1 | |
---|
2 | #include "kalman.h" |
---|
3 | |
---|
4 | namespace bdm { |
---|
5 | |
---|
6 | using std::endl; |
---|
7 | |
---|
8 | |
---|
9 | |
---|
10 | void KalmanFull::bayes ( const vec &yt, const vec &cond ) { |
---|
11 | bdm_assert_debug ( yt.length() == ( dimy ), "KalmanFull::bayes wrong size of dt" ); |
---|
12 | |
---|
13 | const vec &u = cond; // in this case cond=ut |
---|
14 | const vec &y = yt; |
---|
15 | |
---|
16 | vec& mu = est._mu(); |
---|
17 | mat &P = est._R(); |
---|
18 | mat& _Ry = fy._R(); |
---|
19 | vec& yp = fy._mu(); |
---|
20 | //Time update |
---|
21 | mu = A * mu + B * u; |
---|
22 | P = A * P * A.transpose() + (mat)Q; |
---|
23 | |
---|
24 | //Data update |
---|
25 | _Ry = C * P * C.transpose() + (mat)R; |
---|
26 | _K = P * C.transpose() * inv ( _Ry ); |
---|
27 | P -= _K * C * P; // P = P -KCP; |
---|
28 | yp = C * mu + D * u; |
---|
29 | mu += _K * ( y - yp ); |
---|
30 | |
---|
31 | if ( evalll ) { |
---|
32 | ll=fy.evallog(y); |
---|
33 | } |
---|
34 | }; |
---|
35 | |
---|
36 | |
---|
37 | |
---|
38 | /////////////////////////////// EKFS |
---|
39 | EKFfull::EKFfull ( ) : KalmanFull () {}; |
---|
40 | |
---|
41 | void EKFfull::set_parameters ( const shared_ptr<diffbifn> &pfxu0, const shared_ptr<diffbifn> &phxu0, const mat Q0, const mat R0 ) { |
---|
42 | pfxu = pfxu0; |
---|
43 | phxu = phxu0; |
---|
44 | |
---|
45 | set_dim( pfxu0->_dimx()); |
---|
46 | dimy = phxu0->dimension(); |
---|
47 | dimc = pfxu0->_dimu(); |
---|
48 | est.set_parameters( zeros(dimension()), eye(dimension()) ); |
---|
49 | |
---|
50 | A.set_size ( dimension(), dimension() ); |
---|
51 | C.set_size ( dimy, dimension() ); |
---|
52 | //initialize matrices A C, later, these will be only updated! |
---|
53 | pfxu->dfdx_cond ( est._mu(), zeros ( dimc ), A, true ); |
---|
54 | B.clear(); |
---|
55 | phxu->dfdx_cond ( est._mu(), zeros ( dimc ), C, true ); |
---|
56 | D.clear(); |
---|
57 | |
---|
58 | R = R0; |
---|
59 | Q = Q0; |
---|
60 | } |
---|
61 | |
---|
62 | void EKFfull::bayes ( const vec &yt, const vec &cond) { |
---|
63 | bdm_assert_debug ( yt.length() == ( dimy ), "EKFull::bayes wrong size of dt" ); |
---|
64 | bdm_assert_debug ( cond.length() == ( dimc ), "EKFull::bayes wrong size of dt" ); |
---|
65 | |
---|
66 | const vec &u = cond; |
---|
67 | const vec &y = yt; //lazy to change it |
---|
68 | vec &mu = est._mu(); |
---|
69 | mat &P = est._R(); |
---|
70 | mat& _Ry = fy._R(); |
---|
71 | vec& yp = fy._mu(); |
---|
72 | |
---|
73 | pfxu->dfdx_cond ( mu, zeros ( dimc ), A, true ); |
---|
74 | phxu->dfdx_cond ( mu, zeros ( dimc ), C, true ); |
---|
75 | |
---|
76 | //Time update |
---|
77 | mu = pfxu->eval ( mu, u );// A*mu + B*u; |
---|
78 | P = A * P * A.transpose() + (mat)Q; |
---|
79 | |
---|
80 | //Data update |
---|
81 | _Ry = C * P * C.transpose() + (mat)R; |
---|
82 | _K = P * C.transpose() * inv ( _Ry ); |
---|
83 | P -= _K * C * P; // P = P -KCP; |
---|
84 | yp = phxu->eval ( mu, u ); |
---|
85 | mu += _K * ( y - yp ); |
---|
86 | |
---|
87 | if ( BM::evalll ) { |
---|
88 | ll=fy.evallog(y); |
---|
89 | } |
---|
90 | }; |
---|
91 | |
---|
92 | |
---|
93 | |
---|
94 | void KalmanCh::set_parameters ( const mat &A0, const mat &B0, const mat &C0, const mat &D0, const chmat &Q0, const chmat &R0 ) { |
---|
95 | |
---|
96 | ( ( StateSpace<chmat>* ) this )->set_parameters ( A0, B0, C0, D0, Q0, R0 ); |
---|
97 | |
---|
98 | _K=zeros(dimension(),dimy); |
---|
99 | } |
---|
100 | |
---|
101 | void KalmanCh::initialize(){ |
---|
102 | preA = zeros ( dimy + dimension() + dimension(), dimy + dimension() ); |
---|
103 | // preA.clear(); |
---|
104 | preA.set_submatrix ( 0, 0, R._Ch() ); |
---|
105 | preA.set_submatrix ( dimy + dimension(), dimy, Q._Ch() ); |
---|
106 | } |
---|
107 | |
---|
108 | void KalmanCh::bayes ( const vec &yt, const vec &cond ) { |
---|
109 | bdm_assert_debug(yt.length()==dimy, "yt mismatch"); |
---|
110 | bdm_assert_debug(cond.length()==dimc, "yt mismatch"); |
---|
111 | |
---|
112 | const vec &u = cond; |
---|
113 | const vec &y = yt; |
---|
114 | vec pom ( dimy ); |
---|
115 | |
---|
116 | chmat &_P=est._R(); |
---|
117 | vec &_mu = est._mu(); |
---|
118 | mat _K(dimension(),dimy); |
---|
119 | chmat &_Ry=fy._R(); |
---|
120 | vec &_yp = fy._mu(); |
---|
121 | //TODO get rid of Q in qr()! |
---|
122 | // mat Q; |
---|
123 | |
---|
124 | //R and Q are already set in set_parameters() |
---|
125 | preA.set_submatrix ( dimy, 0, ( _P._Ch() ) *C.T() ); |
---|
126 | //Fixme can be more efficient if .T() is not used |
---|
127 | preA.set_submatrix ( dimy, dimy, ( _P._Ch() ) *A.T() ); |
---|
128 | |
---|
129 | if ( !qr ( preA, postA ) ) { |
---|
130 | bdm_warning ( "QR in KalmanCh unstable!" ); |
---|
131 | } |
---|
132 | |
---|
133 | ( _Ry._Ch() ) = postA ( 0, dimy - 1, 0, dimy - 1 ); |
---|
134 | _K = inv ( A ) * ( postA ( 0, dimy - 1 , dimy, dimy + dimension() - 1 ) ).T(); |
---|
135 | ( _P._Ch() ) = postA ( dimy, dimy + dimension() - 1, dimy, dimy + dimension() - 1 ); |
---|
136 | |
---|
137 | _mu = A * ( _mu ) + B * u; |
---|
138 | _yp = C * _mu - D * u; |
---|
139 | |
---|
140 | backward_substitution ( _Ry._Ch(), ( y - _yp ), pom ); |
---|
141 | _mu += ( _K ) * pom; |
---|
142 | |
---|
143 | /* cout << "P:" <<_P.to_mat() <<endl; |
---|
144 | cout << "Ry:" <<_Ry.to_mat() <<endl; |
---|
145 | cout << "_K:" <<_K <<endl;*/ |
---|
146 | |
---|
147 | if ( evalll == true ) { //likelihood of observation y |
---|
148 | ll = fy.evallog ( y ); |
---|
149 | } |
---|
150 | } |
---|
151 | |
---|
152 | |
---|
153 | |
---|
154 | void EKFCh::set_parameters ( const shared_ptr<diffbifn> &pfxu0, const shared_ptr<diffbifn> &phxu0, const chmat Q0, const chmat R0 ) { |
---|
155 | pfxu = pfxu0; |
---|
156 | phxu = phxu0; |
---|
157 | |
---|
158 | set_dim( pfxu0->_dimx()); |
---|
159 | dimy = phxu0->dimension(); |
---|
160 | dimc = pfxu0->_dimu(); |
---|
161 | |
---|
162 | vec &_mu = est._mu(); |
---|
163 | // if mu is not set, set it to zeros, just for constant terms of A and C |
---|
164 | if ( _mu.length() != dimension() ) _mu = zeros ( dimension() ); |
---|
165 | A = zeros ( dimension(), dimension() ); |
---|
166 | C = zeros ( dimy, dimension() ); |
---|
167 | preA = zeros ( dimy + dimension() + dimension(), dimy + dimension() ); |
---|
168 | |
---|
169 | //initialize matrices A C, later, these will be only updated! |
---|
170 | pfxu->dfdx_cond ( _mu, zeros ( dimc ), A, true ); |
---|
171 | // pfxu->dfdu_cond ( *_mu,zeros ( dimu ),B,true ); |
---|
172 | B.clear(); |
---|
173 | phxu->dfdx_cond ( _mu, zeros ( dimc ), C, true ); |
---|
174 | // phxu->dfdu_cond ( *_mu,zeros ( dimu ),D,true ); |
---|
175 | D.clear(); |
---|
176 | |
---|
177 | R = R0; |
---|
178 | Q = Q0; |
---|
179 | |
---|
180 | // Cholesky special! |
---|
181 | preA.clear(); |
---|
182 | preA.set_submatrix ( 0, 0, R._Ch() ); |
---|
183 | preA.set_submatrix ( dimy + dimension(), dimy, Q._Ch() ); |
---|
184 | } |
---|
185 | |
---|
186 | |
---|
187 | void EKFCh::bayes ( const vec &yt, const vec &cond ) { |
---|
188 | |
---|
189 | vec pom ( dimy ); |
---|
190 | const vec &u = cond; |
---|
191 | const vec &y = yt; |
---|
192 | vec &_mu = est._mu(); |
---|
193 | chmat &_P = est._R(); |
---|
194 | chmat &_Ry = fy._R(); |
---|
195 | vec &_yp = fy._mu(); |
---|
196 | |
---|
197 | pfxu->dfdx_cond ( _mu, u, A, false ); //update A by a derivative of fx |
---|
198 | phxu->dfdx_cond ( _mu, u, C, false ); //update A by a derivative of fx |
---|
199 | |
---|
200 | //R and Q are already set in set_parameters() |
---|
201 | preA.set_submatrix ( dimy, 0, ( _P._Ch() ) *C.T() ); |
---|
202 | //Fixme can be more efficient if .T() is not used |
---|
203 | preA.set_submatrix ( dimy, dimy, ( _P._Ch() ) *A.T() ); |
---|
204 | |
---|
205 | // mat Sttm = _P->to_mat(); |
---|
206 | // cout << preA <<endl; |
---|
207 | // cout << "_mu:" << _mu <<endl; |
---|
208 | |
---|
209 | if ( !qr ( preA, postA ) ) { |
---|
210 | bdm_warning ( "QR in EKFCh unstable!" ); |
---|
211 | } |
---|
212 | |
---|
213 | |
---|
214 | ( _Ry._Ch() ) = postA ( 0, dimy - 1, 0, dimy - 1 ); |
---|
215 | _K = inv ( A ) * ( postA ( 0, dimy - 1 , dimy, dimy + dimension() - 1 ) ).T(); |
---|
216 | ( _P._Ch() ) = postA ( dimy, dimy + dimension() - 1, dimy, dimy + dimension() - 1 ); |
---|
217 | |
---|
218 | // mat iRY = inv(_Ry->to_mat()); |
---|
219 | // mat Stt = Sttm - Sttm * C.T() * iRY * C * Sttm; |
---|
220 | // mat _K2 = Stt*C.T()*inv(R.to_mat()); |
---|
221 | |
---|
222 | // prediction |
---|
223 | _mu = pfxu->eval ( _mu , u ); |
---|
224 | _yp = phxu->eval ( _mu, u ); |
---|
225 | |
---|
226 | /* vec mu2 = *_mu + ( _K2 ) * ( y-*_yp );*/ |
---|
227 | |
---|
228 | //correction //= initial value is already prediction! |
---|
229 | backward_substitution ( _Ry._Ch(), ( y - _yp ), pom ); |
---|
230 | _mu += ( _K ) * pom ; |
---|
231 | |
---|
232 | /* _K = (_P->to_mat())*C.transpose() * ( _iRy->to_mat() ); |
---|
233 | *_mu = pfxu->eval ( *_mu ,u ) + ( _K )* ( y-*_yp );*/ |
---|
234 | |
---|
235 | // cout << "P:" <<_P.to_mat() <<endl; |
---|
236 | // cout << "Ry:" <<_Ry.to_mat() <<endl; |
---|
237 | // cout << "_mu:" <<_mu <<endl; |
---|
238 | // cout << "dt:" <<dt <<endl; |
---|
239 | |
---|
240 | if ( evalll == true ) { //likelihood of observation y |
---|
241 | ll = fy.evallog ( y ); |
---|
242 | } |
---|
243 | } |
---|
244 | |
---|
245 | void EKFCh::from_setting ( const Setting &set ) { |
---|
246 | BM::from_setting(set); |
---|
247 | shared_ptr<diffbifn> IM = UI::build<diffbifn> ( set, "IM", UI::compulsory ); |
---|
248 | shared_ptr<diffbifn> OM = UI::build<diffbifn> ( set, "OM", UI::compulsory ); |
---|
249 | |
---|
250 | //statistics |
---|
251 | int dim = IM->dimension(); |
---|
252 | vec mu0; |
---|
253 | if ( !UI::get ( mu0, set, "mu0" ) ) |
---|
254 | mu0 = zeros ( dim ); |
---|
255 | |
---|
256 | mat P0; |
---|
257 | vec dP0; |
---|
258 | if ( UI::get ( dP0, set, "dP0" ) ) |
---|
259 | P0 = diag ( dP0 ); |
---|
260 | else if ( !UI::get ( P0, set, "P0" ) ) |
---|
261 | P0 = eye ( dim ); |
---|
262 | |
---|
263 | set_statistics ( mu0, P0 ); |
---|
264 | |
---|
265 | //parameters |
---|
266 | vec dQ, dR; |
---|
267 | UI::get ( dQ, set, "dQ", UI::compulsory ); |
---|
268 | UI::get ( dR, set, "dR", UI::compulsory ); |
---|
269 | set_parameters ( IM, OM, diag ( dQ ), diag ( dR ) ); |
---|
270 | } |
---|
271 | |
---|
272 | void MultiModel::from_setting ( const Setting &set ) { |
---|
273 | Array<EKFCh*> A; |
---|
274 | UI::get ( A, set, "models", UI::compulsory ); |
---|
275 | |
---|
276 | set_parameters ( A ); |
---|
277 | set_yrv ( A ( 0 )->_yrv() ); |
---|
278 | //set_rv(A(0)->_rv()); |
---|
279 | |
---|
280 | string options; |
---|
281 | if ( set.lookupValue ( "options", options ) ) |
---|
282 | set_options ( options ); |
---|
283 | } |
---|
284 | |
---|
285 | } |
---|