source: ntrip/trunk/BNC/bncmodel.cpp@ 3287

Last change on this file since 3287 was 3287, checked in by mervart, 13 years ago
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1// Part of BNC, a utility for retrieving decoding and
2// converting GNSS data streams from NTRIP broadcasters.
3//
4// Copyright (C) 2007
5// German Federal Agency for Cartography and Geodesy (BKG)
6// http://www.bkg.bund.de
7// Czech Technical University Prague, Department of Geodesy
8// http://www.fsv.cvut.cz
9//
10// Email: euref-ip@bkg.bund.de
11//
12// This program is free software; you can redistribute it and/or
13// modify it under the terms of the GNU General Public License
14// as published by the Free Software Foundation, version 2.
15//
16// This program is distributed in the hope that it will be useful,
17// but WITHOUT ANY WARRANTY; without even the implied warranty of
18// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
19// GNU General Public License for more details.
20//
21// You should have received a copy of the GNU General Public License
22// along with this program; if not, write to the Free Software
23// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
24
25/* -------------------------------------------------------------------------
26 * BKG NTRIP Client
27 * -------------------------------------------------------------------------
28 *
29 * Class: bncParam, bncModel
30 *
31 * Purpose: Model for PPP
32 *
33 * Author: L. Mervart
34 *
35 * Created: 01-Dec-2009
36 *
37 * Changes:
38 *
39 * -----------------------------------------------------------------------*/
40
41#include <iomanip>
42#include <cmath>
43#include <newmatio.h>
44#include <sstream>
45
46#include "bncmodel.h"
47#include "bncapp.h"
48#include "bncpppclient.h"
49#include "bancroft.h"
50#include "bncutils.h"
51#include "bncsettings.h"
52#include "bnctides.h"
53#include "bncantex.h"
54
55using namespace std;
56
57const unsigned MINOBS = 4;
58const double MINELE_GPS = 10.0 * M_PI / 180.0;
59const double MINELE_GLO = 10.0 * M_PI / 180.0;
60const double MINELE_GAL = 10.0 * M_PI / 180.0;
61const double MAXRES_CODE_GPS = 10.0;
62const double MAXRES_PHASE_GPS = 0.10;
63const double MAXRES_PHASE_GLO = 0.05;
64const double MAXRES_CODE_GAL = 10.0;
65const double MAXRES_PHASE_GAL = 0.10;
66
67// Constructor
68////////////////////////////////////////////////////////////////////////////
69bncParam::bncParam(bncParam::parType typeIn, int indexIn,
70 const QString& prnIn) {
71 type = typeIn;
72 index = indexIn;
73 prn = prnIn;
74 index_old = 0;
75 xx = 0.0;
76
77}
78
79// Destructor
80////////////////////////////////////////////////////////////////////////////
81bncParam::~bncParam() {
82}
83
84// Partial
85////////////////////////////////////////////////////////////////////////////
86double bncParam::partial(t_satData* satData, bool phase) {
87
88 // Coordinates
89 // -----------
90 if (type == CRD_X) {
91 return (xx - satData->xx(1)) / satData->rho;
92 }
93 else if (type == CRD_Y) {
94 return (xx - satData->xx(2)) / satData->rho;
95 }
96 else if (type == CRD_Z) {
97 return (xx - satData->xx(3)) / satData->rho;
98 }
99
100 // Receiver Clocks
101 // ---------------
102 else if (type == RECCLK) {
103 return 1.0;
104 }
105
106 // Troposphere
107 // -----------
108 else if (type == TROPO) {
109 return 1.0 / sin(satData->eleSat);
110 }
111
112 // Galileo Offset
113 // --------------
114 else if (type == GALILEO_OFFSET) {
115 if (satData->prn[0] == 'E') {
116 return 1.0;
117 }
118 else {
119 return 0.0;
120 }
121 }
122
123 // Ambiguities
124 // -----------
125 else if (type == AMB_L3) {
126 if (phase && satData->prn == prn) {
127 return 1.0;
128 }
129 else {
130 return 0.0;
131 }
132 }
133
134 // Default return
135 // --------------
136 return 0.0;
137}
138
139// Constructor
140////////////////////////////////////////////////////////////////////////////
141bncModel::bncModel(QByteArray staID) {
142
143 _staID = staID;
144
145 connect(this, SIGNAL(newMessage(QByteArray,bool)),
146 ((bncApp*)qApp), SLOT(slotMessage(const QByteArray,bool)));
147
148 bncSettings settings;
149
150 // Observation Sigmas
151 // ------------------
152 _sigP3 = 5.0;
153 if (!settings.value("pppSigmaCode").toString().isEmpty()) {
154 _sigP3 = settings.value("pppSigmaCode").toDouble();
155 }
156 _sigL3 = 0.02;
157 if (!settings.value("pppSigmaPhase").toString().isEmpty()) {
158 _sigL3 = settings.value("pppSigmaPhase").toDouble();
159 }
160
161 // Parameter Sigmas
162 // ----------------
163 _sigCrd0 = 100.0;
164 if (!settings.value("pppSigCrd0").toString().isEmpty()) {
165 _sigCrd0 = settings.value("pppSigCrd0").toDouble();
166 }
167 _sigCrdP = 100.0;
168 if (!settings.value("pppSigCrdP").toString().isEmpty()) {
169 _sigCrdP = settings.value("pppSigCrdP").toDouble();
170 }
171 _sigTrp0 = 0.1;
172 if (!settings.value("pppSigTrp0").toString().isEmpty()) {
173 _sigTrp0 = settings.value("pppSigTrp0").toDouble();
174 }
175 _sigTrpP = 1e-6;
176 if (!settings.value("pppSigTrpP").toString().isEmpty()) {
177 _sigTrpP = settings.value("pppSigTrpP").toDouble();
178 }
179 _sigClk0 = 1000.0;
180 _sigAmb0 = 1000.0;
181 _sigGalileoOffset0 = 1000.0;
182 _sigGalileoOffsetP = 0.0;
183
184 // Quick-Start Mode
185 // ----------------
186 _quickStart = 0;
187 if (settings.value("pppRefCrdX").toString() != "" &&
188 settings.value("pppRefCrdY").toString() != "" &&
189 settings.value("pppRefCrdZ").toString() != "" &&
190 !settings.value("pppQuickStart").toString().isEmpty()) {
191 _quickStart = settings.value("pppQuickStart").toDouble();
192 }
193
194 // Several options
195 // ---------------
196 _usePhase = false;
197 if ( Qt::CheckState(settings.value("pppUsePhase").toInt()) == Qt::Checked) {
198 _usePhase = true;
199 }
200
201 _estTropo = false;
202 if ( Qt::CheckState(settings.value("pppEstTropo").toInt()) == Qt::Checked) {
203 _estTropo = true;
204 }
205
206 _useGalileo = false;
207 if ( Qt::CheckState(settings.value("pppGalileo").toInt()) == Qt::Checked) {
208 _useGalileo = true;
209 }
210
211 // NMEA Output
212 // -----------
213 QString nmeaFileName = settings.value("nmeaFile").toString();
214 if (nmeaFileName.isEmpty()) {
215 _nmeaFile = 0;
216 _nmeaStream = 0;
217 }
218 else {
219 expandEnvVar(nmeaFileName);
220 _nmeaFile = new QFile(nmeaFileName);
221 if ( Qt::CheckState(settings.value("rnxAppend").toInt()) == Qt::Checked) {
222 _nmeaFile->open(QIODevice::WriteOnly | QIODevice::Append);
223 }
224 else {
225 _nmeaFile->open(QIODevice::WriteOnly);
226 }
227 _nmeaStream = new QTextStream();
228 _nmeaStream->setDevice(_nmeaFile);
229 }
230
231 // Antenna Name, ANTEX File
232 // ------------------------
233 _antex = 0;
234 QString antexFileName = settings.value("pppAntex").toString();
235 if (!antexFileName.isEmpty()) {
236 _antex = new bncAntex();
237 if (_antex->readFile(antexFileName) != success) {
238 emit newMessage("wrong ANTEX file", true);
239 delete _antex;
240 _antex = 0;
241 }
242 else {
243 _antennaName = settings.value("pppAntenna").toString();
244 }
245 }
246
247 // Antenna Eccentricities
248 // ----------------------
249 _dN = settings.value("pppRefdN").toDouble();
250 _dE = settings.value("pppRefdE").toDouble();
251 _dU = settings.value("pppRefdU").toDouble();
252
253 // Bancroft Coordinates
254 // --------------------
255 _xcBanc.ReSize(4); _xcBanc = 0.0;
256 _ellBanc.ReSize(3); _ellBanc = 0.0;
257}
258
259// Destructor
260////////////////////////////////////////////////////////////////////////////
261bncModel::~bncModel() {
262 delete _nmeaStream;
263 delete _nmeaFile;
264 for (int ii = 0; ii < _posAverage.size(); ++ii) {
265 delete _posAverage[ii];
266 }
267 delete _antex;
268 for (int iPar = 1; iPar <= _params.size(); iPar++) {
269 delete _params[iPar-1];
270 }
271}
272
273// Reset Parameters and Variance-Covariance Matrix
274////////////////////////////////////////////////////////////////////////////
275void bncModel::reset() {
276
277 for (int iPar = 1; iPar <= _params.size(); iPar++) {
278 delete _params[iPar-1];
279 }
280 _params.clear();
281
282 int nextPar = 0;
283 _params.push_back(new bncParam(bncParam::CRD_X, ++nextPar, ""));
284 _params.push_back(new bncParam(bncParam::CRD_Y, ++nextPar, ""));
285 _params.push_back(new bncParam(bncParam::CRD_Z, ++nextPar, ""));
286 _params.push_back(new bncParam(bncParam::RECCLK, ++nextPar, ""));
287 if (_estTropo) {
288 _params.push_back(new bncParam(bncParam::TROPO, ++nextPar, ""));
289 }
290 if (_useGalileo) {
291 _params.push_back(new bncParam(bncParam::GALILEO_OFFSET, ++nextPar, ""));
292 }
293
294 _QQ.ReSize(_params.size());
295 _QQ = 0.0;
296 for (int iPar = 1; iPar <= _params.size(); iPar++) {
297 bncParam* pp = _params[iPar-1];
298 pp->xx = 0.0;
299 if (pp->isCrd()) {
300 _QQ(iPar,iPar) = _sigCrd0 * _sigCrd0;
301 }
302 else if (pp->type == bncParam::RECCLK) {
303 _QQ(iPar,iPar) = _sigClk0 * _sigClk0;
304 }
305 else if (pp->type == bncParam::TROPO) {
306 _QQ(iPar,iPar) = _sigTrp0 * _sigTrp0;
307 }
308 else if (pp->type == bncParam::GALILEO_OFFSET) {
309 _QQ(iPar,iPar) = _sigGalileoOffset0 * _sigGalileoOffset0;
310 }
311 }
312}
313
314// Bancroft Solution
315////////////////////////////////////////////////////////////////////////////
316t_irc bncModel::cmpBancroft(t_epoData* epoData) {
317
318 if (epoData->sizeGPS() < MINOBS) {
319 _log += "bncModel::cmpBancroft: not enough data\n";
320 return failure;
321 }
322
323 Matrix BB(epoData->sizeGPS(), 4);
324
325 QMapIterator<QString, t_satData*> it(epoData->satDataGPS);
326 int iObsBanc = 0;
327 while (it.hasNext()) {
328 ++iObsBanc;
329 it.next();
330 QString prn = it.key();
331 t_satData* satData = it.value();
332 BB(iObsBanc, 1) = satData->xx(1);
333 BB(iObsBanc, 2) = satData->xx(2);
334 BB(iObsBanc, 3) = satData->xx(3);
335 BB(iObsBanc, 4) = satData->P3 + satData->clk;
336 }
337
338 bancroft(BB, _xcBanc);
339
340 // Ellipsoidal Coordinates
341 // ------------------------
342 xyz2ell(_xcBanc.data(), _ellBanc.data());
343
344 // Compute Satellite Elevations
345 // ----------------------------
346 QMutableMapIterator<QString, t_satData*> iGPS(epoData->satDataGPS);
347 while (iGPS.hasNext()) {
348 iGPS.next();
349 t_satData* satData = iGPS.value();
350 cmpEle(satData);
351 if (satData->eleSat < MINELE_GPS) {
352 delete satData;
353 iGPS.remove();
354 }
355 }
356
357 QMutableMapIterator<QString, t_satData*> iGlo(epoData->satDataGlo);
358 while (iGlo.hasNext()) {
359 iGlo.next();
360 t_satData* satData = iGlo.value();
361 cmpEle(satData);
362 if (satData->eleSat < MINELE_GLO) {
363 delete satData;
364 iGlo.remove();
365 }
366 }
367
368 QMutableMapIterator<QString, t_satData*> iGal(epoData->satDataGal);
369 while (iGal.hasNext()) {
370 iGal.next();
371 t_satData* satData = iGal.value();
372 cmpEle(satData);
373 if (satData->eleSat < MINELE_GAL) {
374 delete satData;
375 iGal.remove();
376 }
377 }
378
379 return success;
380}
381
382// Computed Value
383////////////////////////////////////////////////////////////////////////////
384double bncModel::cmpValue(t_satData* satData, bool phase) {
385
386 ColumnVector xRec(3);
387 xRec(1) = x();
388 xRec(2) = y();
389 xRec(3) = z();
390
391 double rho0 = (satData->xx - xRec).norm_Frobenius();
392 double dPhi = t_CST::omega * rho0 / t_CST::c;
393
394 xRec(1) = x() * cos(dPhi) - y() * sin(dPhi);
395 xRec(2) = y() * cos(dPhi) + x() * sin(dPhi);
396 xRec(3) = z();
397
398 tides(_time, xRec);
399
400 satData->rho = (satData->xx - xRec).norm_Frobenius();
401
402 double tropDelay = delay_saast(satData->eleSat) +
403 trp() / sin(satData->eleSat);
404
405 double wind = 0.0;
406 if (phase) {
407 wind = windUp(satData->prn, satData->xx, xRec) * satData->lambda3;
408 }
409
410 double offset = 0.0;
411 if (satData->prn[0] == 'E') {
412 offset = Galileo_offset();
413 }
414
415 double phaseCenter = 0.0;
416 if (_antex) {
417 bool found;
418 phaseCenter = _antex->pco(_antennaName, satData->eleSat, found);
419 if (!found) {
420 emit newMessage("ANTEX: antenna >"
421 + _antennaName.toAscii() + "< not found", true);
422 }
423 }
424
425 double antennaOffset = 0.0;
426 if (_dN != 0.0 || _dE != 0.0 || _dU != 0.0) {
427 double cosa = cos(satData->azSat);
428 double sina = sin(satData->azSat);
429 double cose = cos(satData->eleSat);
430 double sine = sin(satData->eleSat);
431 antennaOffset = -_dN * cosa*cose - _dE * sina*cose - _dU * sine;
432 }
433
434 return satData->rho + phaseCenter + antennaOffset + clk()
435 + offset - satData->clk + tropDelay + wind;
436}
437
438// Tropospheric Model (Saastamoinen)
439////////////////////////////////////////////////////////////////////////////
440double bncModel::delay_saast(double Ele) {
441
442 double xyz[3];
443 xyz[0] = x();
444 xyz[1] = y();
445 xyz[2] = z();
446 double ell[3];
447 xyz2ell(xyz, ell);
448 double height = ell[2];
449
450 double pp = 1013.25 * pow(1.0 - 2.26e-5 * height, 5.225);
451 double TT = 18.0 - height * 0.0065 + 273.15;
452 double hh = 50.0 * exp(-6.396e-4 * height);
453 double ee = hh / 100.0 * exp(-37.2465 + 0.213166*TT - 0.000256908*TT*TT);
454
455 double h_km = height / 1000.0;
456
457 if (h_km < 0.0) h_km = 0.0;
458 if (h_km > 5.0) h_km = 5.0;
459 int ii = int(h_km + 1);
460 double href = ii - 1;
461
462 double bCor[6];
463 bCor[0] = 1.156;
464 bCor[1] = 1.006;
465 bCor[2] = 0.874;
466 bCor[3] = 0.757;
467 bCor[4] = 0.654;
468 bCor[5] = 0.563;
469
470 double BB = bCor[ii-1] + (bCor[ii]-bCor[ii-1]) * (h_km - href);
471
472 double zen = M_PI/2.0 - Ele;
473
474 return (0.002277/cos(zen)) * (pp + ((1255.0/TT)+0.05)*ee - BB*(tan(zen)*tan(zen)));
475}
476
477// Prediction Step of the Filter
478////////////////////////////////////////////////////////////////////////////
479void bncModel::predict(t_epoData* epoData) {
480
481 bncSettings settings;
482
483 _time = epoData->tt; // current epoch time
484
485 _maxSolGap = settings.value("pppMaxSolGap").toDouble();
486
487 bool firstCrd = false;
488 if (!_lastTimeOK.valid() || (_maxSolGap > 0 && _time - _lastTimeOK > _maxSolGap)) {
489 firstCrd = true;
490 _startTime = epoData->tt;
491 reset();
492 }
493
494 // Use different white noise for Quick-Start mode
495 // ----------------------------------------------
496 double sigCrdP_used = _sigCrdP;
497 if ( _quickStart > 0.0 && _quickStart > (epoData->tt - _startTime) ) {
498 sigCrdP_used = 0.0;
499 }
500
501 // Predict Parameter values, add white noise
502 // -----------------------------------------
503 for (int iPar = 1; iPar <= _params.size(); iPar++) {
504 bncParam* pp = _params[iPar-1];
505
506 // Coordinates
507 // -----------
508 if (pp->type == bncParam::CRD_X) {
509 if (firstCrd) {
510 if (settings.value("pppRefCrdX").toString() != "" &&
511 settings.value("pppRefCrdY").toString() != "" &&
512 settings.value("pppRefCrdZ").toString() != "") {
513 pp->xx = settings.value("pppRefCrdX").toDouble();
514 }
515 else {
516 pp->xx = _xcBanc(1);
517 }
518 }
519 _QQ(iPar,iPar) += sigCrdP_used * sigCrdP_used;
520 }
521 else if (pp->type == bncParam::CRD_Y) {
522 if (firstCrd) {
523 if (settings.value("pppRefCrdX").toString() != "" &&
524 settings.value("pppRefCrdY").toString() != "" &&
525 settings.value("pppRefCrdZ").toString() != "") {
526 pp->xx = settings.value("pppRefCrdY").toDouble();
527 }
528 else {
529 pp->xx = _xcBanc(2);
530 }
531 }
532 _QQ(iPar,iPar) += sigCrdP_used * sigCrdP_used;
533 }
534 else if (pp->type == bncParam::CRD_Z) {
535 if (firstCrd) {
536 if (settings.value("pppRefCrdX").toString() != "" &&
537 settings.value("pppRefCrdY").toString() != "" &&
538 settings.value("pppRefCrdZ").toString() != "") {
539 pp->xx = settings.value("pppRefCrdZ").toDouble();
540 }
541 else {
542 pp->xx = _xcBanc(3);
543 }
544 }
545 _QQ(iPar,iPar) += sigCrdP_used * sigCrdP_used;
546 }
547
548 // Receiver Clocks
549 // ---------------
550 else if (pp->type == bncParam::RECCLK) {
551 pp->xx = _xcBanc(4);
552 for (int jj = 1; jj <= _params.size(); jj++) {
553 _QQ(iPar, jj) = 0.0;
554 }
555 _QQ(iPar,iPar) = _sigClk0 * _sigClk0;
556 }
557
558 // Tropospheric Delay
559 // ------------------
560 else if (pp->type == bncParam::TROPO) {
561 _QQ(iPar,iPar) += _sigTrpP * _sigTrpP;
562 }
563
564 // Galileo Offset
565 // --------------
566 else if (pp->type == bncParam::GALILEO_OFFSET) {
567 _QQ(iPar,iPar) += _sigGalileoOffsetP * _sigGalileoOffsetP;
568 }
569 }
570
571 // Add New Ambiguities if necessary
572 // --------------------------------
573 if (_usePhase) {
574
575 // Make a copy of QQ and xx, set parameter indices
576 // -----------------------------------------------
577 SymmetricMatrix QQ_old = _QQ;
578
579 for (int iPar = 1; iPar <= _params.size(); iPar++) {
580 _params[iPar-1]->index_old = _params[iPar-1]->index;
581 _params[iPar-1]->index = 0;
582 }
583
584 // Remove Ambiguity Parameters without observations
585 // ------------------------------------------------
586 int iPar = 0;
587 QMutableVectorIterator<bncParam*> it(_params);
588 while (it.hasNext()) {
589 bncParam* par = it.next();
590 bool removed = false;
591 if (par->type == bncParam::AMB_L3) {
592 if (epoData->satDataGPS.find(par->prn) == epoData->satDataGPS.end() &&
593 epoData->satDataGlo.find(par->prn) == epoData->satDataGlo.end() &&
594 epoData->satDataGal.find(par->prn) == epoData->satDataGal.end() ) {
595 removed = true;
596 delete par;
597 it.remove();
598 }
599 }
600 if (! removed) {
601 ++iPar;
602 par->index = iPar;
603 }
604 }
605
606 // Add new ambiguity parameters
607 // ----------------------------
608 QMapIterator<QString, t_satData*> iGPS(epoData->satDataGPS);
609 while (iGPS.hasNext()) {
610 iGPS.next();
611 t_satData* satData = iGPS.value();
612 addAmb(satData);
613 }
614
615 QMapIterator<QString, t_satData*> iGlo(epoData->satDataGlo);
616 while (iGlo.hasNext()) {
617 iGlo.next();
618 t_satData* satData = iGlo.value();
619 addAmb(satData);
620 }
621
622 QMapIterator<QString, t_satData*> iGal(epoData->satDataGal);
623 while (iGal.hasNext()) {
624 iGal.next();
625 t_satData* satData = iGal.value();
626 addAmb(satData);
627 }
628
629 int nPar = _params.size();
630 _QQ.ReSize(nPar); _QQ = 0.0;
631 for (int i1 = 1; i1 <= nPar; i1++) {
632 bncParam* p1 = _params[i1-1];
633 if (p1->index_old != 0) {
634 _QQ(p1->index, p1->index) = QQ_old(p1->index_old, p1->index_old);
635 for (int i2 = 1; i2 <= nPar; i2++) {
636 bncParam* p2 = _params[i2-1];
637 if (p2->index_old != 0) {
638 _QQ(p1->index, p2->index) = QQ_old(p1->index_old, p2->index_old);
639 }
640 }
641 }
642 }
643
644 for (int ii = 1; ii <= nPar; ii++) {
645 bncParam* par = _params[ii-1];
646 if (par->index_old == 0) {
647 _QQ(par->index, par->index) = _sigAmb0 * _sigAmb0;
648 }
649 par->index_old = par->index;
650 }
651 }
652}
653
654// Update Step of the Filter (currently just a single-epoch solution)
655////////////////////////////////////////////////////////////////////////////
656t_irc bncModel::update(t_epoData* epoData) {
657
658 bncSettings settings;
659
660 _log.clear();
661
662 if (settings.value("pppSPP").toString() == "PPP") {
663 _log += "Precise Point Positioning of Epoch "
664 + QByteArray(_time.timestr(1).c_str()) +
665 "\n---------------------------------------------------------------\n";
666 }
667 else {
668 _log += "Single Point Positioning of Epoch "
669 + QByteArray(_time.timestr(1).c_str()) +
670 "\n--------------------------------------------------------------\n";
671 }
672
673 SymmetricMatrix QQsav;
674 ColumnVector dx;
675 ColumnVector vv;
676
677 // Loop over all outliers
678 // ----------------------
679 do {
680
681 // Bancroft Solution
682 // -----------------
683 if (cmpBancroft(epoData) != success) {
684 emit newMessage(_log, false);
685 return failure;
686 }
687
688 // Status Prediction
689 // -----------------
690 predict(epoData);
691
692 // Create First-Design Matrix
693 // --------------------------
694 unsigned nPar = _params.size();
695 unsigned nObs = 0;
696 if (_usePhase) {
697 nObs = 2 * (epoData->sizeGPS() + epoData->sizeGal()) + epoData->sizeGlo();
698 }
699 else {
700 nObs = epoData->sizeGPS() + epoData->sizeGal(); // Glonass code not used
701 }
702
703 if (nObs < nPar) {
704 _log += "bncModel::update: nObs < nPar\n";
705 emit newMessage(_log, false);
706 return failure;
707 }
708
709 Matrix AA(nObs, nPar); // first design matrix
710 ColumnVector ll(nObs); // tems observed-computed
711 DiagonalMatrix PP(nObs); PP = 0.0;
712
713 unsigned iObs = 0;
714
715 // GPS code and (optionally) phase observations
716 // --------------------------------------------
717 QMapIterator<QString, t_satData*> itGPS(epoData->satDataGPS);
718 while (itGPS.hasNext()) {
719 itGPS.next();
720 t_satData* satData = itGPS.value();
721 addObs(iObs, satData, AA, ll, PP);
722 }
723
724 // Glonass phase observations
725 // --------------------------
726 QMapIterator<QString, t_satData*> itGlo(epoData->satDataGlo);
727 while (itGlo.hasNext()) {
728 itGlo.next();
729 t_satData* satData = itGlo.value();
730 addObs(iObs, satData, AA, ll, PP);
731 }
732
733 // Galileo code and (optionally) phase observations
734 // ------------------------------------------------
735 QMapIterator<QString, t_satData*> itGal(epoData->satDataGal);
736 while (itGal.hasNext()) {
737 itGal.next();
738 t_satData* satData = itGal.value();
739 addObs(iObs, satData, AA, ll, PP);
740 }
741
742 // Compute Filter Update
743 // ---------------------
744 QQsav = _QQ;
745
746 kalman(AA, ll, PP, _QQ, dx);
747
748 vv = ll - AA * dx;
749
750 // Print Residuals
751 // ---------------
752 if (true) {
753 ostringstream str;
754 str.setf(ios::fixed);
755
756 QMapIterator<QString, t_satData*> itGPS(epoData->satDataGPS);
757 while (itGPS.hasNext()) {
758 itGPS.next();
759 t_satData* satData = itGPS.value();
760 printRes(vv, str, satData);
761 }
762 QMapIterator<QString, t_satData*> itGlo(epoData->satDataGlo);
763 while (itGlo.hasNext()) {
764 itGlo.next();
765 t_satData* satData = itGlo.value();
766 printRes(vv, str, satData);
767 }
768 QMapIterator<QString, t_satData*> itGal(epoData->satDataGal);
769 while (itGal.hasNext()) {
770 itGal.next();
771 t_satData* satData = itGal.value();
772 printRes(vv, str, satData);
773 }
774 _log += str.str().c_str();
775 }
776
777 } while (outlierDetection(QQsav, vv, epoData->satDataGPS,
778 epoData->satDataGlo, epoData->satDataGal) != 0);
779
780 // Remember the Epoch-specific Results for the computation of means
781 // ----------------------------------------------------------------
782 pppPos* newPos = new pppPos;
783 newPos->time = epoData->tt;
784
785 // Set Solution Vector
786 // -------------------
787 ostringstream strB;
788 strB.setf(ios::fixed);
789 QVectorIterator<bncParam*> itPar(_params);
790 while (itPar.hasNext()) {
791 bncParam* par = itPar.next();
792 par->xx += dx(par->index);
793
794 if (par->type == bncParam::RECCLK) {
795 strB << "\n clk = " << setw(10) << setprecision(3) << par->xx
796 << " +- " << setw(6) << setprecision(3)
797 << sqrt(_QQ(par->index,par->index));
798 }
799 else if (par->type == bncParam::AMB_L3) {
800 strB << "\n amb " << par->prn.toAscii().data() << " = "
801 << setw(10) << setprecision(3) << par->xx
802 << " +- " << setw(6) << setprecision(3)
803 << sqrt(_QQ(par->index,par->index));
804 }
805 else if (par->type == bncParam::TROPO) {
806 double aprTrp = delay_saast(M_PI/2.0);
807 strB << "\n trp = " << par->prn.toAscii().data()
808 << setw(7) << setprecision(3) << aprTrp << " "
809 << setw(6) << setprecision(3) << showpos << par->xx << noshowpos
810 << " +- " << setw(6) << setprecision(3)
811 << sqrt(_QQ(par->index,par->index));
812 newPos->xnt[6] = aprTrp + par->xx;
813 }
814 else if (par->type == bncParam::GALILEO_OFFSET) {
815 strB << "\n offset = " << setw(10) << setprecision(3) << par->xx
816 << " +- " << setw(6) << setprecision(3)
817 << sqrt(_QQ(par->index,par->index));
818 }
819 }
820 strB << '\n';
821 _log += strB.str().c_str();
822 emit newMessage(_log, false);
823
824 // Final Message (both log file and screen)
825 // ----------------------------------------
826 ostringstream strC;
827 strC.setf(ios::fixed);
828 strC << _staID.data() << " PPP "
829 << epoData->tt.timestr(1) << " " << epoData->sizeAll() << " "
830 << setw(14) << setprecision(3) << x() << " +- "
831 << setw(6) << setprecision(3) << sqrt(_QQ(1,1)) << " "
832 << setw(14) << setprecision(3) << y() << " +- "
833 << setw(6) << setprecision(3) << sqrt(_QQ(2,2)) << " "
834 << setw(14) << setprecision(3) << z() << " +- "
835 << setw(6) << setprecision(3) << sqrt(_QQ(3,3));
836
837 // NEU Output
838 // ----------
839 double xyzRef[3];
840
841 if (settings.value("pppRefCrdX").toString() != "" &&
842 settings.value("pppRefCrdY").toString() != "" &&
843 settings.value("pppRefCrdZ").toString() != "") {
844
845 xyzRef[0] = settings.value("pppRefCrdX").toDouble();
846 xyzRef[1] = settings.value("pppRefCrdY").toDouble();
847 xyzRef[2] = settings.value("pppRefCrdZ").toDouble();
848
849 newPos->xnt[0] = x() - xyzRef[0];
850 newPos->xnt[1] = y() - xyzRef[1];
851 newPos->xnt[2] = z() - xyzRef[2];
852
853 double ellRef[3];
854 xyz2ell(xyzRef, ellRef);
855 xyz2neu(ellRef, newPos->xnt, &newPos->xnt[3]);
856
857 strC << " NEU "
858 << setw(8) << setprecision(3) << newPos->xnt[3] << " "
859 << setw(8) << setprecision(3) << newPos->xnt[4] << " "
860 << setw(8) << setprecision(3) << newPos->xnt[5] << endl;
861
862 }
863
864 emit newMessage(QByteArray(strC.str().c_str()), true);
865
866 if (settings.value("pppAverage").toString() == "") {
867 delete newPos;
868 }
869 else {
870
871 _posAverage.push_back(newPos);
872
873 // Time Span for Average Computation
874 // ---------------------------------
875 double tRangeAverage = settings.value("pppAverage").toDouble() * 60.;
876 if (tRangeAverage < 0) {
877 tRangeAverage = 0;
878 }
879 if (tRangeAverage > 86400) {
880 tRangeAverage = 86400;
881 }
882
883 // Compute the Mean
884 // ----------------
885 ColumnVector mean(7); mean = 0.0;
886
887 QMutableVectorIterator<pppPos*> it(_posAverage);
888 while (it.hasNext()) {
889 pppPos* pp = it.next();
890 if ( (epoData->tt - pp->time) >= tRangeAverage ) {
891 delete pp;
892 it.remove();
893 }
894 else {
895 for (int ii = 0; ii < 7; ++ii) {
896 mean[ii] += pp->xnt[ii];
897 }
898 }
899 }
900
901 int nn = _posAverage.size();
902
903 if (nn > 0) {
904
905 mean /= nn;
906
907 // Compute the Deviation
908 // ---------------------
909 ColumnVector std(7); std = 0.0;
910 QVectorIterator<pppPos*> it2(_posAverage);
911 while (it2.hasNext()) {
912 pppPos* pp = it2.next();
913 for (int ii = 0; ii < 7; ++ii) {
914 std[ii] += (pp->xnt[ii] - mean[ii]) * (pp->xnt[ii] - mean[ii]);
915 }
916 }
917 for (int ii = 0; ii < 7; ++ii) {
918 std[ii] = sqrt(std[ii] / nn);
919 }
920
921 if (settings.value("pppRefCrdX").toString() != "" &&
922 settings.value("pppRefCrdY").toString() != "" &&
923 settings.value("pppRefCrdZ").toString() != "") {
924
925 ostringstream strD; strD.setf(ios::fixed);
926 strD << _staID.data() << " AVE-XYZ "
927 << epoData->tt.timestr(1) << " "
928 << setw(13) << setprecision(3) << mean[0] + xyzRef[0] << " +- "
929 << setw(6) << setprecision(3) << std[0] << " "
930 << setw(14) << setprecision(3) << mean[1] + xyzRef[1] << " +- "
931 << setw(6) << setprecision(3) << std[1] << " "
932 << setw(14) << setprecision(3) << mean[2] + xyzRef[2] << " +- "
933 << setw(6) << setprecision(3) << std[2];
934 emit newMessage(QByteArray(strD.str().c_str()), true);
935
936 ostringstream strE; strE.setf(ios::fixed);
937 strE << _staID.data() << " AVE-NEU "
938 << epoData->tt.timestr(1) << " "
939 << setw(13) << setprecision(3) << mean[3] << " +- "
940 << setw(6) << setprecision(3) << std[3] << " "
941 << setw(14) << setprecision(3) << mean[4] << " +- "
942 << setw(6) << setprecision(3) << std[4] << " "
943 << setw(14) << setprecision(3) << mean[5] << " +- "
944 << setw(6) << setprecision(3) << std[5];
945 emit newMessage(QByteArray(strE.str().c_str()), true);
946
947 if ( Qt::CheckState(settings.value("pppEstTropo").toInt()) == Qt::Checked) {
948 ostringstream strF; strF.setf(ios::fixed);
949 strF << _staID.data() << " AVE-TRP "
950 << epoData->tt.timestr(1) << " "
951 << setw(13) << setprecision(3) << mean[6] << " +- "
952 << setw(6) << setprecision(3) << std[6] << endl;
953 emit newMessage(QByteArray(strF.str().c_str()), true);
954 }
955 }
956 }
957 }
958
959 // NMEA Output
960 // -----------
961 double xyz[3];
962 xyz[0] = x();
963 xyz[1] = y();
964 xyz[2] = z();
965 double ell[3];
966 xyz2ell(xyz, ell);
967 double phiDeg = ell[0] * 180 / M_PI;
968 double lamDeg = ell[1] * 180 / M_PI;
969
970 char phiCh = 'N';
971 if (phiDeg < 0) {
972 phiDeg = -phiDeg;
973 phiCh = 'S';
974 }
975 char lamCh = 'E';
976 if (lamDeg < 0) {
977 lamDeg = -lamDeg;
978 lamCh = 'W';
979 }
980
981 string datestr = epoData->tt.datestr(0); // yyyymmdd
982 ostringstream strRMC;
983 strRMC.setf(ios::fixed);
984 strRMC << "GPRMC,"
985 << epoData->tt.timestr(0,0) << ",A,"
986 << setw(2) << setfill('0') << int(phiDeg)
987 << setw(6) << setprecision(3) << setfill('0')
988 << fmod(60*phiDeg,60) << ',' << phiCh << ','
989 << setw(3) << setfill('0') << int(lamDeg)
990 << setw(6) << setprecision(3) << setfill('0')
991 << fmod(60*lamDeg,60) << ',' << lamCh << ",,,"
992 << datestr[6] << datestr[7] << datestr[4] << datestr[5]
993 << datestr[2] << datestr[3] << ",,";
994
995 writeNMEAstr(QString(strRMC.str().c_str()));
996
997 double dop = 2.0; // TODO
998
999 ostringstream strGGA;
1000 strGGA.setf(ios::fixed);
1001 strGGA << "GPGGA,"
1002 << epoData->tt.timestr(0,0) << ','
1003 << setw(2) << setfill('0') << int(phiDeg)
1004 << setw(10) << setprecision(7) << setfill('0')
1005 << fmod(60*phiDeg,60) << ',' << phiCh << ','
1006 << setw(3) << setfill('0') << int(lamDeg)
1007 << setw(10) << setprecision(7) << setfill('0')
1008 << fmod(60*lamDeg,60) << ',' << lamCh
1009 << ",1," << setw(2) << setfill('0') << epoData->sizeAll() << ','
1010 << setw(3) << setprecision(1) << dop << ','
1011 << setprecision(3) << ell[2] << ",M,0.0,M,,";
1012
1013 writeNMEAstr(QString(strGGA.str().c_str()));
1014
1015 _lastTimeOK = _time; // remember time of last successful update
1016 return success;
1017}
1018
1019// Outlier Detection
1020////////////////////////////////////////////////////////////////////////////
1021int bncModel::outlierDetection(const SymmetricMatrix& QQsav,
1022 const ColumnVector& vv,
1023 QMap<QString, t_satData*>& satDataGPS,
1024 QMap<QString, t_satData*>& satDataGlo,
1025 QMap<QString, t_satData*>& satDataGal) {
1026
1027 QString prnCode;
1028 QString prnPhase;
1029 double maxResCode = 0.0;
1030 double maxResPhase = 0.0;
1031
1032 QString prnRemoved;
1033 double maxRes;
1034
1035 int irc = 0;
1036
1037 // Check GPS Code
1038 // --------------
1039 if (irc == 0) {
1040 findMaxRes(vv,satDataGPS, prnCode, maxResCode, prnPhase, maxResPhase);
1041 if (maxResCode > MAXRES_CODE_GPS) {
1042 satDataGPS.remove(prnCode);
1043 prnRemoved = prnCode;
1044 maxRes = maxResCode;
1045 irc = 1;
1046 }
1047 }
1048
1049 // Check Galileo Code
1050 // ------------------
1051 if (irc == 0) {
1052 findMaxRes(vv,satDataGal, prnCode, maxResCode, prnPhase, maxResPhase);
1053 if (maxResCode > MAXRES_CODE_GAL) {
1054 satDataGal.remove(prnCode);
1055 prnRemoved = prnCode;
1056 maxRes = maxResCode;
1057 irc = 1;
1058 }
1059 }
1060
1061 // Check Glonass Phase
1062 // -------------------
1063 if (irc == 0) {
1064 findMaxRes(vv,satDataGlo, prnCode, maxResCode, prnPhase, maxResPhase);
1065 if (maxResPhase > MAXRES_PHASE_GLO) {
1066 satDataGlo.remove(prnPhase);
1067 prnRemoved = prnPhase;
1068 maxRes = maxResPhase;
1069 irc = 1;
1070 }
1071 }
1072
1073 // Check Galileo Phase
1074 // -------------------
1075 if (irc == 0) {
1076 findMaxRes(vv,satDataGal, prnCode, maxResCode, prnPhase, maxResPhase);
1077 if (maxResPhase > MAXRES_PHASE_GAL) {
1078 satDataGal.remove(prnPhase);
1079 prnRemoved = prnPhase;
1080 maxRes = maxResPhase;
1081 irc = 1;
1082 }
1083 }
1084
1085 // Check GPS Phase
1086 // ---------------
1087 if (irc == 0) {
1088 findMaxRes(vv,satDataGPS, prnCode, maxResCode, prnPhase, maxResPhase);
1089 if (maxResPhase > MAXRES_PHASE_GPS) {
1090 satDataGPS.remove(prnPhase);
1091 prnRemoved = prnPhase;
1092 maxRes = maxResPhase;
1093 irc = 1;
1094 }
1095 }
1096
1097 if (irc != 0) {
1098 _log += "Outlier " + prnRemoved.toAscii() + " "
1099 + QByteArray::number(maxRes, 'f', 3) + "\n";
1100 _QQ = QQsav;
1101 }
1102
1103 return irc;
1104}
1105
1106//
1107////////////////////////////////////////////////////////////////////////////
1108void bncModel::writeNMEAstr(const QString& nmStr) {
1109
1110 unsigned char XOR = 0;
1111 for (int ii = 0; ii < nmStr.length(); ii++) {
1112 XOR ^= (unsigned char) nmStr[ii].toAscii();
1113 }
1114
1115 QString outStr = '$' + nmStr
1116 + QString("*%1\n").arg(int(XOR), 0, 16).toUpper();
1117
1118 if (_nmeaStream) {
1119 *_nmeaStream << outStr;
1120 _nmeaStream->flush();
1121 }
1122
1123 emit newNMEAstr(outStr.toAscii());
1124}
1125
1126////
1127//////////////////////////////////////////////////////////////////////////////
1128void bncModel::kalman(const Matrix& AA, const ColumnVector& ll,
1129 const DiagonalMatrix& PP,
1130 SymmetricMatrix& QQ, ColumnVector& dx) {
1131
1132 int nObs = AA.Nrows();
1133 int nPar = AA.Ncols();
1134
1135 UpperTriangularMatrix SS = Cholesky(QQ).t();
1136
1137 Matrix SA = SS*AA.t();
1138 Matrix SRF(nObs+nPar, nObs+nPar); SRF = 0;
1139 for (int ii = 1; ii <= nObs; ++ii) {
1140 SRF(ii,ii) = 1.0 / sqrt(PP(ii,ii));
1141 }
1142
1143 SRF.SubMatrix (nObs+1, nObs+nPar, 1, nObs) = SA;
1144 SRF.SymSubMatrix(nObs+1, nObs+nPar) = SS;
1145
1146 UpperTriangularMatrix UU;
1147 QRZ(SRF, UU);
1148
1149 SS = UU.SymSubMatrix(nObs+1, nObs+nPar);
1150 UpperTriangularMatrix SH_rt = UU.SymSubMatrix(1, nObs);
1151 Matrix YY = UU.SubMatrix(1, nObs, nObs+1, nObs+nPar);
1152
1153 UpperTriangularMatrix SHi = SH_rt.i();
1154
1155 Matrix KT = SHi * YY;
1156 SymmetricMatrix Hi; Hi << SHi * SHi.t();
1157
1158 dx = KT.t() * ll;
1159 QQ << (SS.t() * SS);
1160}
1161
1162// Phase Wind-Up Correction
1163///////////////////////////////////////////////////////////////////////////
1164double bncModel::windUp(const QString& prn, const ColumnVector& rSat,
1165 const ColumnVector& rRec) {
1166
1167 double Mjd = _time.mjd() + _time.daysec() / 86400.0;
1168
1169 // First time - initialize to zero
1170 // -------------------------------
1171 if (!_windUpTime.contains(prn)) {
1172 _windUpSum[prn] = 0.0;
1173 }
1174
1175 // Compute the correction for new time
1176 // -----------------------------------
1177 if (!_windUpTime.contains(prn) || _windUpTime[prn] != Mjd) {
1178 _windUpTime[prn] = Mjd;
1179
1180 // Unit Vector GPS Satellite --> Receiver
1181 // --------------------------------------
1182 ColumnVector rho = rRec - rSat;
1183 rho /= rho.norm_Frobenius();
1184
1185 // GPS Satellite unit Vectors sz, sy, sx
1186 // -------------------------------------
1187 ColumnVector sz = -rSat / rSat.norm_Frobenius();
1188
1189 ColumnVector xSun = Sun(Mjd);
1190 xSun /= xSun.norm_Frobenius();
1191
1192 ColumnVector sy = crossproduct(sz, xSun);
1193 ColumnVector sx = crossproduct(sy, sz);
1194
1195 // Effective Dipole of the GPS Satellite Antenna
1196 // ---------------------------------------------
1197 ColumnVector dipSat = sx - rho * DotProduct(rho,sx)
1198 - crossproduct(rho, sy);
1199
1200 // Receiver unit Vectors rx, ry
1201 // ----------------------------
1202 ColumnVector rx(3);
1203 ColumnVector ry(3);
1204
1205 double recEll[3]; xyz2ell(rRec.data(), recEll) ;
1206 double neu[3];
1207
1208 neu[0] = 1.0;
1209 neu[1] = 0.0;
1210 neu[2] = 0.0;
1211 neu2xyz(recEll, neu, rx.data());
1212
1213 neu[0] = 0.0;
1214 neu[1] = -1.0;
1215 neu[2] = 0.0;
1216 neu2xyz(recEll, neu, ry.data());
1217
1218 // Effective Dipole of the Receiver Antenna
1219 // ----------------------------------------
1220 ColumnVector dipRec = rx - rho * DotProduct(rho,rx)
1221 + crossproduct(rho, ry);
1222
1223 // Resulting Effect
1224 // ----------------
1225 double alpha = DotProduct(dipSat,dipRec) /
1226 (dipSat.norm_Frobenius() * dipRec.norm_Frobenius());
1227
1228 if (alpha > 1.0) alpha = 1.0;
1229 if (alpha < -1.0) alpha = -1.0;
1230
1231 double dphi = acos(alpha) / 2.0 / M_PI; // in cycles
1232
1233 if ( DotProduct(rho, crossproduct(dipSat, dipRec)) < 0.0 ) {
1234 dphi = -dphi;
1235 }
1236
1237 _windUpSum[prn] = floor(_windUpSum[prn] - dphi + 0.5) + dphi;
1238 }
1239
1240 return _windUpSum[prn];
1241}
1242
1243//
1244///////////////////////////////////////////////////////////////////////////
1245void bncModel::cmpEle(t_satData* satData) {
1246 ColumnVector rr = satData->xx - _xcBanc.Rows(1,3);
1247 double rho = rr.norm_Frobenius();
1248
1249 double neu[3];
1250 xyz2neu(_ellBanc.data(), rr.data(), neu);
1251
1252 satData->eleSat = acos( sqrt(neu[0]*neu[0] + neu[1]*neu[1]) / rho );
1253 if (neu[2] < 0) {
1254 satData->eleSat *= -1.0;
1255 }
1256 satData->azSat = atan2(neu[1], neu[0]);
1257}
1258
1259//
1260///////////////////////////////////////////////////////////////////////////
1261void bncModel::addAmb(t_satData* satData) {
1262 bool found = false;
1263 for (int iPar = 1; iPar <= _params.size(); iPar++) {
1264 if (_params[iPar-1]->type == bncParam::AMB_L3 &&
1265 _params[iPar-1]->prn == satData->prn) {
1266 found = true;
1267 break;
1268 }
1269 }
1270 if (!found) {
1271 bncParam* par = new bncParam(bncParam::AMB_L3,
1272 _params.size()+1, satData->prn);
1273 _params.push_back(par);
1274 par->xx = satData->L3 - cmpValue(satData, true);
1275 }
1276}
1277
1278//
1279///////////////////////////////////////////////////////////////////////////
1280void bncModel::addObs(unsigned& iObs, t_satData* satData,
1281 Matrix& AA, ColumnVector& ll, DiagonalMatrix& PP) {
1282
1283 // Code Observations
1284 // -----------------
1285 if (satData->system() != 'R') {
1286 ++iObs;
1287 ll(iObs) = satData->P3 - cmpValue(satData, false);
1288 PP(iObs,iObs) = 1.0 / (_sigP3 * _sigP3);
1289 for (int iPar = 1; iPar <= _params.size(); iPar++) {
1290 AA(iObs, iPar) = _params[iPar-1]->partial(satData, false);
1291 }
1292 satData->indexCode = iObs;
1293 }
1294
1295 // Phase Observations
1296 // ------------------
1297 if (_usePhase) {
1298 ++iObs;
1299 ll(iObs) = satData->L3 - cmpValue(satData, true);
1300 PP(iObs,iObs) = 1.0 / (_sigL3 * _sigL3);
1301 for (int iPar = 1; iPar <= _params.size(); iPar++) {
1302 if (_params[iPar-1]->type == bncParam::AMB_L3 &&
1303 _params[iPar-1]->prn == satData->prn) {
1304 ll(iObs) -= _params[iPar-1]->xx;
1305 }
1306 AA(iObs, iPar) = _params[iPar-1]->partial(satData, true);
1307 }
1308 satData->indexPhase = iObs;
1309 }
1310}
1311
1312//
1313///////////////////////////////////////////////////////////////////////////
1314void bncModel::printRes(const ColumnVector& vv,
1315 ostringstream& str, t_satData* satData) {
1316 if (satData->indexPhase) {
1317 str << _time.timestr(1)
1318 << " RES " << satData->prn.toAscii().data() << " L3 "
1319 << setw(9) << setprecision(4) << vv(satData->indexPhase);
1320 if (satData->indexCode) {
1321 str << " P3 " << setw(9) << setprecision(4) << vv(satData->indexCode);
1322 }
1323 str << endl;
1324 }
1325}
1326
1327//
1328///////////////////////////////////////////////////////////////////////////
1329void bncModel::findMaxRes(const ColumnVector& vv,
1330 const QMap<QString, t_satData*>& satData,
1331 QString& prnCode, double& maxResCode,
1332 QString& prnPhase, double& maxResPhase) {
1333 maxResCode = 0.0;
1334 maxResPhase = 0.0;
1335
1336 QMapIterator<QString, t_satData*> it(satData);
1337 while (it.hasNext()) {
1338 it.next();
1339 t_satData* satData = it.value();
1340 if (satData->indexCode) {
1341 if (fabs(vv(satData->indexCode)) > maxResCode) {
1342 maxResCode = fabs(vv(satData->indexCode));
1343 prnCode = satData->prn;
1344 }
1345 }
1346 if (satData->indexPhase) {
1347 if (fabs(vv(satData->indexPhase)) > maxResPhase) {
1348 maxResPhase = fabs(vv(satData->indexPhase));
1349 prnPhase = satData->prn;
1350 }
1351 }
1352 }
1353}
1354
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