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 | num2str(yt.length()) + ", expected size is " + num2str(dimy) ); |
---|
13 | bdm_assert_debug ( cond.length() == ( dimc ), "KalmanFull::bayes wrong size of cond, " + |
---|
14 | num2str(cond.length()) + ", expected size is " + num2str(dimc) ); |
---|
15 | |
---|
16 | const vec &u = cond; // in this case cond=ut |
---|
17 | const vec &y = yt; |
---|
18 | |
---|
19 | vec& mu = est._mu(); |
---|
20 | mat &P = est._R(); |
---|
21 | mat& _Ry = fy._R(); |
---|
22 | vec& yp = fy._mu(); |
---|
23 | //Time update |
---|
24 | mu = A * mu + B * u; |
---|
25 | P = A * P * A.transpose() + ( mat ) Q; |
---|
26 | |
---|
27 | //Data update |
---|
28 | _Ry = C * P * C.transpose() + ( mat ) R; |
---|
29 | _K = P * C.transpose() * inv ( _Ry ); |
---|
30 | P -= _K * C * P; // P = P -KCP; |
---|
31 | yp = C * mu + D * u; |
---|
32 | mu += _K * ( y - yp ); |
---|
33 | |
---|
34 | if ( evalll ) { |
---|
35 | ll = fy.evallog ( y ); |
---|
36 | } |
---|
37 | }; |
---|
38 | |
---|
39 | |
---|
40 | |
---|
41 | /////////////////////////////// EKFS |
---|
42 | EKFfull::EKFfull ( ) : KalmanFull () {}; |
---|
43 | |
---|
44 | void EKFfull::set_parameters ( const shared_ptr<diffbifn> &pfxu0, const shared_ptr<diffbifn> &phxu0, const mat Q0, const mat R0 ) { |
---|
45 | pfxu = pfxu0; |
---|
46 | phxu = phxu0; |
---|
47 | |
---|
48 | set_dim ( pfxu0->_dimx() ); |
---|
49 | dimy = phxu0->dimension(); |
---|
50 | dimc = pfxu0->_dimu(); |
---|
51 | est.set_parameters ( zeros ( dimension() ), eye ( dimension() ) ); |
---|
52 | |
---|
53 | A.set_size ( dimension(), dimension() ); |
---|
54 | C.set_size ( dimy, dimension() ); |
---|
55 | //initialize matrices A C, later, these will be only updated! |
---|
56 | pfxu->dfdx_cond ( est._mu(), zeros ( dimc ), A, true ); |
---|
57 | B.clear(); |
---|
58 | phxu->dfdx_cond ( est._mu(), zeros ( dimc ), C, true ); |
---|
59 | D.clear(); |
---|
60 | |
---|
61 | R = R0; |
---|
62 | Q = Q0; |
---|
63 | } |
---|
64 | |
---|
65 | void EKFfull::bayes ( const vec &yt, const vec &cond ) { |
---|
66 | bdm_assert_debug ( yt.length() == ( dimy ), "EKFull::bayes wrong size of dt" ); |
---|
67 | bdm_assert_debug ( cond.length() == ( dimc ), "EKFull::bayes wrong size of dt" ); |
---|
68 | |
---|
69 | const vec &u = cond; |
---|
70 | const vec &y = yt; //lazy to change it |
---|
71 | vec &mu = est._mu(); |
---|
72 | mat &P = est._R(); |
---|
73 | mat& _Ry = fy._R(); |
---|
74 | vec& yp = fy._mu(); |
---|
75 | |
---|
76 | pfxu->dfdx_cond ( mu, zeros ( dimc ), A, true ); |
---|
77 | phxu->dfdx_cond ( mu, zeros ( dimc ), C, true ); |
---|
78 | |
---|
79 | //Time update |
---|
80 | mu = pfxu->eval ( mu, u );// A*mu + B*u; |
---|
81 | P = A * P * A.transpose() + ( mat ) Q; |
---|
82 | |
---|
83 | //Data update |
---|
84 | _Ry = C * P * C.transpose() + ( mat ) R; |
---|
85 | _K = P * C.transpose() * inv ( _Ry ); |
---|
86 | P -= _K * C * P; // P = P -KCP; |
---|
87 | yp = phxu->eval ( mu, u ); |
---|
88 | mu += _K * ( y - yp ); |
---|
89 | |
---|
90 | if ( BM::evalll ) { |
---|
91 | ll = fy.evallog ( y ); |
---|
92 | } |
---|
93 | }; |
---|
94 | |
---|
95 | |
---|
96 | |
---|
97 | void KalmanCh::set_parameters ( const mat &A0, const mat &B0, const mat &C0, const mat &D0, const chmat &Q0, const chmat &R0 ) { |
---|
98 | |
---|
99 | ( ( StateSpace<chmat>* ) this )->set_parameters ( A0, B0, C0, D0, Q0, R0 ); |
---|
100 | |
---|
101 | _K = zeros ( dimension(), dimy ); |
---|
102 | } |
---|
103 | |
---|
104 | void KalmanCh::initialize() { |
---|
105 | preA = zeros ( dimy + dimension() + dimension(), dimy + dimension() ); |
---|
106 | // preA.clear(); |
---|
107 | preA.set_submatrix ( 0, 0, R._Ch() ); |
---|
108 | preA.set_submatrix ( dimy + dimension(), dimy, Q._Ch() ); |
---|
109 | } |
---|
110 | |
---|
111 | void KalmanCh::bayes ( const vec &yt, const vec &cond ) { |
---|
112 | bdm_assert_debug ( yt.length() == dimy, "yt mismatch" ); |
---|
113 | bdm_assert_debug ( cond.length() == dimc, "yt mismatch" ); |
---|
114 | |
---|
115 | const vec &u = cond; |
---|
116 | const vec &y = yt; |
---|
117 | vec pom ( dimy ); |
---|
118 | |
---|
119 | chmat &_P = est._R(); |
---|
120 | vec &_mu = est._mu(); |
---|
121 | mat _K ( dimension(), dimy ); |
---|
122 | chmat &_Ry = fy._R(); |
---|
123 | vec &_yp = fy._mu(); |
---|
124 | //TODO get rid of Q in qr()! |
---|
125 | // mat Q; |
---|
126 | |
---|
127 | //R and Q are already set in set_parameters() |
---|
128 | preA.set_submatrix ( dimy, 0, ( _P._Ch() ) *C.T() ); |
---|
129 | //Fixme can be more efficient if .T() is not used |
---|
130 | preA.set_submatrix ( dimy, dimy, ( _P._Ch() ) *A.T() ); |
---|
131 | |
---|
132 | if ( !qr ( preA, postA ) ) { |
---|
133 | bdm_warning ( "QR in KalmanCh unstable!" ); |
---|
134 | } |
---|
135 | |
---|
136 | ( _Ry._Ch() ) = postA ( 0, dimy - 1, 0, dimy - 1 ); |
---|
137 | _K = inv ( A ) * ( postA ( 0, dimy - 1 , dimy, dimy + dimension() - 1 ) ).T(); |
---|
138 | ( _P._Ch() ) = postA ( dimy, dimy + dimension() - 1, dimy, dimy + dimension() - 1 ); |
---|
139 | |
---|
140 | _mu = A * ( _mu ) + B * u; |
---|
141 | _yp = C * _mu - D * u; |
---|
142 | |
---|
143 | backward_substitution ( _Ry._Ch(), ( y - _yp ), pom ); |
---|
144 | _mu += ( _K ) * pom; |
---|
145 | |
---|
146 | /* cout << "P:" <<_P.to_mat() <<endl; |
---|
147 | cout << "Ry:" <<_Ry.to_mat() <<endl; |
---|
148 | cout << "_K:" <<_K <<endl;*/ |
---|
149 | |
---|
150 | if ( evalll == true ) { //likelihood of observation y |
---|
151 | ll = fy.evallog ( y ); |
---|
152 | } |
---|
153 | } |
---|
154 | |
---|
155 | void StateCanonical::connect_mlnorm ( const mlnorm<fsqmat> &ml ) { |
---|
156 | //get ids of yrv |
---|
157 | const RV &yrv = ml._rv(); |
---|
158 | //need to determine u_t - it is all in _rvc that is not in ml._rv() |
---|
159 | RV rgr0 = ml._rvc().remove_time(); |
---|
160 | RV urv = rgr0.subt ( yrv ); |
---|
161 | |
---|
162 | //We can do only 1d now... :( |
---|
163 | bdm_assert ( yrv._dsize() == 1, "Only for SISO so far..." ); |
---|
164 | |
---|
165 | // create names for |
---|
166 | RV xrv; //empty |
---|
167 | RV Crv; //empty |
---|
168 | int td = ml._rvc().mint(); |
---|
169 | // assuming strictly proper function!!! |
---|
170 | for ( int t = -1; t >= td; t-- ) { |
---|
171 | xrv.add ( yrv.copy_t ( t ) ); |
---|
172 | Crv.add ( urv.copy_t ( t ) ); |
---|
173 | } |
---|
174 | |
---|
175 | // get mapp |
---|
176 | th2A.set_connection ( xrv, ml._rvc() ); |
---|
177 | th2C.set_connection ( Crv, ml._rvc() ); |
---|
178 | th2D.set_connection ( urv, ml._rvc() ); |
---|
179 | |
---|
180 | //set matrix sizes |
---|
181 | this->A = zeros ( xrv._dsize(), xrv._dsize() ); |
---|
182 | for ( int j = 1; j < xrv._dsize(); j++ ) { |
---|
183 | A ( j, j - 1 ) = 1.0; // off diagonal |
---|
184 | } |
---|
185 | this->B = zeros ( xrv._dsize(), 1 ); |
---|
186 | this->B ( 0 ) = 1.0; |
---|
187 | this->C = zeros ( 1, xrv._dsize() ); |
---|
188 | this->D = zeros ( 1, urv._dsize() ); |
---|
189 | this->Q = zeros ( xrv._dsize(), xrv._dsize() ); |
---|
190 | // R is set by update |
---|
191 | |
---|
192 | //set cache |
---|
193 | this->A1row = zeros ( xrv._dsize() ); |
---|
194 | this->C1row = zeros ( xrv._dsize() ); |
---|
195 | this->D1row = zeros ( urv._dsize() ); |
---|
196 | |
---|
197 | update_from ( ml ); |
---|
198 | validate(); |
---|
199 | }; |
---|
200 | |
---|
201 | void StateCanonical::update_from ( const mlnorm<fsqmat> &ml ) { |
---|
202 | |
---|
203 | vec theta = ml._A().get_row ( 0 ); // this |
---|
204 | |
---|
205 | th2A.filldown ( theta, A1row ); |
---|
206 | th2C.filldown ( theta, C1row ); |
---|
207 | th2D.filldown ( theta, D1row ); |
---|
208 | |
---|
209 | R = ml._R(); |
---|
210 | |
---|
211 | A.set_row ( 0, A1row ); |
---|
212 | C.set_row ( 0, C1row + D1row ( 0 ) *A1row ); |
---|
213 | D.set_row ( 0, D1row ); |
---|
214 | } |
---|
215 | |
---|
216 | void StateFromARX::connect_mlnorm ( const mlnorm<chmat> &ml, RV &xrv, RV &urv ) { |
---|
217 | //get ids of yrv |
---|
218 | const RV &yrv = ml._rv(); |
---|
219 | //need to determine u_t - it is all in _rvc that is not in ml._rv() |
---|
220 | const RV &rgr = ml._rvc(); |
---|
221 | RV rgr0 = rgr.remove_time(); |
---|
222 | urv = rgr0.subt ( yrv ); |
---|
223 | |
---|
224 | // create names for state variables |
---|
225 | xrv = yrv; |
---|
226 | |
---|
227 | int y_multiplicity = -rgr.mint ( yrv ); |
---|
228 | int y_block_size = yrv.length() * ( y_multiplicity ); // current yt + all delayed yts |
---|
229 | for ( int m = 0; m < y_multiplicity - 1; m++ ) { // ========= -1 is important see arx2statespace_notes |
---|
230 | xrv.add ( yrv.copy_t ( -m - 1 ) ); //add delayed yt |
---|
231 | } |
---|
232 | //! temporary RV for connection to ml.rvc, since notation of xrv and ml.rvc does not match |
---|
233 | RV xrv_ml = xrv.copy_t ( -1 ); |
---|
234 | |
---|
235 | // add regressors |
---|
236 | ivec u_block_sizes ( urv.length() ); // no_blocks = yt + unique rgr |
---|
237 | for ( int r = 0; r < urv.length(); r++ ) { |
---|
238 | RV R = urv.subselect ( vec_1 ( r ) ); //non-delayed element of rgr |
---|
239 | int r_size = urv.size ( r ); |
---|
240 | int r_multiplicity = -rgr.mint ( R ); |
---|
241 | u_block_sizes ( r ) = r_size * r_multiplicity ; |
---|
242 | for ( int m = 0; m < r_multiplicity; m++ ) { |
---|
243 | xrv.add ( R.copy_t ( -m - 1 ) ); //add delayed yt |
---|
244 | xrv_ml.add ( R.copy_t ( -m - 1 ) ); //add delayed yt |
---|
245 | } |
---|
246 | } |
---|
247 | // add constant |
---|
248 | if ( any ( ml._mu_const() != 0.0 ) ) { |
---|
249 | have_constant = true; |
---|
250 | xrv.add ( RV ( "bdm_reserved_constant_one", 1 ) ); |
---|
251 | } else { |
---|
252 | have_constant = false; |
---|
253 | } |
---|
254 | |
---|
255 | |
---|
256 | // get mapp |
---|
257 | th2A.set_connection ( xrv_ml, ml._rvc() ); |
---|
258 | th2B.set_connection ( urv, ml._rvc() ); |
---|
259 | |
---|
260 | //set matrix sizes |
---|
261 | this->A = zeros ( xrv._dsize(), xrv._dsize() ); |
---|
262 | //create y block |
---|
263 | diagonal_part ( this->A, yrv._dsize(), 0, y_block_size - yrv._dsize() ); |
---|
264 | |
---|
265 | this->B = zeros ( xrv._dsize(), urv._dsize() ); |
---|
266 | //add diagonals for rgr |
---|
267 | int active_x = y_block_size; |
---|
268 | int active_Bcol = 0; |
---|
269 | for ( int r = 0; r < urv.length(); r++ ) { |
---|
270 | if (u_block_sizes(r)>0) { |
---|
271 | diagonal_part ( this->A, active_x + urv.size ( r ), active_x, u_block_sizes ( r ) - urv.size ( r ) ); |
---|
272 | this->B.set_submatrix ( active_x, active_Bcol, eye ( urv.size ( r ) ) ); |
---|
273 | active_Bcol+=u_block_sizes(r); |
---|
274 | } |
---|
275 | active_x += u_block_sizes ( r ); |
---|
276 | } |
---|
277 | this->C = zeros ( yrv._dsize(), xrv._dsize() ); |
---|
278 | this->C.set_submatrix ( 0, 0, eye ( yrv._dsize() ) ); |
---|
279 | this->D = zeros ( yrv._dsize(), urv._dsize() ); |
---|
280 | this->R.setCh ( zeros ( yrv._dsize(), yrv._dsize() ) ); |
---|
281 | this->Q.setCh ( zeros ( xrv._dsize(), xrv._dsize() ) ); |
---|
282 | // Q is set by update |
---|
283 | |
---|
284 | update_from ( ml ); |
---|
285 | validate(); |
---|
286 | } |
---|
287 | |
---|
288 | void StateFromARX::update_from ( const mlnorm<chmat> &ml ) { |
---|
289 | vec Arow = zeros ( A.cols() ); |
---|
290 | vec Brow = zeros ( B.cols() ); |
---|
291 | // ROW- WISE EVALUATION ===== |
---|
292 | for ( int i = 0; i < ml._rv()._dsize(); i++ ) { |
---|
293 | |
---|
294 | vec theta = ml._A().get_row ( i ); |
---|
295 | |
---|
296 | th2A.filldown ( theta, Arow ); |
---|
297 | if ( have_constant ) { |
---|
298 | // constant is always at the end no need for datalink |
---|
299 | Arow ( A.cols() - 1 ) = ml._mu_const() ( i ); |
---|
300 | } |
---|
301 | this->A.set_row ( i, Arow ); |
---|
302 | |
---|
303 | th2B.filldown ( theta, Brow ); |
---|
304 | this->B.set_row ( i, Brow ); |
---|
305 | } |
---|
306 | this->Q._Ch().set_submatrix ( 0, 0, ml.__R()._Ch() ); |
---|
307 | |
---|
308 | } |
---|
309 | |
---|
310 | |
---|
311 | void EKFCh::set_parameters ( const shared_ptr<diffbifn> &pfxu0, const shared_ptr<diffbifn> &phxu0, const chmat Q0, const chmat R0 ) { |
---|
312 | pfxu = pfxu0; |
---|
313 | phxu = phxu0; |
---|
314 | |
---|
315 | set_dim ( pfxu0->_dimx() ); |
---|
316 | dimy = phxu0->dimension(); |
---|
317 | dimc = pfxu0->_dimu(); |
---|
318 | |
---|
319 | vec &_mu = est._mu(); |
---|
320 | // if mu is not set, set it to zeros, just for constant terms of A and C |
---|
321 | if ( _mu.length() != dimension() ) _mu = zeros ( dimension() ); |
---|
322 | A = zeros ( dimension(), dimension() ); |
---|
323 | C = zeros ( dimy, dimension() ); |
---|
324 | preA = zeros ( dimy + dimension() + dimension(), dimy + dimension() ); |
---|
325 | |
---|
326 | //initialize matrices A C, later, these will be only updated! |
---|
327 | pfxu->dfdx_cond ( _mu, zeros ( dimc ), A, true ); |
---|
328 | // pfxu->dfdu_cond ( *_mu,zeros ( dimu ),B,true ); |
---|
329 | B.clear(); |
---|
330 | phxu->dfdx_cond ( _mu, zeros ( dimc ), C, true ); |
---|
331 | // phxu->dfdu_cond ( *_mu,zeros ( dimu ),D,true ); |
---|
332 | D.clear(); |
---|
333 | |
---|
334 | R = R0; |
---|
335 | Q = Q0; |
---|
336 | |
---|
337 | // Cholesky special! |
---|
338 | preA.clear(); |
---|
339 | preA.set_submatrix ( 0, 0, R._Ch() ); |
---|
340 | preA.set_submatrix ( dimy + dimension(), dimy, Q._Ch() ); |
---|
341 | } |
---|
342 | |
---|
343 | |
---|
344 | void EKFCh::bayes ( const vec &yt, const vec &cond ) { |
---|
345 | |
---|
346 | vec pom ( dimy ); |
---|
347 | const vec &u = cond; |
---|
348 | const vec &y = yt; |
---|
349 | vec &_mu = est._mu(); |
---|
350 | chmat &_P = est._R(); |
---|
351 | chmat &_Ry = fy._R(); |
---|
352 | vec &_yp = fy._mu(); |
---|
353 | |
---|
354 | pfxu->dfdx_cond ( _mu, u, A, false ); //update A by a derivative of fx |
---|
355 | phxu->dfdx_cond ( _mu, u, C, false ); //update A by a derivative of fx |
---|
356 | |
---|
357 | //R and Q are already set in set_parameters() |
---|
358 | preA.set_submatrix ( dimy, 0, ( _P._Ch() ) *C.T() ); |
---|
359 | //Fixme can be more efficient if .T() is not used |
---|
360 | preA.set_submatrix ( dimy, dimy, ( _P._Ch() ) *A.T() ); |
---|
361 | |
---|
362 | // mat Sttm = _P->to_mat(); |
---|
363 | // cout << preA <<endl; |
---|
364 | // cout << "_mu:" << _mu <<endl; |
---|
365 | |
---|
366 | if ( !qr ( preA, postA ) ) { |
---|
367 | bdm_warning ( "QR in EKFCh unstable!" ); |
---|
368 | } |
---|
369 | |
---|
370 | |
---|
371 | ( _Ry._Ch() ) = postA ( 0, dimy - 1, 0, dimy - 1 ); |
---|
372 | _K = inv ( A ) * ( postA ( 0, dimy - 1 , dimy, dimy + dimension() - 1 ) ).T(); |
---|
373 | ( _P._Ch() ) = postA ( dimy, dimy + dimension() - 1, dimy, dimy + dimension() - 1 ); |
---|
374 | |
---|
375 | // mat iRY = inv(_Ry->to_mat()); |
---|
376 | // mat Stt = Sttm - Sttm * C.T() * iRY * C * Sttm; |
---|
377 | // mat _K2 = Stt*C.T()*inv(R.to_mat()); |
---|
378 | |
---|
379 | // prediction |
---|
380 | _mu = pfxu->eval ( _mu , u ); |
---|
381 | _yp = phxu->eval ( _mu, u ); |
---|
382 | |
---|
383 | /* vec mu2 = *_mu + ( _K2 ) * ( y-*_yp );*/ |
---|
384 | |
---|
385 | //correction //= initial value is already prediction! |
---|
386 | backward_substitution ( _Ry._Ch(), ( y - _yp ), pom ); |
---|
387 | _mu += ( _K ) * pom ; |
---|
388 | |
---|
389 | /* _K = (_P->to_mat())*C.transpose() * ( _iRy->to_mat() ); |
---|
390 | *_mu = pfxu->eval ( *_mu ,u ) + ( _K )* ( y-*_yp );*/ |
---|
391 | |
---|
392 | // cout << "P:" <<_P.to_mat() <<endl; |
---|
393 | // cout << "Ry:" <<_Ry.to_mat() <<endl; |
---|
394 | // cout << "_mu:" <<_mu <<endl; |
---|
395 | // cout << "dt:" <<dt <<endl; |
---|
396 | |
---|
397 | if ( evalll == true ) { //likelihood of observation y |
---|
398 | ll = fy.evallog ( y ); |
---|
399 | } |
---|
400 | } |
---|
401 | |
---|
402 | void EKFCh::from_setting ( const Setting &set ) { |
---|
403 | BM::from_setting ( set ); |
---|
404 | shared_ptr<diffbifn> IM = UI::build<diffbifn> ( set, "IM", UI::compulsory ); |
---|
405 | shared_ptr<diffbifn> OM = UI::build<diffbifn> ( set, "OM", UI::compulsory ); |
---|
406 | |
---|
407 | //statistics |
---|
408 | int dim = IM->dimension(); |
---|
409 | vec mu0; |
---|
410 | if ( !UI::get ( mu0, set, "mu0" ) ) |
---|
411 | mu0 = zeros ( dim ); |
---|
412 | |
---|
413 | mat P0; |
---|
414 | vec dP0; |
---|
415 | if ( UI::get ( dP0, set, "dP0" ) ) |
---|
416 | P0 = diag ( dP0 ); |
---|
417 | else if ( !UI::get ( P0, set, "P0" ) ) |
---|
418 | P0 = eye ( dim ); |
---|
419 | |
---|
420 | set_statistics ( mu0, P0 ); |
---|
421 | |
---|
422 | //parameters |
---|
423 | vec dQ, dR; |
---|
424 | UI::get ( dQ, set, "dQ", UI::compulsory ); |
---|
425 | UI::get ( dR, set, "dR", UI::compulsory ); |
---|
426 | set_parameters ( IM, OM, diag ( dQ ), diag ( dR ) ); |
---|
427 | } |
---|
428 | |
---|
429 | void MultiModel::from_setting ( const Setting &set ) { |
---|
430 | Array<EKFCh*> A; |
---|
431 | UI::get ( A, set, "models", UI::compulsory ); |
---|
432 | |
---|
433 | set_parameters ( A ); |
---|
434 | set_yrv ( A ( 0 )->_yrv() ); |
---|
435 | //set_rv(A(0)->_rv()); |
---|
436 | } |
---|
437 | |
---|
438 | void EKF_UD::set_parameters ( const shared_ptr<diffbifn> &pfxu0, const shared_ptr<diffbifn> &phxu0, const mat Q0, const vec R0 ) { |
---|
439 | pfxu = pfxu0; |
---|
440 | phxu = phxu0; |
---|
441 | |
---|
442 | set_dim ( pfxu0->_dimx() ); |
---|
443 | dimy = phxu0->dimension(); |
---|
444 | dimc = pfxu0->_dimu(); |
---|
445 | |
---|
446 | vec &_mu = est._mu(); |
---|
447 | // if mu is not set, set it to zeros, just for constant terms of A and C |
---|
448 | if ( _mu.length() != dimension() ) _mu = zeros ( dimension() ); |
---|
449 | A = zeros ( dimension(), dimension() ); |
---|
450 | C = zeros ( dimy, dimension() ); |
---|
451 | |
---|
452 | //initialize matrices A C, later, these will be only updated! |
---|
453 | pfxu->dfdx_cond ( _mu, zeros ( dimc ), A, true ); |
---|
454 | // pfxu->dfdu_cond ( *_mu,zeros ( dimu ),B,true ); |
---|
455 | phxu->dfdx_cond ( _mu, zeros ( dimc ), C, true ); |
---|
456 | // phxu->dfdu_cond ( *_mu,zeros ( dimu ),D,true ); |
---|
457 | |
---|
458 | R = R0; |
---|
459 | Q = Q0; |
---|
460 | |
---|
461 | // |
---|
462 | } |
---|
463 | |
---|
464 | |
---|
465 | void EKF_UD::bayes ( const vec &yt, const vec &cond ) { |
---|
466 | //preparatory |
---|
467 | vec &_mu=est._mu(); |
---|
468 | const vec &u=cond; |
---|
469 | int dim = dimension(); |
---|
470 | |
---|
471 | U = est._R()._L().T(); |
---|
472 | D = est._R()._D(); |
---|
473 | |
---|
474 | //////////// |
---|
475 | |
---|
476 | pfxu->dfdx_cond ( _mu, u, A, false ); //update A by a derivative of fx |
---|
477 | phxu->dfdx_cond ( _mu, u, C, false ); //update A by a derivative of fx |
---|
478 | |
---|
479 | mat PhiU = A*U; |
---|
480 | |
---|
481 | vec Din = D; |
---|
482 | int i,j,k; |
---|
483 | double sigma; |
---|
484 | mat G = eye(dim); |
---|
485 | //////// thorton |
---|
486 | |
---|
487 | //move mean; |
---|
488 | _mu = pfxu->eval(_mu,u); |
---|
489 | |
---|
490 | for (i=dim-1; i>=0;i--){ |
---|
491 | sigma = 0.0; |
---|
492 | for (j=0; j<dim; j++) { |
---|
493 | sigma += PhiU(i,j)*PhiU(i,j) *Din(j); |
---|
494 | sigma += G(i,j)*G(i,j) * Q(j,j); |
---|
495 | } |
---|
496 | D(i) = sigma; |
---|
497 | /////////////// !!!!!!!!!!!!! |
---|
498 | if (D(i) > 1579000) D(i) =1579000; |
---|
499 | |
---|
500 | for (j=0;j<i;j++){ |
---|
501 | sigma = 0.0; |
---|
502 | for (k=0;k<dim;k++){ |
---|
503 | sigma += PhiU(i,k)*Din(k)*PhiU(j,k); |
---|
504 | } |
---|
505 | for (k=0;k<dim;k++){ |
---|
506 | sigma += G(i,k)*Q(k,k)*G(j,k); |
---|
507 | } |
---|
508 | // |
---|
509 | U(j,i) = sigma/D(i); |
---|
510 | for (k=0;k<dim;k++){ |
---|
511 | PhiU(j,k) = PhiU(j,k) - U(j,i)*PhiU(i,k); |
---|
512 | } |
---|
513 | for (k=0;k<dim;k++){ |
---|
514 | G(j,k) = G(j,k) - U(j,i)*G(i,k); |
---|
515 | } |
---|
516 | } |
---|
517 | } |
---|
518 | |
---|
519 | if ( log_level[logU] ){ |
---|
520 | // transformed U |
---|
521 | mat tU; |
---|
522 | mat P= U*diag(D)*U.T(); |
---|
523 | |
---|
524 | vec xref(4); |
---|
525 | xref(0)= 30.0*1.4142 *4.; |
---|
526 | xref(1)= 30.0*1.4142 *4.; |
---|
527 | xref(2)= 6.283185*200.*4.; |
---|
528 | xref(3) = 3.141593; |
---|
529 | //xref(4) = 34.0; |
---|
530 | |
---|
531 | mat T = diag(1.0/(xref)); |
---|
532 | mat Pf = T*P*T; |
---|
533 | |
---|
534 | mat TQT = T*Q*T; |
---|
535 | |
---|
536 | ldmat Pld(Pf); |
---|
537 | |
---|
538 | //vec tmp=vec(U._data(),dimension()*dimension()); |
---|
539 | vec tmp=vec(Pld._L()._data(),dimension()*dimension()); |
---|
540 | log_level.store(logU,round(((int)1<<15)*tmp)); |
---|
541 | log_level.store(logD,(Pld._D()*(1<<15))); |
---|
542 | |
---|
543 | mat Atr=T*A*diag(xref)*(1<<15); |
---|
544 | mat Att=Atr.T(); |
---|
545 | vec vA(Att._data(), dimension()*dimension()); |
---|
546 | log_level.store(logA,vA); |
---|
547 | |
---|
548 | } |
---|
549 | if ( log_level[logG] ){ |
---|
550 | vec tmp=vec(G._data(),dimension()*dimension()); |
---|
551 | log_level.store(logG,tmp); |
---|
552 | } |
---|
553 | //cout << "Ut: " << U << endl; |
---|
554 | //cout << "Dt: " << D << endl; |
---|
555 | // bierman |
---|
556 | |
---|
557 | double dz,alpha,gamma,beta,lambda; |
---|
558 | vec a; |
---|
559 | vec b; |
---|
560 | vec yp = phxu->eval(_mu,u); |
---|
561 | for (int iy=0; iy<dimy; iy++){ |
---|
562 | a = U.T()*C.get_row(iy); // a is not modified, but |
---|
563 | b = elem_mult(D,a); // b is modified to become unscaled Kalman gain. |
---|
564 | dz = yt(iy) - yp(iy); |
---|
565 | |
---|
566 | alpha = R(iy); |
---|
567 | gamma = 1/alpha; |
---|
568 | for (j=0;j<dim;j++){ |
---|
569 | beta = alpha; |
---|
570 | alpha = alpha + a(j)*b(j); |
---|
571 | lambda = -a(j)*gamma; |
---|
572 | gamma = 1.0/alpha; |
---|
573 | D(j) = beta*gamma*D(j); |
---|
574 | |
---|
575 | // cout << "a: " << alpha << "g: " << gamma << endl; |
---|
576 | for (i=0;i<j;i++){ |
---|
577 | beta = U(i,j); |
---|
578 | U(i,j) = beta + b(i)*lambda; |
---|
579 | b(i) = b(i) + b(j)*beta; |
---|
580 | } |
---|
581 | } |
---|
582 | double dzs = gamma*dz; // apply scaling to innovations |
---|
583 | _mu = _mu + dzs*b; // multiply by unscaled Kalman gain |
---|
584 | |
---|
585 | //cout << "Ub: " << U << endl; |
---|
586 | //cout << "Db: " << D << endl <<endl; |
---|
587 | |
---|
588 | } |
---|
589 | |
---|
590 | ///// |
---|
591 | est._R().__L()=U.T(); |
---|
592 | est._R().__D()=D; |
---|
593 | |
---|
594 | if ( evalll == true ) { //likelihood of observation y |
---|
595 | } |
---|
596 | } |
---|
597 | |
---|
598 | void EKF_UD::from_setting ( const Setting &set ) { |
---|
599 | BM::from_setting ( set ); |
---|
600 | shared_ptr<diffbifn> IM = UI::build<diffbifn> ( set, "IM", UI::compulsory ); |
---|
601 | shared_ptr<diffbifn> OM = UI::build<diffbifn> ( set, "OM", UI::compulsory ); |
---|
602 | |
---|
603 | //statistics |
---|
604 | int dim = IM->dimension(); |
---|
605 | vec mu0; |
---|
606 | if ( !UI::get ( mu0, set, "mu0" ) ) |
---|
607 | mu0 = zeros ( dim ); |
---|
608 | |
---|
609 | mat P0; |
---|
610 | vec dP0; |
---|
611 | if ( UI::get ( dP0, set, "dP0" ) ) |
---|
612 | P0 = diag ( dP0 ); |
---|
613 | else if ( !UI::get ( P0, set, "P0" ) ) |
---|
614 | P0 = eye ( dim ); |
---|
615 | |
---|
616 | est._mu()=mu0; |
---|
617 | est._R()=ldmat(P0); |
---|
618 | |
---|
619 | //parameters |
---|
620 | vec dQ, dR; |
---|
621 | UI::get ( dQ, set, "dQ", UI::compulsory ); |
---|
622 | UI::get ( dR, set, "dR", UI::compulsory ); |
---|
623 | set_parameters ( IM, OM, diag ( dQ ), dR ); |
---|
624 | |
---|
625 | UI::get(log_level, set, "log_level", UI::optional); |
---|
626 | } |
---|
627 | |
---|
628 | } |
---|