1 | |
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2 | #include "kalman.h" |
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3 | |
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4 | namespace bdm { |
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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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10 | void KalmanFull::bayes ( const vec &dt ) { |
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11 | bdm_assert_debug ( dt.length() == ( dimy + dimu ), "KalmanFull::bayes wrong size of dt" ); |
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12 | |
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13 | vec u = dt.get ( dimy, dimy + dimu - 1 ); |
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14 | vec y = dt.get ( 0, dimy - 1 ); |
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15 | vec& mu = est->_mu(); |
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16 | mat &P = est->_R(); |
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17 | mat& _Ry = fy._R(); |
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18 | //Time update |
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19 | mu = A * mu + B * u; |
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20 | P = A * P * A.transpose() + (mat)Q; |
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21 | |
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22 | //Data update |
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23 | _Ry = C * P * C.transpose() + (mat)R; |
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24 | _K = P * C.transpose() * inv ( _Ry ); |
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25 | P -= _K * C * P; // P = P -KCP; |
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26 | mu += _K * ( y - C * mu - D * u ); |
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27 | |
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28 | if ( evalll ) { |
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29 | ll=est->evallog(y); |
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30 | } |
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31 | }; |
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32 | |
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33 | |
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34 | |
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35 | /////////////////////////////// EKFS |
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36 | EKFfull::EKFfull ( ) : KalmanFull () {}; |
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37 | |
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38 | void EKFfull::set_parameters ( const shared_ptr<diffbifn> &pfxu0, const shared_ptr<diffbifn> &phxu0, const mat Q0, const mat R0 ) { |
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39 | pfxu = pfxu0; |
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40 | phxu = phxu0; |
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41 | |
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42 | dimx = pfxu0->_dimx(); |
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43 | dimy = phxu0->dimension(); |
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44 | dimu = pfxu0->_dimu(); |
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45 | est->set_parameters( zeros(dimx), eye(dimx) ); |
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46 | |
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47 | A.set_size ( dimx, dimx ); |
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48 | C.set_size ( dimy, dimx ); |
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49 | //initialize matrices A C, later, these will be only updated! |
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50 | pfxu->dfdx_cond ( est->_mu(), zeros ( dimu ), A, true ); |
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51 | B.clear(); |
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52 | phxu->dfdx_cond ( est->_mu(), zeros ( dimu ), C, true ); |
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53 | D.clear(); |
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54 | |
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55 | R = R0; |
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56 | Q = Q0; |
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57 | } |
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58 | |
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59 | void EKFfull::bayes ( const vec &dt ) { |
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60 | bdm_assert_debug ( dt.length() == ( dimy + dimu ), "EKFull::bayes wrong size of dt" ); |
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61 | |
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62 | vec u = dt.get ( dimy, dimy + dimu - 1 ); |
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63 | vec y = dt.get ( 0, dimy - 1 ); |
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64 | vec &mu = est->_mu(); |
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65 | mat &P = est->_R(); |
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66 | mat& _Ry = fy._R(); |
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67 | |
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68 | pfxu->dfdx_cond ( mu, zeros ( dimu ), A, true ); |
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69 | phxu->dfdx_cond ( mu, zeros ( dimu ), C, true ); |
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70 | |
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71 | //Time update |
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72 | mu = pfxu->eval ( mu, u );// A*mu + B*u; |
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73 | P = A * P * A.transpose() + (mat)Q; |
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74 | |
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75 | //Data update |
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76 | _Ry = C * P * C.transpose() + (mat)R; |
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77 | _K = P * C.transpose() * inv ( _Ry ); |
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78 | P -= _K * C * P; // P = P -KCP; |
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79 | vec yp = phxu->eval ( mu, u ); |
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80 | mu += _K * ( y - yp ); |
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81 | |
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82 | if ( BM::evalll ) { |
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83 | ll=fy.evallog(y); |
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84 | } |
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85 | }; |
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86 | |
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87 | |
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88 | |
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89 | 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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90 | |
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91 | ( ( StateSpace<chmat>* ) this )->set_parameters ( A0, B0, C0, D0, Q0, R0 ); |
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92 | |
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93 | _K=zeros(dimx,dimy); |
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94 | // Cholesky special! |
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95 | initialize(); |
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96 | } |
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97 | |
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98 | void KalmanCh::initialize(){ |
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99 | preA = zeros ( dimy + dimx + dimx, dimy + dimx ); |
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100 | // preA.clear(); |
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101 | preA.set_submatrix ( 0, 0, R._Ch() ); |
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102 | preA.set_submatrix ( dimy + dimx, dimy, Q._Ch() ); |
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103 | } |
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104 | |
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105 | void KalmanCh::bayes ( const vec &dt ) { |
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106 | |
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107 | vec u = dt.get ( dimy, dimy + dimu - 1 ); |
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108 | vec y = dt.get ( 0, dimy - 1 ); |
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109 | vec pom ( dimy ); |
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110 | |
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111 | chmat &_P=est->_R(); |
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112 | vec &_mu = est->_mu(); |
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113 | mat _K(dimx,dimy); |
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114 | chmat &_Ry=fy._R(); |
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115 | vec &_yp = fy._mu(); |
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116 | //TODO get rid of Q in qr()! |
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117 | // mat Q; |
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118 | |
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119 | //R and Q are already set in set_parameters() |
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120 | preA.set_submatrix ( dimy, 0, ( _P._Ch() ) *C.T() ); |
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121 | //Fixme can be more efficient if .T() is not used |
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122 | preA.set_submatrix ( dimy, dimy, ( _P._Ch() ) *A.T() ); |
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123 | |
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124 | if ( !qr ( preA, postA ) ) { |
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125 | bdm_warning ( "QR in KalmanCh unstable!" ); |
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126 | } |
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127 | |
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128 | ( _Ry._Ch() ) = postA ( 0, dimy - 1, 0, dimy - 1 ); |
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129 | _K = inv ( A ) * ( postA ( 0, dimy - 1 , dimy, dimy + dimx - 1 ) ).T(); |
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130 | ( _P._Ch() ) = postA ( dimy, dimy + dimx - 1, dimy, dimy + dimx - 1 ); |
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131 | |
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132 | _mu = A * ( _mu ) + B * u; |
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133 | _yp = C * _mu - D * u; |
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134 | |
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135 | backward_substitution ( _Ry._Ch(), ( y - _yp ), pom ); |
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136 | _mu += ( _K ) * pom; |
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137 | |
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138 | /* cout << "P:" <<_P.to_mat() <<endl; |
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139 | cout << "Ry:" <<_Ry.to_mat() <<endl; |
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140 | cout << "_K:" <<_K <<endl;*/ |
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141 | |
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142 | if ( evalll == true ) { //likelihood of observation y |
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143 | ll = fy.evallog ( y ); |
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144 | } |
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145 | } |
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146 | |
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147 | |
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148 | |
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149 | void EKFCh::set_parameters ( const shared_ptr<diffbifn> &pfxu0, const shared_ptr<diffbifn> &phxu0, const chmat Q0, const chmat R0 ) { |
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150 | pfxu = pfxu0; |
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151 | phxu = phxu0; |
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152 | |
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153 | dimx = pfxu0->dimension(); |
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154 | dimy = phxu0->dimension(); |
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155 | dimu = pfxu0->_dimu(); |
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156 | |
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157 | vec &_mu = est->_mu(); |
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158 | // if mu is not set, set it to zeros, just for constant terms of A and C |
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159 | if ( _mu.length() != dimx ) _mu = zeros ( dimx ); |
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160 | A = zeros ( dimx, dimx ); |
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161 | C = zeros ( dimy, dimx ); |
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162 | preA = zeros ( dimy + dimx + dimx, dimy + dimx ); |
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163 | |
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164 | //initialize matrices A C, later, these will be only updated! |
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165 | pfxu->dfdx_cond ( _mu, zeros ( dimu ), A, true ); |
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166 | // pfxu->dfdu_cond ( *_mu,zeros ( dimu ),B,true ); |
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167 | B.clear(); |
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168 | phxu->dfdx_cond ( _mu, zeros ( dimu ), C, true ); |
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169 | // phxu->dfdu_cond ( *_mu,zeros ( dimu ),D,true ); |
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170 | D.clear(); |
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171 | |
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172 | R = R0; |
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173 | Q = Q0; |
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174 | |
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175 | // Cholesky special! |
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176 | preA.clear(); |
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177 | preA.set_submatrix ( 0, 0, R._Ch() ); |
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178 | preA.set_submatrix ( dimy + dimx, dimy, Q._Ch() ); |
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179 | } |
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180 | |
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181 | |
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182 | void EKFCh::bayes ( const vec &dt ) { |
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183 | |
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184 | vec pom ( dimy ); |
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185 | vec u = dt.get ( dimy, dimy + dimu - 1 ); |
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186 | vec y = dt.get ( 0, dimy - 1 ); |
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187 | vec &_mu = est->_mu(); |
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188 | chmat &_P = est->_R(); |
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189 | chmat &_Ry = fy._R(); |
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190 | vec &_yp = fy._mu(); |
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191 | |
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192 | pfxu->dfdx_cond ( _mu, u, A, false ); //update A by a derivative of fx |
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193 | phxu->dfdx_cond ( _mu, u, C, false ); //update A by a derivative of fx |
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194 | |
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195 | //R and Q are already set in set_parameters() |
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196 | preA.set_submatrix ( dimy, 0, ( _P._Ch() ) *C.T() ); |
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197 | //Fixme can be more efficient if .T() is not used |
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198 | preA.set_submatrix ( dimy, dimy, ( _P._Ch() ) *A.T() ); |
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199 | |
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200 | // mat Sttm = _P->to_mat(); |
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201 | // cout << preA <<endl; |
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202 | // cout << "_mu:" << _mu <<endl; |
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203 | |
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204 | if ( !qr ( preA, postA ) ) { |
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205 | bdm_warning ( "QR in EKFCh unstable!" ); |
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206 | } |
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207 | |
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208 | |
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209 | ( _Ry._Ch() ) = postA ( 0, dimy - 1, 0, dimy - 1 ); |
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210 | _K = inv ( A ) * ( postA ( 0, dimy - 1 , dimy, dimy + dimx - 1 ) ).T(); |
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211 | ( _P._Ch() ) = postA ( dimy, dimy + dimx - 1, dimy, dimy + dimx - 1 ); |
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212 | |
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213 | // mat iRY = inv(_Ry->to_mat()); |
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214 | // mat Stt = Sttm - Sttm * C.T() * iRY * C * Sttm; |
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215 | // mat _K2 = Stt*C.T()*inv(R.to_mat()); |
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216 | |
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217 | // prediction |
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218 | _mu = pfxu->eval ( _mu , u ); |
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219 | _yp = phxu->eval ( _mu, u ); |
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220 | |
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221 | /* vec mu2 = *_mu + ( _K2 ) * ( y-*_yp );*/ |
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222 | |
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223 | //correction //= initial value is already prediction! |
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224 | backward_substitution ( _Ry._Ch(), ( y - _yp ), pom ); |
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225 | _mu += ( _K ) * pom ; |
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226 | |
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227 | /* _K = (_P->to_mat())*C.transpose() * ( _iRy->to_mat() ); |
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228 | *_mu = pfxu->eval ( *_mu ,u ) + ( _K )* ( y-*_yp );*/ |
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229 | |
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230 | // cout << "P:" <<_P.to_mat() <<endl; |
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231 | // cout << "Ry:" <<_Ry.to_mat() <<endl; |
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232 | // cout << "_mu:" <<_mu <<endl; |
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233 | // cout << "dt:" <<dt <<endl; |
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234 | |
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235 | if ( evalll == true ) { //likelihood of observation y |
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236 | ll = fy.evallog ( y ); |
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237 | } |
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238 | } |
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239 | |
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240 | void EKFCh::from_setting ( const Setting &set ) { |
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241 | shared_ptr<diffbifn> IM = UI::build<diffbifn> ( set, "IM", UI::compulsory ); |
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242 | shared_ptr<diffbifn> OM = UI::build<diffbifn> ( set, "OM", UI::compulsory ); |
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243 | |
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244 | //statistics |
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245 | int dim = IM->dimension(); |
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246 | vec mu0; |
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247 | if ( !UI::get ( mu0, set, "mu0" ) ) |
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248 | mu0 = zeros ( dim ); |
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249 | |
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250 | mat P0; |
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251 | vec dP0; |
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252 | if ( UI::get ( dP0, set, "dP0" ) ) |
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253 | P0 = diag ( dP0 ); |
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254 | else if ( !UI::get ( P0, set, "P0" ) ) |
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255 | P0 = eye ( dim ); |
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256 | |
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257 | set_statistics ( mu0, P0 ); |
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258 | |
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259 | //parameters |
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260 | vec dQ, dR; |
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261 | UI::get ( dQ, set, "dQ", UI::compulsory ); |
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262 | UI::get ( dR, set, "dR", UI::compulsory ); |
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263 | set_parameters ( IM, OM, diag ( dQ ), diag ( dR ) ); |
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264 | |
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265 | //connect |
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266 | shared_ptr<RV> drv = UI::build<RV> ( set, "drv", UI::compulsory ); |
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267 | set_drv ( *drv ); |
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268 | shared_ptr<RV> rv = UI::build<RV> ( set, "rv", UI::compulsory ); |
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269 | set_rv ( *rv ); |
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270 | |
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271 | string options; |
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272 | if ( UI::get ( options, set, "options" ) ) |
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273 | set_options ( options ); |
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274 | } |
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275 | |
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276 | void MultiModel::from_setting ( const Setting &set ) { |
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277 | Array<EKFCh*> A; |
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278 | UI::get ( A, set, "models", UI::compulsory ); |
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279 | |
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280 | set_parameters ( A ); |
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281 | set_drv ( A ( 0 )->_drv() ); |
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282 | //set_rv(A(0)->_rv()); |
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283 | |
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284 | string options; |
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285 | if ( set.lookupValue ( "options", options ) ) |
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286 | set_options ( options ); |
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287 | } |
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288 | |
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289 | } |
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