[262] | 1 | |
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[384] | 2 | #include "kalman.h" |
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[7] | 3 | |
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[477] | 4 | namespace bdm { |
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[7] | 5 | |
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| 6 | using std::endl; |
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| 7 | |
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| 8 | |
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| 9 | |
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[679] | 10 | void KalmanFull::bayes ( const vec &yt, const vec &cond ) { |
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[1064] | 11 | bdm_assert_debug ( yt.length() == ( dimy ), "KalmanFull::bayes wrong size of dt, " + |
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| 12 | num2str(yt.length()) + ", expected size is " + num2str(dimy) ); |
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| 13 | bdm_assert_debug ( cond.length() == ( dimc ), "KalmanFull::bayes wrong size of cond, " + |
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| 14 | num2str(cond.length()) + ", expected size is " + num2str(dimc) ); |
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[737] | 15 | |
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[1064] | 16 | const vec &u = cond; // in this case cond=ut |
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| 17 | const vec &y = yt; |
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[7] | 18 | |
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[1064] | 19 | vec& mu = est._mu(); |
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| 20 | mat &P = est._R(); |
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| 21 | mat& _Ry = fy._R(); |
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| 22 | vec& yp = fy._mu(); |
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| 23 | //Time update |
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| 24 | mu = A * mu + B * u; |
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| 25 | P = A * P * A.transpose() + ( mat ) Q; |
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[37] | 26 | |
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[1064] | 27 | //Data update |
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| 28 | _Ry = C * P * C.transpose() + ( mat ) R; |
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| 29 | _K = P * C.transpose() * inv ( _Ry ); |
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| 30 | P -= _K * C * P; // P = P -KCP; |
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| 31 | yp = C * mu + D * u; |
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| 32 | mu += _K * ( y - yp ); |
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| 33 | |
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| 34 | if ( evalll ) { |
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| 35 | ll = fy.evallog ( y ); |
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| 36 | } |
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[7] | 37 | }; |
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| 38 | |
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| 39 | |
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[62] | 40 | |
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[477] | 41 | /////////////////////////////// EKFS |
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[583] | 42 | EKFfull::EKFfull ( ) : KalmanFull () {}; |
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[62] | 43 | |
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[527] | 44 | void EKFfull::set_parameters ( const shared_ptr<diffbifn> &pfxu0, const shared_ptr<diffbifn> &phxu0, const mat Q0, const mat R0 ) { |
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[1064] | 45 | pfxu = pfxu0; |
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| 46 | phxu = phxu0; |
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[62] | 47 | |
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[1064] | 48 | set_dim ( pfxu0->_dimx() ); |
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| 49 | dimy = phxu0->dimension(); |
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| 50 | dimc = pfxu0->_dimu(); |
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| 51 | est.set_parameters ( zeros ( dimension() ), eye ( dimension() ) ); |
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[477] | 52 | |
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[1064] | 53 | A.set_size ( dimension(), dimension() ); |
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| 54 | C.set_size ( dimy, dimension() ); |
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| 55 | //initialize matrices A C, later, these will be only updated! |
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| 56 | pfxu->dfdx_cond ( est._mu(), zeros ( dimc ), A, true ); |
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| 57 | B.clear(); |
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| 58 | phxu->dfdx_cond ( est._mu(), zeros ( dimc ), C, true ); |
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| 59 | D.clear(); |
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[62] | 60 | |
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[1064] | 61 | R = R0; |
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| 62 | Q = Q0; |
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[62] | 63 | } |
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| 64 | |
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[737] | 65 | void EKFfull::bayes ( const vec &yt, const vec &cond ) { |
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[1064] | 66 | bdm_assert_debug ( yt.length() == ( dimy ), "EKFull::bayes wrong size of dt" ); |
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| 67 | bdm_assert_debug ( cond.length() == ( dimc ), "EKFull::bayes wrong size of dt" ); |
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[737] | 68 | |
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[1064] | 69 | const vec &u = cond; |
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| 70 | const vec &y = yt; //lazy to change it |
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| 71 | vec &mu = est._mu(); |
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| 72 | mat &P = est._R(); |
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| 73 | mat& _Ry = fy._R(); |
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| 74 | vec& yp = fy._mu(); |
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[737] | 75 | |
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[1064] | 76 | pfxu->dfdx_cond ( mu, zeros ( dimc ), A, true ); |
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| 77 | phxu->dfdx_cond ( mu, zeros ( dimc ), C, true ); |
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[477] | 78 | |
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[1064] | 79 | //Time update |
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| 80 | mu = pfxu->eval ( mu, u );// A*mu + B*u; |
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| 81 | P = A * P * A.transpose() + ( mat ) Q; |
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[62] | 82 | |
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[1064] | 83 | //Data update |
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| 84 | _Ry = C * P * C.transpose() + ( mat ) R; |
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| 85 | _K = P * C.transpose() * inv ( _Ry ); |
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| 86 | P -= _K * C * P; // P = P -KCP; |
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| 87 | yp = phxu->eval ( mu, u ); |
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| 88 | mu += _K * ( y - yp ); |
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[62] | 89 | |
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[1064] | 90 | if ( BM::evalll ) { |
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| 91 | ll = fy.evallog ( y ); |
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| 92 | } |
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[62] | 93 | }; |
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| 94 | |
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| 95 | |
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| 96 | |
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[477] | 97 | void KalmanCh::set_parameters ( const mat &A0, const mat &B0, const mat &C0, const mat &D0, const chmat &Q0, const chmat &R0 ) { |
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[37] | 98 | |
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[1064] | 99 | ( ( StateSpace<chmat>* ) this )->set_parameters ( A0, B0, C0, D0, Q0, R0 ); |
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[737] | 100 | |
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[1064] | 101 | _K = zeros ( dimension(), dimy ); |
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[583] | 102 | } |
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| 103 | |
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[737] | 104 | void KalmanCh::initialize() { |
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[1064] | 105 | preA = zeros ( dimy + dimension() + dimension(), dimy + dimension() ); |
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[271] | 106 | // preA.clear(); |
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[1064] | 107 | preA.set_submatrix ( 0, 0, R._Ch() ); |
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| 108 | preA.set_submatrix ( dimy + dimension(), dimy, Q._Ch() ); |
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[37] | 109 | } |
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| 110 | |
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[679] | 111 | void KalmanCh::bayes ( const vec &yt, const vec &cond ) { |
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[1064] | 112 | bdm_assert_debug ( yt.length() == dimy, "yt mismatch" ); |
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| 113 | bdm_assert_debug ( cond.length() == dimc, "yt mismatch" ); |
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[737] | 114 | |
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[1064] | 115 | const vec &u = cond; |
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| 116 | const vec &y = yt; |
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| 117 | vec pom ( dimy ); |
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[477] | 118 | |
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[1064] | 119 | chmat &_P = est._R(); |
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| 120 | vec &_mu = est._mu(); |
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| 121 | mat _K ( dimension(), dimy ); |
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| 122 | chmat &_Ry = fy._R(); |
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| 123 | vec &_yp = fy._mu(); |
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| 124 | //TODO get rid of Q in qr()! |
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| 125 | // mat Q; |
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[37] | 126 | |
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[1064] | 127 | //R and Q are already set in set_parameters() |
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| 128 | preA.set_submatrix ( dimy, 0, ( _P._Ch() ) *C.T() ); |
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| 129 | //Fixme can be more efficient if .T() is not used |
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| 130 | preA.set_submatrix ( dimy, dimy, ( _P._Ch() ) *A.T() ); |
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[37] | 131 | |
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[1064] | 132 | if ( !qr ( preA, postA ) ) { |
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| 133 | bdm_warning ( "QR in KalmanCh unstable!" ); |
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| 134 | } |
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[37] | 135 | |
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[1064] | 136 | ( _Ry._Ch() ) = postA ( 0, dimy - 1, 0, dimy - 1 ); |
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| 137 | _K = inv ( A ) * ( postA ( 0, dimy - 1 , dimy, dimy + dimension() - 1 ) ).T(); |
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| 138 | ( _P._Ch() ) = postA ( dimy, dimy + dimension() - 1, dimy, dimy + dimension() - 1 ); |
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[37] | 139 | |
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[1064] | 140 | _mu = A * ( _mu ) + B * u; |
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| 141 | _yp = C * _mu - D * u; |
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[477] | 142 | |
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[1064] | 143 | backward_substitution ( _Ry._Ch(), ( y - _yp ), pom ); |
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| 144 | _mu += ( _K ) * pom; |
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[477] | 145 | |
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[1064] | 146 | /* cout << "P:" <<_P.to_mat() <<endl; |
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| 147 | cout << "Ry:" <<_Ry.to_mat() <<endl; |
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| 148 | cout << "_K:" <<_K <<endl;*/ |
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[477] | 149 | |
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[1064] | 150 | if ( evalll == true ) { //likelihood of observation y |
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| 151 | ll = fy.evallog ( y ); |
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| 152 | } |
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[37] | 153 | } |
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| 154 | |
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[739] | 155 | void StateCanonical::connect_mlnorm ( const mlnorm<fsqmat> &ml ) { |
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[1064] | 156 | //get ids of yrv |
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| 157 | const RV &yrv = ml._rv(); |
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| 158 | //need to determine u_t - it is all in _rvc that is not in ml._rv() |
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| 159 | RV rgr0 = ml._rvc().remove_time(); |
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| 160 | RV urv = rgr0.subt ( yrv ); |
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[37] | 161 | |
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[1064] | 162 | //We can do only 1d now... :( |
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| 163 | bdm_assert ( yrv._dsize() == 1, "Only for SISO so far..." ); |
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[37] | 164 | |
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[1064] | 165 | // create names for |
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| 166 | RV xrv; //empty |
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| 167 | RV Crv; //empty |
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| 168 | int td = ml._rvc().mint(); |
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| 169 | // assuming strictly proper function!!! |
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| 170 | for ( int t = -1; t >= td; t-- ) { |
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| 171 | xrv.add ( yrv.copy_t ( t ) ); |
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| 172 | Crv.add ( urv.copy_t ( t ) ); |
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| 173 | } |
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[739] | 174 | |
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[1064] | 175 | // get mapp |
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| 176 | th2A.set_connection ( xrv, ml._rvc() ); |
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| 177 | th2C.set_connection ( Crv, ml._rvc() ); |
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| 178 | th2D.set_connection ( urv, ml._rvc() ); |
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[739] | 179 | |
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[1064] | 180 | //set matrix sizes |
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| 181 | this->A = zeros ( xrv._dsize(), xrv._dsize() ); |
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| 182 | for ( int j = 1; j < xrv._dsize(); j++ ) { |
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| 183 | A ( j, j - 1 ) = 1.0; // off diagonal |
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| 184 | } |
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| 185 | this->B = zeros ( xrv._dsize(), 1 ); |
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| 186 | this->B ( 0 ) = 1.0; |
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| 187 | this->C = zeros ( 1, xrv._dsize() ); |
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| 188 | this->D = zeros ( 1, urv._dsize() ); |
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| 189 | this->Q = zeros ( xrv._dsize(), xrv._dsize() ); |
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| 190 | // R is set by update |
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[739] | 191 | |
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[1064] | 192 | //set cache |
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| 193 | this->A1row = zeros ( xrv._dsize() ); |
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| 194 | this->C1row = zeros ( xrv._dsize() ); |
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| 195 | this->D1row = zeros ( urv._dsize() ); |
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[739] | 196 | |
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[1064] | 197 | update_from ( ml ); |
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| 198 | validate(); |
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[739] | 199 | }; |
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| 200 | |
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| 201 | void StateCanonical::update_from ( const mlnorm<fsqmat> &ml ) { |
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| 202 | |
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[1064] | 203 | vec theta = ml._A().get_row ( 0 ); // this |
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[739] | 204 | |
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[1064] | 205 | th2A.filldown ( theta, A1row ); |
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| 206 | th2C.filldown ( theta, C1row ); |
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| 207 | th2D.filldown ( theta, D1row ); |
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[739] | 208 | |
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[1064] | 209 | R = ml._R(); |
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[739] | 210 | |
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[1064] | 211 | A.set_row ( 0, A1row ); |
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| 212 | C.set_row ( 0, C1row + D1row ( 0 ) *A1row ); |
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| 213 | D.set_row ( 0, D1row ); |
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[739] | 214 | } |
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| 215 | |
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| 216 | void StateFromARX::connect_mlnorm ( const mlnorm<chmat> &ml, RV &xrv, RV &urv ) { |
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[1064] | 217 | //get ids of yrv |
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| 218 | const RV &yrv = ml._rv(); |
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| 219 | //need to determine u_t - it is all in _rvc that is not in ml._rv() |
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| 220 | const RV &rgr = ml._rvc(); |
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| 221 | RV rgr0 = rgr.remove_time(); |
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| 222 | urv = rgr0.subt ( yrv ); |
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[739] | 223 | |
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[1064] | 224 | // create names for state variables |
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| 225 | xrv = yrv; |
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[739] | 226 | |
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[1064] | 227 | int y_multiplicity = -rgr.mint ( yrv ); |
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| 228 | int y_block_size = yrv.length() * ( y_multiplicity ); // current yt + all delayed yts |
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| 229 | for ( int m = 0; m < y_multiplicity - 1; m++ ) { // ========= -1 is important see arx2statespace_notes |
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| 230 | xrv.add ( yrv.copy_t ( -m - 1 ) ); //add delayed yt |
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| 231 | } |
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| 232 | //! temporary RV for connection to ml.rvc, since notation of xrv and ml.rvc does not match |
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| 233 | RV xrv_ml = xrv.copy_t ( -1 ); |
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[739] | 234 | |
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[1064] | 235 | // add regressors |
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| 236 | ivec u_block_sizes ( urv.length() ); // no_blocks = yt + unique rgr |
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| 237 | for ( int r = 0; r < urv.length(); r++ ) { |
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| 238 | RV R = urv.subselect ( vec_1 ( r ) ); //non-delayed element of rgr |
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| 239 | int r_size = urv.size ( r ); |
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| 240 | int r_multiplicity = -rgr.mint ( R ); |
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| 241 | u_block_sizes ( r ) = r_size * r_multiplicity ; |
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| 242 | for ( int m = 0; m < r_multiplicity; m++ ) { |
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| 243 | xrv.add ( R.copy_t ( -m - 1 ) ); //add delayed yt |
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| 244 | xrv_ml.add ( R.copy_t ( -m - 1 ) ); //add delayed yt |
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| 245 | } |
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| 246 | } |
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| 247 | // add constant |
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| 248 | if ( any ( ml._mu_const() != 0.0 ) ) { |
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| 249 | have_constant = true; |
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| 250 | xrv.add ( RV ( "bdm_reserved_constant_one", 1 ) ); |
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| 251 | } else { |
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| 252 | have_constant = false; |
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| 253 | } |
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[739] | 254 | |
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| 255 | |
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[1064] | 256 | // get mapp |
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| 257 | th2A.set_connection ( xrv_ml, ml._rvc() ); |
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| 258 | th2B.set_connection ( urv, ml._rvc() ); |
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[739] | 259 | |
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[1064] | 260 | //set matrix sizes |
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| 261 | this->A = zeros ( xrv._dsize(), xrv._dsize() ); |
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| 262 | //create y block |
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| 263 | diagonal_part ( this->A, yrv._dsize(), 0, y_block_size - yrv._dsize() ); |
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[739] | 264 | |
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[1064] | 265 | this->B = zeros ( xrv._dsize(), urv._dsize() ); |
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| 266 | //add diagonals for rgr |
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| 267 | int active_x = y_block_size; |
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| 268 | int active_Bcol = 0; |
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| 269 | for ( int r = 0; r < urv.length(); r++ ) { |
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| 270 | if (u_block_sizes(r)>0) { |
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| 271 | diagonal_part ( this->A, active_x + urv.size ( r ), active_x, u_block_sizes ( r ) - urv.size ( r ) ); |
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| 272 | this->B.set_submatrix ( active_x, active_Bcol, eye ( urv.size ( r ) ) ); |
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| 273 | active_Bcol+=u_block_sizes(r); |
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| 274 | } |
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| 275 | active_x += u_block_sizes ( r ); |
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| 276 | } |
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| 277 | this->C = zeros ( yrv._dsize(), xrv._dsize() ); |
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| 278 | this->C.set_submatrix ( 0, 0, eye ( yrv._dsize() ) ); |
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| 279 | this->D = zeros ( yrv._dsize(), urv._dsize() ); |
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| 280 | this->R.setCh ( zeros ( yrv._dsize(), yrv._dsize() ) ); |
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| 281 | this->Q.setCh ( zeros ( xrv._dsize(), xrv._dsize() ) ); |
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| 282 | // Q is set by update |
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[739] | 283 | |
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[1064] | 284 | update_from ( ml ); |
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| 285 | validate(); |
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[739] | 286 | } |
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[1064] | 287 | |
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[739] | 288 | void StateFromARX::update_from ( const mlnorm<chmat> &ml ) { |
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[1064] | 289 | vec Arow = zeros ( A.cols() ); |
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| 290 | vec Brow = zeros ( B.cols() ); |
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| 291 | // ROW- WISE EVALUATION ===== |
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| 292 | for ( int i = 0; i < ml._rv()._dsize(); i++ ) { |
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[739] | 293 | |
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[1064] | 294 | vec theta = ml._A().get_row ( i ); |
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[739] | 295 | |
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[1064] | 296 | th2A.filldown ( theta, Arow ); |
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| 297 | if ( have_constant ) { |
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| 298 | // constant is always at the end no need for datalink |
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| 299 | Arow ( A.cols() - 1 ) = ml._mu_const() ( i ); |
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| 300 | } |
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| 301 | this->A.set_row ( i, Arow ); |
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[739] | 302 | |
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[1064] | 303 | th2B.filldown ( theta, Brow ); |
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| 304 | this->B.set_row ( i, Brow ); |
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| 305 | } |
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| 306 | this->Q._Ch().set_submatrix ( 0, 0, ml.__R()._Ch() ); |
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[739] | 307 | |
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| 308 | } |
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| 309 | |
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| 310 | |
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[527] | 311 | void EKFCh::set_parameters ( const shared_ptr<diffbifn> &pfxu0, const shared_ptr<diffbifn> &phxu0, const chmat Q0, const chmat R0 ) { |
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[1064] | 312 | pfxu = pfxu0; |
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| 313 | phxu = phxu0; |
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[37] | 314 | |
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[1064] | 315 | set_dim ( pfxu0->_dimx() ); |
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| 316 | dimy = phxu0->dimension(); |
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| 317 | dimc = pfxu0->_dimu(); |
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[737] | 318 | |
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[1064] | 319 | vec &_mu = est._mu(); |
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| 320 | // if mu is not set, set it to zeros, just for constant terms of A and C |
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| 321 | if ( _mu.length() != dimension() ) _mu = zeros ( dimension() ); |
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| 322 | A = zeros ( dimension(), dimension() ); |
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| 323 | C = zeros ( dimy, dimension() ); |
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| 324 | preA = zeros ( dimy + dimension() + dimension(), dimy + dimension() ); |
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[477] | 325 | |
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[1064] | 326 | //initialize matrices A C, later, these will be only updated! |
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| 327 | pfxu->dfdx_cond ( _mu, zeros ( dimc ), A, true ); |
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[37] | 328 | // pfxu->dfdu_cond ( *_mu,zeros ( dimu ),B,true ); |
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[1064] | 329 | B.clear(); |
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| 330 | phxu->dfdx_cond ( _mu, zeros ( dimc ), C, true ); |
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[37] | 331 | // phxu->dfdu_cond ( *_mu,zeros ( dimu ),D,true ); |
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[1064] | 332 | D.clear(); |
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[37] | 333 | |
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[1064] | 334 | R = R0; |
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| 335 | Q = Q0; |
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[37] | 336 | |
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[1064] | 337 | // Cholesky special! |
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| 338 | preA.clear(); |
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| 339 | preA.set_submatrix ( 0, 0, R._Ch() ); |
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| 340 | preA.set_submatrix ( dimy + dimension(), dimy, Q._Ch() ); |
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[37] | 341 | } |
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| 342 | |
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| 343 | |
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[679] | 344 | void EKFCh::bayes ( const vec &yt, const vec &cond ) { |
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[37] | 345 | |
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[1064] | 346 | vec pom ( dimy ); |
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| 347 | const vec &u = cond; |
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| 348 | const vec &y = yt; |
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| 349 | vec &_mu = est._mu(); |
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| 350 | chmat &_P = est._R(); |
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| 351 | chmat &_Ry = fy._R(); |
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| 352 | vec &_yp = fy._mu(); |
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[737] | 353 | |
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[1064] | 354 | pfxu->dfdx_cond ( _mu, u, A, false ); //update A by a derivative of fx |
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| 355 | phxu->dfdx_cond ( _mu, u, C, false ); //update A by a derivative of fx |
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[37] | 356 | |
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[1064] | 357 | //R and Q are already set in set_parameters() |
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| 358 | preA.set_submatrix ( dimy, 0, ( _P._Ch() ) *C.T() ); |
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| 359 | //Fixme can be more efficient if .T() is not used |
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| 360 | preA.set_submatrix ( dimy, dimy, ( _P._Ch() ) *A.T() ); |
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[37] | 361 | |
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[62] | 362 | // mat Sttm = _P->to_mat(); |
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[225] | 363 | // cout << preA <<endl; |
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| 364 | // cout << "_mu:" << _mu <<endl; |
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[62] | 365 | |
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[1064] | 366 | if ( !qr ( preA, postA ) ) { |
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| 367 | bdm_warning ( "QR in EKFCh unstable!" ); |
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| 368 | } |
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[37] | 369 | |
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[225] | 370 | |
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[1064] | 371 | ( _Ry._Ch() ) = postA ( 0, dimy - 1, 0, dimy - 1 ); |
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| 372 | _K = inv ( A ) * ( postA ( 0, dimy - 1 , dimy, dimy + dimension() - 1 ) ).T(); |
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| 373 | ( _P._Ch() ) = postA ( dimy, dimy + dimension() - 1, dimy, dimy + dimension() - 1 ); |
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[477] | 374 | |
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[62] | 375 | // mat iRY = inv(_Ry->to_mat()); |
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| 376 | // mat Stt = Sttm - Sttm * C.T() * iRY * C * Sttm; |
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| 377 | // mat _K2 = Stt*C.T()*inv(R.to_mat()); |
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| 378 | |
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[1064] | 379 | // prediction |
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| 380 | _mu = pfxu->eval ( _mu , u ); |
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| 381 | _yp = phxu->eval ( _mu, u ); |
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[477] | 382 | |
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[1064] | 383 | /* vec mu2 = *_mu + ( _K2 ) * ( y-*_yp );*/ |
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[477] | 384 | |
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[1064] | 385 | //correction //= initial value is already prediction! |
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| 386 | backward_substitution ( _Ry._Ch(), ( y - _yp ), pom ); |
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| 387 | _mu += ( _K ) * pom ; |
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[62] | 388 | |
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[1064] | 389 | /* _K = (_P->to_mat())*C.transpose() * ( _iRy->to_mat() ); |
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| 390 | *_mu = pfxu->eval ( *_mu ,u ) + ( _K )* ( y-*_yp );*/ |
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[477] | 391 | |
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[215] | 392 | // cout << "P:" <<_P.to_mat() <<endl; |
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| 393 | // cout << "Ry:" <<_Ry.to_mat() <<endl; |
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[225] | 394 | // cout << "_mu:" <<_mu <<endl; |
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| 395 | // cout << "dt:" <<dt <<endl; |
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[37] | 396 | |
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[1064] | 397 | if ( evalll == true ) { //likelihood of observation y |
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| 398 | ll = fy.evallog ( y ); |
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| 399 | } |
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[37] | 400 | } |
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| 401 | |
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[477] | 402 | void EKFCh::from_setting ( const Setting &set ) { |
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[1064] | 403 | BM::from_setting ( set ); |
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| 404 | shared_ptr<diffbifn> IM = UI::build<diffbifn> ( set, "IM", UI::compulsory ); |
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| 405 | shared_ptr<diffbifn> OM = UI::build<diffbifn> ( set, "OM", UI::compulsory ); |
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[477] | 406 | |
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[1064] | 407 | //statistics |
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| 408 | int dim = IM->dimension(); |
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| 409 | vec mu0; |
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| 410 | if ( !UI::get ( mu0, set, "mu0" ) ) |
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| 411 | mu0 = zeros ( dim ); |
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[357] | 412 | |
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[1064] | 413 | mat P0; |
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| 414 | vec dP0; |
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| 415 | if ( UI::get ( dP0, set, "dP0" ) ) |
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| 416 | P0 = diag ( dP0 ); |
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| 417 | else if ( !UI::get ( P0, set, "P0" ) ) |
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| 418 | P0 = eye ( dim ); |
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[477] | 419 | |
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[1064] | 420 | set_statistics ( mu0, P0 ); |
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[477] | 421 | |
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[1064] | 422 | //parameters |
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| 423 | vec dQ, dR; |
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| 424 | UI::get ( dQ, set, "dQ", UI::compulsory ); |
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| 425 | UI::get ( dR, set, "dR", UI::compulsory ); |
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| 426 | set_parameters ( IM, OM, diag ( dQ ), diag ( dR ) ); |
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[262] | 427 | } |
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[357] | 428 | |
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[477] | 429 | void MultiModel::from_setting ( const Setting &set ) { |
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[1064] | 430 | Array<EKFCh*> A; |
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| 431 | UI::get ( A, set, "models", UI::compulsory ); |
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[477] | 432 | |
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[1064] | 433 | set_parameters ( A ); |
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| 434 | set_yrv ( A ( 0 )->_yrv() ); |
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| 435 | //set_rv(A(0)->_rv()); |
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[357] | 436 | } |
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| 437 | |
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[1158] | 438 | void EKF_UD::set_parameters ( const shared_ptr<diffbifn> &pfxu0, const shared_ptr<diffbifn> &phxu0, const mat Q0, const vec R0 ) { |
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| 439 | pfxu = pfxu0; |
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| 440 | phxu = phxu0; |
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| 441 | |
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| 442 | set_dim ( pfxu0->_dimx() ); |
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| 443 | dimy = phxu0->dimension(); |
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| 444 | dimc = pfxu0->_dimu(); |
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| 445 | |
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| 446 | vec &_mu = est._mu(); |
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| 447 | // if mu is not set, set it to zeros, just for constant terms of A and C |
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| 448 | if ( _mu.length() != dimension() ) _mu = zeros ( dimension() ); |
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| 449 | A = zeros ( dimension(), dimension() ); |
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| 450 | C = zeros ( dimy, dimension() ); |
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| 451 | |
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| 452 | //initialize matrices A C, later, these will be only updated! |
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| 453 | pfxu->dfdx_cond ( _mu, zeros ( dimc ), A, true ); |
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| 454 | // pfxu->dfdu_cond ( *_mu,zeros ( dimu ),B,true ); |
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| 455 | phxu->dfdx_cond ( _mu, zeros ( dimc ), C, true ); |
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| 456 | // phxu->dfdu_cond ( *_mu,zeros ( dimu ),D,true ); |
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| 457 | |
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| 458 | R = R0; |
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| 459 | Q = Q0; |
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| 460 | |
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| 461 | // |
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[357] | 462 | } |
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[1158] | 463 | |
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| 464 | |
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| 465 | void EKF_UD::bayes ( const vec &yt, const vec &cond ) { |
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| 466 | //preparatory |
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| 467 | vec &_mu=est._mu(); |
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| 468 | const vec &u=cond; |
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| 469 | int dim = dimension(); |
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| 470 | |
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| 471 | U = est._R()._L().T(); |
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| 472 | D = est._R()._D(); |
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| 473 | |
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| 474 | //////////// |
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| 475 | |
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| 476 | pfxu->dfdx_cond ( _mu, u, A, false ); //update A by a derivative of fx |
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| 477 | phxu->dfdx_cond ( _mu, u, C, false ); //update A by a derivative of fx |
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| 478 | |
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| 479 | mat PhiU = A*U; |
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| 480 | |
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| 481 | vec Din = D; |
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| 482 | int i,j,k; |
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| 483 | double sigma; |
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| 484 | mat G = eye(dim); |
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| 485 | //////// thorton |
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| 486 | |
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| 487 | //move mean; |
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| 488 | _mu = pfxu->eval(_mu,u); |
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| 489 | |
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| 490 | for (i=dim-1; i>=0;i--){ |
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| 491 | sigma = 0.0; |
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| 492 | for (j=0; j<dim; j++) { |
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| 493 | sigma += PhiU(i,j)*PhiU(i,j) *Din(j); |
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| 494 | sigma += G(i,j)*G(i,j) * Q(j,j); |
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| 495 | } |
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| 496 | D(i) = sigma; |
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| 497 | for (j=0;j<i;j++){ |
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| 498 | sigma = 0.0; |
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| 499 | for (k=0;k<dim;k++){ |
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| 500 | sigma += PhiU(i,k)*Din(k)*PhiU(j,k); |
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| 501 | } |
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| 502 | for (k=0;k<dim;k++){ |
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| 503 | sigma += G(i,k)*Q(k,k)*G(j,k); |
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| 504 | } |
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| 505 | // |
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| 506 | U(j,i) = sigma/D(i); |
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| 507 | for (k=0;k<dim;k++){ |
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| 508 | PhiU(j,k) = PhiU(j,k) - U(j,i)*PhiU(i,k); |
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| 509 | } |
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| 510 | for (k=0;k<dim;k++){ |
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| 511 | G(j,k) = G(j,k) - U(j,i)*G(i,k); |
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| 512 | } |
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| 513 | } |
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| 514 | } |
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[1168] | 515 | |
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| 516 | if ( log_level[logU] ){ |
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| 517 | // transformed U |
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| 518 | mat tU; |
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| 519 | mat P= U*diag(D)*U.T(); |
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| 520 | |
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| 521 | vec xref(5); |
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| 522 | xref(0)= 30.0*1.4142; |
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| 523 | xref(1)= 30.0*1.4142; |
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| 524 | xref(2)= 6.283185*200.; |
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| 525 | xref(3) = 3.141593; |
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| 526 | xref(4) = 34.0; |
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| 527 | |
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| 528 | mat T = diag(1.0/(xref)); |
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| 529 | mat Pf = T*P*T; |
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| 530 | |
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| 531 | ldmat Pld(Pf); |
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| 532 | |
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| 533 | //vec tmp=vec(U._data(),dimension()*dimension()); |
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| 534 | vec tmp=vec(Pld._L()._data(),dimension()*dimension()); |
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| 535 | log_level.store(logU,round(((int)1<<14)*tmp)); |
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[1173] | 536 | log_level.store(logD,Pld._D()); |
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[1168] | 537 | } |
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| 538 | if ( log_level[logG] ){ |
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| 539 | vec tmp=vec(G._data(),dimension()*dimension()); |
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| 540 | log_level.store(logG,tmp); |
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| 541 | } |
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[1158] | 542 | //cout << "Ut: " << U << endl; |
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| 543 | //cout << "Dt: " << D << endl; |
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| 544 | // bierman |
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| 545 | |
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| 546 | double dz,alpha,gamma,beta,lambda; |
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| 547 | vec a; |
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| 548 | vec b; |
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| 549 | vec yp = phxu->eval(_mu,u); |
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| 550 | for (int iy=0; iy<dimy; iy++){ |
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| 551 | a = U.T()*C.get_row(iy); // a is not modified, but |
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| 552 | b = elem_mult(D,a); // b is modified to become unscaled Kalman gain. |
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| 553 | dz = yt(iy) - yp(iy); |
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| 554 | |
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| 555 | alpha = R(iy); |
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| 556 | gamma = 1/alpha; |
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| 557 | for (j=0;j<dim;j++){ |
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| 558 | beta = alpha; |
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| 559 | alpha = alpha + a(j)*b(j); |
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| 560 | lambda = -a(j)*gamma; |
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| 561 | gamma = 1.0/alpha; |
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| 562 | D(j) = beta*gamma*D(j); |
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| 563 | |
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[1168] | 564 | // cout << "a: " << alpha << "g: " << gamma << endl; |
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[1158] | 565 | for (i=0;i<j;i++){ |
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| 566 | beta = U(i,j); |
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| 567 | U(i,j) = beta + b(i)*lambda; |
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| 568 | b(i) = b(i) + b(j)*beta; |
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| 569 | } |
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| 570 | } |
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| 571 | double dzs = gamma*dz; // apply scaling to innovations |
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| 572 | _mu = _mu + dzs*b; // multiply by unscaled Kalman gain |
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| 573 | |
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| 574 | //cout << "Ub: " << U << endl; |
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| 575 | //cout << "Db: " << D << endl <<endl; |
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| 576 | |
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| 577 | } |
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| 578 | |
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| 579 | ///// |
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| 580 | est._R().__L()=U.T(); |
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| 581 | est._R().__D()=D; |
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| 582 | |
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| 583 | if ( evalll == true ) { //likelihood of observation y |
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| 584 | } |
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| 585 | } |
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| 586 | |
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| 587 | void EKF_UD::from_setting ( const Setting &set ) { |
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| 588 | BM::from_setting ( set ); |
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| 589 | shared_ptr<diffbifn> IM = UI::build<diffbifn> ( set, "IM", UI::compulsory ); |
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| 590 | shared_ptr<diffbifn> OM = UI::build<diffbifn> ( set, "OM", UI::compulsory ); |
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| 591 | |
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| 592 | //statistics |
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| 593 | int dim = IM->dimension(); |
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| 594 | vec mu0; |
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| 595 | if ( !UI::get ( mu0, set, "mu0" ) ) |
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| 596 | mu0 = zeros ( dim ); |
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| 597 | |
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| 598 | mat P0; |
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| 599 | vec dP0; |
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| 600 | if ( UI::get ( dP0, set, "dP0" ) ) |
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| 601 | P0 = diag ( dP0 ); |
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| 602 | else if ( !UI::get ( P0, set, "P0" ) ) |
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| 603 | P0 = eye ( dim ); |
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| 604 | |
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| 605 | est._mu()=mu0; |
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| 606 | est._R()=ldmat(P0); |
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| 607 | |
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| 608 | //parameters |
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| 609 | vec dQ, dR; |
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| 610 | UI::get ( dQ, set, "dQ", UI::compulsory ); |
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| 611 | UI::get ( dR, set, "dR", UI::compulsory ); |
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| 612 | set_parameters ( IM, OM, diag ( dQ ), dR ); |
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[1168] | 613 | |
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| 614 | UI::get(log_level, set, "log_level", UI::optional); |
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[1158] | 615 | } |
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| 616 | |
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| 617 | } |
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