- Main Page
- Related Pages
- Modules
- Classes
- Files

- File List
- File Members

# libKF.h

Go to the documentation of this file.

    00001
    00013 #ifndef KF_H
    00014 #define KF_H
    00015
    00016
    00017 #include "../stat/libFN.h"
    00018 #include "../stat/libEF.h"
    00019 #include "../math/chmat.h"
    00020
    00021 namespace bdm
    00022 {
    00023
    00028         class KalmanFull
    00029         {
    00030                 protected:
    00031                         int dimx, dimy, dimu;
    00032                         mat A, B, C, D, R, Q;
    00033
    00034                         //cache
    00035                         mat _Pp, _Ry, _iRy, _K;
    00036                 public:
    00037                         //posterior
    00039                         vec mu;
    00041                         mat P;
    00042
    00043                         bool evalll;
    00044                         double ll;
    00045                 public:
    00047                         KalmanFull ( mat A, mat B, mat C, mat D, mat R, mat Q, mat P0, vec mu0 );
    00049                         void bayes ( const vec &dt );
    00051                         friend std::ostream &operator<< ( std::ostream &os, const KalmanFull &kf );
    00053                         KalmanFull() {};
    00054         };
    00055
    00056
    00064         template<class sq_T>
    00065
    00066         class Kalman : public BM
    00067         {
    00068                 protected:
    00070                         RV rvy;
    00072                         RV rvu;
    00074                         int dimx;
    00076                         int dimy;
    00078                         int dimu;
    00080                         mat A;
    00082                         mat B;
    00084                         mat C;
    00086                         mat D;
    00088                         sq_T Q;
    00090                         sq_T R;
    00091
    00093                         enorm<sq_T> est;
    00095                         enorm<sq_T> fy;
    00096
    00098                         mat _K;
    00100                         vec& _yp;
    00102                         sq_T& _Ry;
    00104                         vec& _mu;
    00106                         sq_T& _P;
    00107
    00108                 public:
    00110                         Kalman ( );
    00112                         Kalman ( const Kalman<sq_T> &K0 );
    00114                         void set_parameters ( const mat &A0,const mat &B0,const mat &C0,const mat &D0,const sq_T &Q0,const sq_T &R0 );
    00116                         void set_est ( const vec &mu0, const sq_T &P0 )
    00117                         {
    00118                                 sq_T pom ( dimy );
    00119                                 est.set_parameters ( mu0,P0 );
    00120                                 P0.mult_sym ( C,pom );
    00121                                 fy.set_parameters ( C*mu0, pom );
    00122                         };
    00123
    00125                         void bayes ( const vec &dt );
    00127                         const epdf& posterior() const {return est;}
    00128                         const enorm<sq_T>* _e() const {return &est;}
    00130                         mat& __K() {return _K;}
    00132                         vec _dP() {return _P->getD();}
    00133         };
    00134
    00141         class KalmanCh : public Kalman<chmat>
    00142         {
    00143                 protected:
    00145                         mat preA;
    00147                         mat postA;
    00148
    00149                 public:
    00151                         BM* _copy_() const
    00152                         {
    00153                                 KalmanCh* K=new KalmanCh;
    00154                                 K->set_parameters ( A,B,C,D,Q,R );
    00155                                 K->set_statistics ( _mu,_P );
    00156                                 return K;
    00157                         }
    00159                         void set_parameters ( const mat &A0,const mat &B0,const mat &C0,const mat &D0,const chmat &Q0,const chmat &R0 );
    00160                         void set_statistics ( const vec &mu0, const chmat &P0 )
    00161                         {
    00162                                 est.set_parameters ( mu0,P0 );
    00163                         };
    00164
    00165
    00179                         void bayes ( const vec &dt );
    00180         };
    00181
    00187         class EKFfull : public KalmanFull, public BM
    00188         {
    00189                 protected:
    00191                         diffbifn* pfxu;
    00193                         diffbifn* phxu;
    00194
    00195                         enorm<fsqmat> E;
    00196                 public:
    00198                         EKFfull ( );
    00200                         void set_parameters ( diffbifn* pfxu, diffbifn* phxu, const mat Q0, const mat R0 );
    00202                         void bayes ( const vec &dt );
    00204                         void set_statistics ( vec mu0, mat P0 ) {mu=mu0;P=P0;};
    00206                         const epdf& posterior() const{return E;};
    00207                         const enorm<fsqmat>* _e() const{return &E;};
    00208                         const mat _R() {return P;}
    00209         };
    00210
    00216         template<class sq_T>
    00217         class EKF : public Kalman<fsqmat>
    00218         {
    00220                         diffbifn* pfxu;
    00222                         diffbifn* phxu;
    00223                 public:
    00225                         EKF ( RV rvx, RV rvy, RV rvu );
    00227                         EKF<sq_T>* _copy_() const { return new EKF<sq_T> ( this ); }
    00229                         void set_parameters ( diffbifn* pfxu, diffbifn* phxu, const sq_T Q0, const sq_T R0 );
    00231                         void bayes ( const vec &dt );
    00232         };
    00233
    00240         class EKFCh : public KalmanCh
    00241         {
    00242                 protected:
    00244                         diffbifn* pfxu;
    00246                         diffbifn* phxu;
    00247                 public:
    00249                         BM* _copy_() const
    00250                         {
    00251                                 EKFCh* E=new EKFCh;
    00252                                 E->set_parameters ( pfxu,phxu,Q,R );
    00253                                 E->set_statistics ( _mu,_P );
    00254                                 return E;
    00255                         }
    00257                         void set_parameters ( diffbifn* pfxu, diffbifn* phxu, const chmat Q0, const chmat R0 );
    00259                         void bayes ( const vec &dt );
    00260         };
    00261
    00266         class KFcondQR : public Kalman<ldmat>
    00267         {
    00268 //protected:
    00269                 public:
    00270                         void condition ( const vec &QR )
    00271                         {
    00272                                 it_assert_debug ( QR.length() == ( dimx+dimy ),"KFcondRQ: conditioning by incompatible vector" );
    00273
    00274                                 Q.setD ( QR ( 0, dimx-1 ) );
    00275                                 R.setD ( QR ( dimx, -1 ) );
    00276                         };
    00277         };
    00278
    00283         class KFcondR : public Kalman<ldmat>
    00284         {
    00285 //protected:
    00286                 public:
    00288                         KFcondR ( ) : Kalman<ldmat> ( ) {};
    00289
    00290                         void condition ( const vec &R0 )
    00291                         {
    00292                                 it_assert_debug ( R0.length() == ( dimy ),"KFcondR: conditioning by incompatible vector" );
    00293
    00294                                 R.setD ( R0 );
    00295                         };
    00296
    00297         };
    00298
    00300
    00301         template<class sq_T>
    00302         Kalman<sq_T>::Kalman ( const Kalman<sq_T> &K0 ) : BM ( ),rvy ( K0.rvy ),rvu ( K0.rvu ),
    00303                         dimx ( K0.dimx ), dimy ( K0.dimy ),dimu ( K0.dimu ),
    00304                         A ( K0.A ), B ( K0.B ), C ( K0.C ), D ( K0.D ),
    00305                         Q ( K0.Q ), R ( K0.R ),
    00306                         est ( K0.est ), fy ( K0.fy ), _yp ( fy._mu() ),_Ry ( fy._R() ), _mu ( est._mu() ), _P ( est._R() )
    00307         {
    00308
    00309 // copy values in pointers
    00310 //      _mu = K0._mu;
    00311 //      _P = K0._P;
    00312 //      _yp = K0._yp;
    00313 //      _Ry = K0._Ry;
    00314
    00315         }
    00316
    00317         template<class sq_T>
    00318         Kalman<sq_T>::Kalman ( ) : BM (), est ( ), fy (),  _yp ( fy._mu() ), _Ry ( fy._R() ), _mu ( est._mu() ), _P ( est._R() )
    00319         {
    00320         };
    00321
    00322         template<class sq_T>
    00323         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 )
    00324         {
    00325                 dimx = A0.rows();
    00326                 dimy = C0.rows();
    00327                 dimu = B0.cols();
    00328
    00329                 it_assert_debug ( A0.cols() ==dimx, "Kalman: A is not square" );
    00330                 it_assert_debug ( B0.rows() ==dimx, "Kalman: B is not compatible" );
    00331                 it_assert_debug ( C0.cols() ==dimx, "Kalman: C is not square" );
    00332                 it_assert_debug ( ( D0.rows() ==dimy ) || ( D0.cols() ==dimu ), "Kalman: D is not compatible" );
    00333                 it_assert_debug ( ( R0.cols() ==dimy ) || ( R0.rows() ==dimy ), "Kalman: R is not compatible" );
    00334                 it_assert_debug ( ( Q0.cols() ==dimx ) || ( Q0.rows() ==dimx ), "Kalman: Q is not compatible" );
    00335
    00336                 A = A0;
    00337                 B = B0;
    00338                 C = C0;
    00339                 D = D0;
    00340                 R = R0;
    00341                 Q = Q0;
    00342         }
    00343
    00344         template<class sq_T>
    00345         void Kalman<sq_T>::bayes ( const vec &dt )
    00346         {
    00347                 it_assert_debug ( dt.length() == ( dimy+dimu ),"KalmanFull::bayes wrong size of dt" );
    00348
    00349                 sq_T iRy ( dimy );
    00350                 vec u = dt.get ( dimy,dimy+dimu-1 );
    00351                 vec y = dt.get ( 0,dimy-1 );
    00352                 //Time update
    00353                 _mu = A* _mu + B*u;
    00354                 //P  = A*P*A.transpose() + Q; in sq_T
    00355                 _P.mult_sym ( A );
    00356                 _P  +=Q;
    00357
    00358                 //Data update
    00359                 //_Ry = C*P*C.transpose() + R; in sq_T
    00360                 _P.mult_sym ( C, _Ry );
    00361                 _Ry  +=R;
    00362
    00363                 mat Pfull = _P.to_mat();
    00364
    00365                 _Ry.inv ( iRy ); // result is in _iRy;
    00366                 _K = Pfull*C.transpose() * ( iRy.to_mat() );
    00367
    00368                 sq_T pom ( ( int ) Pfull.rows() );
    00369                 iRy.mult_sym_t ( C*Pfull,pom );
    00370                 ( _P ) -= pom; // P = P -PC'iRy*CP;
    00371                 ( _yp ) = C* _mu  +D*u; //y prediction
    00372                 ( _mu ) += _K* ( y- _yp );
    00373
    00374
    00375                 if ( evalll==true )   //likelihood of observation y
    00376                 {
    00377                         ll=fy.evallog ( y );
    00378                 }
    00379
    00380 //cout << "y: " << y-(*_yp) <<" R: " << _Ry->to_mat() << " iR: " << _iRy->to_mat() << " ll: " << ll <<endl;
    00381
    00382         };
    00383
    00391         class MultiModel: public BM
    00392         {
    00393                 protected:
    00395                         Array<EKFCh*> Models;
    00397                         vec w;
    00399                         vec _lls;
    00401                         int policy;
    00403                         enorm<chmat> est;
    00404                 public:
    00405                         void set_parameters ( Array<EKFCh*> A, int pol0=1 )
    00406                         {
    00407                                 Models=A;//TODO: test if evalll is set
    00408                                 w.set_length ( A.length() );
    00409                                 _lls.set_length ( A.length() );
    00410                                 policy=pol0;
    00411
    00412                                 est.set_rv(RV("MM",A(0)->posterior().dimension(),0));
    00413                                 est.set_parameters(A(0)->_e()->mean(), A(0)->_e()->_R());
    00414                         }
    00415                         void bayes ( const vec &dt )
    00416                         {
    00417                                 int n = Models.length();
    00418                                 int i;
    00419                                 for ( i=0;i<n;i++ )
    00420                                 {
    00421                                         Models ( i )->bayes ( dt );
    00422                                         _lls ( i ) = Models ( i )->_ll();
    00423                                 }
    00424                                 double mlls=max ( _lls );
    00425                                 w=exp ( _lls-mlls );
    00426                                 w/=sum ( w ); //normalization
    00427                                 //set statistics
    00428                                 switch ( policy )
    00429                                 {
    00430                                         case 1:
    00431                                         {
    00432                                                 int mi=max_index ( w );
    00433                                                 const enorm<chmat>* st=(Models(mi)->_e());
    00434                                                 est.set_parameters(st->mean(), st->_R());
    00435                                         }
    00436                                         break;
    00437                                         default: it_error ( "unknown policy" );
    00438                                 }
    00439                                 // copy result to all models
    00440                                 for ( i=0;i<n;i++ )
    00441                                 {
    00442                                                 Models ( i )->set_statistics ( est.mean(),est._R());
    00443                                 }
    00444                         }
    00445                         //all posterior densities are equal => return the first one
    00446                         const enorm<chmat>* _e() const {return &est;}
    00447                                 //all posterior densities are equal => return the first one
    00448                         const enorm<chmat>& posterior() const {return est;}
    00449         };
    00450
    00451
    00452 //TODO why not const pointer??
    00453
    00454         template<class sq_T>
    00455         EKF<sq_T>::EKF ( RV rvx0, RV rvy0, RV rvu0 ) : Kalman<sq_T> ( rvx0,rvy0,rvu0 ) {}
    00456
    00457         template<class sq_T>
    00458         void EKF<sq_T>::set_parameters ( diffbifn* pfxu0,  diffbifn* phxu0,const sq_T Q0,const sq_T R0 )
    00459         {
    00460                 pfxu = pfxu0;
    00461                 phxu = phxu0;
    00462
    00463                 //initialize matrices A C, later, these will be only updated!
    00464                 pfxu->dfdx_cond ( _mu,zeros ( dimu ),A,true );
    00465 //      pfxu->dfdu_cond ( *_mu,zeros ( dimu ),B,true );
    00466                 B.clear();
    00467                 phxu->dfdx_cond ( _mu,zeros ( dimu ),C,true );
    00468 //      phxu->dfdu_cond ( *_mu,zeros ( dimu ),D,true );
    00469                 D.clear();
    00470
    00471                 R = R0;
    00472                 Q = Q0;
    00473         }
    00474
    00475         template<class sq_T>
    00476         void EKF<sq_T>::bayes ( const vec &dt )
    00477         {
    00478                 it_assert_debug ( dt.length() == ( dimy+dimu ),"KalmanFull::bayes wrong size of dt" );
    00479
    00480                 sq_T iRy ( dimy,dimy );
    00481                 vec u = dt.get ( dimy,dimy+dimu-1 );
    00482                 vec y = dt.get ( 0,dimy-1 );
    00483                 //Time update
    00484                 _mu = pfxu->eval ( _mu, u );
    00485                 pfxu->dfdx_cond ( _mu,u,A,false ); //update A by a derivative of fx
    00486
    00487                 //P  = A*P*A.transpose() + Q; in sq_T
    00488                 _P.mult_sym ( A );
    00489                 _P +=Q;
    00490
    00491                 //Data update
    00492                 phxu->dfdx_cond ( _mu,u,C,false ); //update C by a derivative hx
    00493                 //_Ry = C*P*C.transpose() + R; in sq_T
    00494                 _P.mult_sym ( C, _Ry );
    00495                 ( _Ry ) +=R;
    00496
    00497                 mat Pfull = _P.to_mat();
    00498
    00499                 _Ry.inv ( iRy ); // result is in _iRy;
    00500                 _K = Pfull*C.transpose() * ( iRy.to_mat() );
    00501
    00502                 sq_T pom ( ( int ) Pfull.rows() );
    00503                 iRy.mult_sym_t ( C*Pfull,pom );
    00504                 ( _P ) -= pom; // P = P -PC'iRy*CP;
    00505                 _yp = phxu->eval ( _mu,u ); //y prediction
    00506                 ( _mu ) += _K* ( y-_yp );
    00507
    00508                 if ( evalll==true ) {ll+=fy.evallog ( y );}
    00509         };
    00510
    00511
    00512 }
    00513 #endif // KF_H
    00514
    00515