFcondR : public Kalman<ldmat> {
//protected:
public:
        //!Default constructor
        KFcondR ( ) : Kalman<ldmat> ( ) {};

        void condition ( const vec &R0 ) {
                it_assert_debug ( R0.length() == ( dimy ),"KFcondR: conditioning by incompatible vector" );

                R.setD ( R0 );
        };

};

//////// INstance

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

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

}

template<class sq_T>
Kalman<sq_T>::Kalman ( ) : BM (), est ( ), fy (),  _yp ( fy._mu() ), _Ry ( fy._R() ), _mu ( est._mu() ), _P ( est._R() ) {
};

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 &Q0, const sq_T &R0 ) {
        dimx = A0.rows();
        dimy = C0.rows();
        dimu = B0.cols();

        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" );

        sq_T iRy ( dimy );
        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;
        _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.evallog ( 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" );

        sq_T iRy ( dimy,dimy );
        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;
        _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.evallog ( y );}
};


}
#endif // KF_H