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# work/mixpp/bdm/estim/libKF.h

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    00001
    00013 #ifndef KF_H
    00014 #define KF_H
    00015
    00016 #include <itpp/itbase.h>
    00017 #include "../stat/libFN.h"
    00018 #include "../stat/libEF.h"
    00019 #include "../math/chmat.h"
    00020
    00021 using namespace itpp;
    00022
    00027 class KalmanFull {
    00028         int dimx, dimy, dimu;
    00029         mat A, B, C, D, R, Q;
    00030
    00031         //cache
    00032         mat _Pp, _Ry, _iRy, _K;
    00033 public:
    00034         //posterior
    00036         vec mu;
    00038         mat P;
    00039
    00040 public:
    00042         KalmanFull ( mat A, mat B, mat C, mat D, mat R, mat Q, mat P0, vec mu0 );
    00044         void bayes ( const vec &dt );
    00046         friend std::ostream &operator<< ( std::ostream &os, const KalmanFull &kf );
    00047
    00048 };
    00049
    00050
    00058 template<class sq_T>
    00059
    00060 class Kalman : public BM {
    00061 protected:
    00063         RV rvy;
    00065         RV rvu;
    00067         int dimx;
    00069         int dimy;
    00071         int dimu;
    00073         mat A;
    00075         mat B;
    00077         mat C;
    00079         mat D;
    00081         sq_T Q;
    00083         sq_T R;
    00084
    00086         enorm<sq_T> est;
    00088         enorm<sq_T> fy;
    00089
    00091         mat _K;
    00093         vec* _yp;
    00095         sq_T* _Ry;
    00097         sq_T* _iRy;
    00099         vec* _mu;
    00101         sq_T* _P;
    00103         sq_T* _iP;
    00104
    00105 public:
    00107         Kalman ( RV rvx0, RV rvy0, RV rvu0 );
    00109         Kalman ( const Kalman<sq_T> &K0 );
    00111         void set_parameters ( const mat &A0,const mat &B0,const mat &C0,const mat &D0,const sq_T &R0,const sq_T &Q0 );
    00113         void set_est ( const vec &mu0, const sq_T &P0 ) {
    00114                 sq_T pom(dimy);
    00115                 est.set_parameters ( mu0,P0 );
    00116                 P0.mult_sym(C,pom);
    00117                 fy.set_parameters ( C*mu0, pom );
    00118         };
    00119
    00121         void bayes ( const vec &dt );
    00123         epdf& _epdf() {return est;}
    00124 };
    00125
    00128 class KalmanCh : public BM{
    00129 protected:
    00131         RV rvy;
    00133         RV rvu;
    00135         int dimx;
    00137         int dimy;
    00139         int dimu;
    00141         mat A;
    00143         mat B;
    00145         mat C;
    00147         mat D;
    00149         chmat Q;
    00151         chmat R;
    00152
    00154 mat preA;
    00156 mat postA;
    00157
    00159         enorm<chmat> pred;
    00161         enorm<chmat> fy;
    00162
    00163 vec* _mu;
    00164 chmat* _P;
    00165 vec* _yp;
    00166 chmat* _Ry;
    00167
    00168 public:
    00170         KalmanCh ( RV rvx0, RV rvy0, RV rvu0 );
    00172         KalmanCh ( const KalmanCh &K0 );
    00174         void set_parameters ( const mat &A0,const mat &B0,const mat &C0,const mat &D0,const chmat &R0,const chmat &Q0 );
    00176         void set_pred ( const vec &mu0, const chmat &P0 ) {
    00177                 pred.set_parameters ( mu0,P0 );
    00178         };
    00179
    00190         void bayes ( const vec &dt );
    00192         epdf& _epdf() {it_warning("this is predictor, not estimator");return pred;}
    00194         epdf& _pred() {return pred;}
    00195 };
    00196
    00202 template<class sq_T>
    00203 class EKF : public Kalman<ldmat> {
    00205         diffbifn* pfxu;
    00207         diffbifn* phxu;
    00208 public:
    00210         EKF ( RV rvx, RV rvy, RV rvu );
    00212         void set_parameters ( diffbifn* pfxu, diffbifn* phxu, const sq_T Q0, const sq_T R0 );
    00214         void bayes ( const vec &dt );
    00215 };
    00216
    00221 class KFcondQR : public Kalman<ldmat>, public BMcond {
    00222 //protected:
    00223 public:
    00225         KFcondQR ( RV rvx, RV rvy, RV rvu, RV rvRQ ) : Kalman<ldmat> ( rvx, rvy,rvu ),BMcond ( rvRQ ) {};
    00226
    00227         void condition ( const vec &RQ );
    00228 };
    00229
    00234 class KFcondR : public Kalman<ldmat>, public BMcond {
    00235 //protected:
    00236 public:
    00238         KFcondR ( RV rvx, RV rvy, RV rvu, RV rvR ) : Kalman<ldmat> ( rvx, rvy,rvu ),BMcond ( rvR ) {};
    00239
    00240         void condition ( const vec &R );
    00241 };
    00242
    00244
    00245 template<class sq_T>
    00246 Kalman<sq_T>::Kalman ( const Kalman<sq_T> &K0 ) : BM ( K0.rv ),rvy ( K0.rvy ),rvu ( K0.rvu ),
    00247                 dimx ( rv.count() ), dimy ( rvy.count() ),dimu ( rvu.count() ),
    00248                 A ( dimx,dimx ), B ( dimx,dimu ), C ( dimy,dimx ), D ( dimy,dimu ),est ( rv ), fy ( rvy ) {
    00249
    00250         this->set_parameters ( K0.A, K0.B, K0.C, K0.D, K0.R, K0.Q );
    00251
    00252 //establish pointers
    00253         _mu = est._mu();
    00254         est._R ( _P,_iP );
    00255
    00256 //fy
    00257         _yp = fy._mu();
    00258         fy._R ( _Ry,_iRy );
    00259
    00260 // copy values in pointers
    00261         *_mu = *K0._mu;
    00262         *_P = *K0._P;
    00263         *_iP = *K0._iP;
    00264         *_yp = *K0._yp;
    00265         *_iRy = *K0._iRy;
    00266         *_Ry = *K0._Ry;
    00267
    00268 }
    00269
    00270 template<class sq_T>
    00271 Kalman<sq_T>::Kalman ( RV rvx, RV rvy0, RV rvu0 ) : BM ( rvx ),rvy ( rvy0 ),rvu ( rvu0 ),
    00272                 dimx ( rvx.count() ), dimy ( rvy.count() ),dimu ( rvu.count() ),
    00273                 A ( dimx,dimx ), B ( dimx,dimu ), C ( dimy,dimx ), D ( dimy,dimu ),
    00274                 Q(dimx), R (dimy),
    00275                 est ( rvx ), fy ( rvy ) {
    00276 //assign cache
    00277 //est
    00278         _mu = est._mu();
    00279         est._R ( _P,_iP );
    00280
    00281 //fy
    00282         _yp = fy._mu();
    00283         fy._R ( _Ry,_iRy );
    00284 };
    00285
    00286 template<class sq_T>
    00287 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 ) {
    00288         it_assert_debug ( A0.cols() ==dimx, "Kalman: A is not square" );
    00289         it_assert_debug ( B0.rows() ==dimx, "Kalman: B is not compatible" );
    00290         it_assert_debug ( C0.cols() ==dimx, "Kalman: C is not square" );
    00291         it_assert_debug ( ( D0.rows() ==dimy ) || ( D0.cols() ==dimu ), "Kalman: D is not compatible" );
    00292         it_assert_debug ( ( R0.cols() ==dimy ) || ( R0.rows() ==dimy ), "Kalman: R is not compatible" );
    00293         it_assert_debug ( ( Q0.cols() ==dimx ) || ( Q0.rows() ==dimx ), "Kalman: Q is not compatible" );
    00294
    00295         A = A0;
    00296         B = B0;
    00297         C = C0;
    00298         D = D0;
    00299         R = R0;
    00300         Q = Q0;
    00301 }
    00302
    00303 template<class sq_T>
    00304 void Kalman<sq_T>::bayes ( const vec &dt ) {
    00305         it_assert_debug ( dt.length() == ( dimy+dimu ),"KalmanFull::bayes wrong size of dt" );
    00306
    00307         vec u = dt.get ( dimy,dimy+dimu-1 );
    00308         vec y = dt.get ( 0,dimy-1 );
    00309         //Time update
    00310         *_mu = A* ( *_mu ) + B*u;
    00311         //P  = A*P*A.transpose() + Q; in sq_T
    00312         _P->mult_sym ( A );
    00313         ( *_P ) +=Q;
    00314
    00315         //Data update
    00316         //_Ry = C*P*C.transpose() + R; in sq_T
    00317         _P->mult_sym ( C, *_Ry );
    00318         ( *_Ry ) +=R;
    00319
    00320         mat Pfull = _P->to_mat();
    00321
    00322         _Ry->inv ( *_iRy ); // result is in _iRy;
    00323         fy._cached ( true );
    00324         _K = Pfull*C.transpose() * ( _iRy->to_mat() );
    00325
    00326         sq_T pom ( ( int ) Pfull.rows() );
    00327         _iRy->mult_sym_t ( C*Pfull,pom );
    00328         ( *_P ) -= pom; // P = P -PC'iRy*CP;
    00329         ( *_yp ) = C* ( *_mu ) +D*u; //y prediction
    00330         ( *_mu ) += _K* ( y- ( *_yp ) );
    00331
    00332
    00333         if ( evalll==true ) { //likelihood of observation y
    00334                 ll=fy.evalpdflog ( y );
    00335         }
    00336
    00337 //cout << "y: " << y-(*_yp) <<" R: " << _Ry->to_mat() << " iR: " << _iRy->to_mat() << " ll: " << ll <<endl;
    00338
    00339 };
    00340
    00341 //TODO why not const pointer??
    00342
    00343 template<class sq_T>
    00344 EKF<sq_T>::EKF ( RV rvx0, RV rvy0, RV rvu0 ) : Kalman<ldmat> ( rvx0,rvy0,rvu0 ) {}
    00345
    00346 template<class sq_T>
    00347 void EKF<sq_T>::set_parameters ( diffbifn* pfxu0,  diffbifn* phxu0,const sq_T Q0,const sq_T R0 ) {
    00348         pfxu = pfxu0;
    00349         phxu = phxu0;
    00350
    00351         //initialize matrices A C, later, these will be only updated!
    00352         pfxu->dfdx_cond ( *_mu,zeros ( dimu ),A,true );
    00353 //      pfxu->dfdu_cond ( *_mu,zeros ( dimu ),B,true );
    00354         B.clear();
    00355         phxu->dfdx_cond ( *_mu,zeros ( dimu ),C,true );
    00356 //      phxu->dfdu_cond ( *_mu,zeros ( dimu ),D,true );
    00357         D.clear();
    00358
    00359         R = R0;
    00360         Q = Q0;
    00361 }
    00362
    00363 template<class sq_T>
    00364 void EKF<sq_T>::bayes ( const vec &dt ) {
    00365         it_assert_debug ( dt.length() == ( dimy+dimu ),"KalmanFull::bayes wrong size of dt" );
    00366
    00367         vec u = dt.get ( dimy,dimy+dimu-1 );
    00368         vec y = dt.get ( 0,dimy-1 );
    00369         //Time update
    00370         *_mu = pfxu->eval ( *_mu, u );
    00371         pfxu->dfdx_cond ( *_mu,u,A,false ); //update A by a derivative of fx
    00372
    00373         //P  = A*P*A.transpose() + Q; in sq_T
    00374         _P->mult_sym ( A );
    00375         ( *_P ) +=Q;
    00376
    00377         //Data update
    00378         phxu->dfdx_cond ( *_mu,u,C,false ); //update C by a derivative hx
    00379         //_Ry = C*P*C.transpose() + R; in sq_T
    00380         _P->mult_sym ( C, *_Ry );
    00381         ( *_Ry ) +=R;
    00382
    00383         mat Pfull = _P->to_mat();
    00384
    00385         _Ry->inv ( *_iRy ); // result is in _iRy;
    00386         fy._cached ( true );
    00387         _K = Pfull*C.transpose() * ( _iRy->to_mat() );
    00388
    00389         sq_T pom ( ( int ) Pfull.rows() );
    00390         _iRy->mult_sym_t ( C*Pfull,pom );
    00391         ( *_P ) -= pom; // P = P -PC'iRy*CP;
    00392         *_yp = phxu->eval ( *_mu,u ); //y prediction
    00393         ( *_mu ) += _K* ( y-*_yp );
    00394
    00395         if ( evalll==true ) {ll+=fy.evalpdflog ( y );}
    00396 };
    00397
    00398
    00399 #endif // KF_H
    00400
    00401