Backward smoothing for precise GNSS applications
The Extended Kalman filter is widely used for its robustness and simple implementation. Parameters estimated for solving dynamical systems usually require certain time to converge and need to be smoothed by a dedicated algorithms. The purpose of our study was to implement smoothing algorithms for pr...
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| Published in | Advances in space research Vol. 56; no. 8; pp. 1627 - 1634 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier Ltd
15.10.2015
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| Subjects | |
| Online Access | Get full text |
| ISSN | 0273-1177 1879-1948 |
| DOI | 10.1016/j.asr.2015.07.020 |
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| Abstract | The Extended Kalman filter is widely used for its robustness and simple implementation. Parameters estimated for solving dynamical systems usually require certain time to converge and need to be smoothed by a dedicated algorithms. The purpose of our study was to implement smoothing algorithms for processing both code and carrier phase observations with Precise Point Positioning method. We implemented and used the well known Rauch–Tung–Striebel smoother (RTS). It has been found out that the RTS suffer from significant numerical instability in smoothed state covariance matrix determination. We improved the processing with algorithms based on Singular Value Decomposition, which was more robust. Observations from many permanent stations have been processed with final orbits and clocks provided by the International GNSS service (IGS), and the smoothing improved stability and precision in every cases. Moreover, (re)convergence of the parameters were always successfully eliminated. |
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| AbstractList | The Extended Kalman filter is widely used for its robustness and simple implementation. Parameters estimated for solving dynamical systems usually require certain time to converge and need to be smoothed by a dedicated algorithms. The purpose of our study was to implement smoothing algorithms for processing both code and carrier phase observations with Precise Point Positioning method. We implemented and used the well known Rauch-Tung-Striebel smoother (RTS). It has been found out that the RTS suffer from significant numerical instability in smoothed state covariance matrix determination. We improved the processing with algorithms based on Singular Value Decomposition, which was more robust. Observations from many permanent stations have been processed with final orbits and clocks provided by the International GNSS service (IGS), and the smoothing improved stability and precision in every cases. Moreover, (re)convergence of the parameters were always successfully eliminated. |
| Author | Dousa, Jan Vaclavovic, Pavel |
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| Cites_doi | 10.1007/PL00012883 10.2514/3.3166 10.1016/j.asr.2014.02.021 10.1109/ITSC.2008.4732683 10.1007/s00190-008-0300-3 |
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| Keywords | Backward smoothing GNSS Kalman filter Precise Point Positioning Ambiguity |
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| References | Vaclavovic, Dousa, Gyori (b0050) 2013; 10 Anderson, Moore (b0005) 1979 Dow, Neilan, Rizos (b0025) 2009; 83 Cao, Y., Mao, X., 2008. Improved filtering-smoothing algorithm for GPS positioning. In: Proceedings of the 11th International IEEE Conference on Intelligent Transportation Systems, Beijing, China, October 12–15. Kouba, Heroux (b0030) 2001; 5 Park, P., Kailath, T., 1994. New square-root smoothing algorithms. In: Proceedings of the 33rd Conference on Decision and Control, Lake Buena Vista FL, December, pp. 1215–1220. Dousa, Vaclavovic (b0020) 2014; 53 Mervart, L., Lukes, Z., Rocken, Ch., Tetsuya, I., 2008. Precise point positioning with ambiguity resolution in real-time. In: Proceedings of the 21st International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS 2008), Savannah, GA, September, pp. 397–405. Bryson, A.E., Frazier, M., 1962. Smoothing for linear and nonlinear dynamic systems. In: Proceedings of the Optimum Systems Synthesis Conference, Ohio, September 11–13, pp. 353–364. Zhang, Y., Li, X.R., 1996. Fixed-interval smoothing algorithm based on singular value decomposition. In: Proceedings of the 1996 IEEE International Conference on Control Applications, Dearborn, September 15–18, pp. 916–921. Rauch, Tung, Striebel (b0045) August 1965; 3 10.1016/j.asr.2015.07.020_b0010 Dousa (10.1016/j.asr.2015.07.020_b0020) 2014; 53 Kouba (10.1016/j.asr.2015.07.020_b0030) 2001; 5 Anderson (10.1016/j.asr.2015.07.020_b0005) 1979 Rauch (10.1016/j.asr.2015.07.020_b0045) 1965; 3 10.1016/j.asr.2015.07.020_b0040 10.1016/j.asr.2015.07.020_b0035 Dow (10.1016/j.asr.2015.07.020_b0025) 2009; 83 10.1016/j.asr.2015.07.020_b0055 10.1016/j.asr.2015.07.020_b0015 Vaclavovic (10.1016/j.asr.2015.07.020_b0050) 2013; 10 |
| References_xml | – volume: 5 start-page: 12 year: 2001 end-page: 28 ident: b0030 article-title: Precise point positioning using IGS and clock products publication-title: GPS Sol. – volume: 3 start-page: 1445 year: August 1965 end-page: 1450 ident: b0045 article-title: Maximum likelihood estimates of linear dynamic systems publication-title: AIAA J. – reference: Bryson, A.E., Frazier, M., 1962. Smoothing for linear and nonlinear dynamic systems. In: Proceedings of the Optimum Systems Synthesis Conference, Ohio, September 11–13, pp. 353–364. – volume: 83 start-page: 191 year: 2009 end-page: 198 ident: b0025 article-title: The international GNSS service in a changing landscape of global navigation satellite systems publication-title: J. Geod. – reference: Cao, Y., Mao, X., 2008. Improved filtering-smoothing algorithm for GPS positioning. In: Proceedings of the 11th International IEEE Conference on Intelligent Transportation Systems, Beijing, China, October 12–15. – reference: Mervart, L., Lukes, Z., Rocken, Ch., Tetsuya, I., 2008. Precise point positioning with ambiguity resolution in real-time. In: Proceedings of the 21st International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS 2008), Savannah, GA, September, pp. 397–405. – volume: 53 start-page: 1347 year: 2014 end-page: 1358 ident: b0020 article-title: Real-time zenith tropospheric delays in support of numerical weather prediction applications publication-title: Adv. Space Res. – volume: 10 start-page: 431 year: 2013 end-page: 436 ident: b0050 article-title: G-Nut software library – state of development and first results publication-title: Acta Geodyn. Geomater. – reference: Park, P., Kailath, T., 1994. New square-root smoothing algorithms. In: Proceedings of the 33rd Conference on Decision and Control, Lake Buena Vista FL, December, pp. 1215–1220. – year: 1979 ident: b0005 article-title: Optimal Filtering – reference: Zhang, Y., Li, X.R., 1996. Fixed-interval smoothing algorithm based on singular value decomposition. In: Proceedings of the 1996 IEEE International Conference on Control Applications, Dearborn, September 15–18, pp. 916–921. – volume: 5 start-page: 12 issue: 2 year: 2001 ident: 10.1016/j.asr.2015.07.020_b0030 article-title: Precise point positioning using IGS and clock products publication-title: GPS Sol. doi: 10.1007/PL00012883 – volume: 3 start-page: 1445 issue: 8 year: 1965 ident: 10.1016/j.asr.2015.07.020_b0045 article-title: Maximum likelihood estimates of linear dynamic systems publication-title: AIAA J. doi: 10.2514/3.3166 – ident: 10.1016/j.asr.2015.07.020_b0035 – ident: 10.1016/j.asr.2015.07.020_b0010 – ident: 10.1016/j.asr.2015.07.020_b0040 – year: 1979 ident: 10.1016/j.asr.2015.07.020_b0005 – ident: 10.1016/j.asr.2015.07.020_b0055 – volume: 10 start-page: 431 issue: 4 year: 2013 ident: 10.1016/j.asr.2015.07.020_b0050 article-title: G-Nut software library – state of development and first results publication-title: Acta Geodyn. Geomater. – volume: 53 start-page: 1347 issue: 9 year: 2014 ident: 10.1016/j.asr.2015.07.020_b0020 article-title: Real-time zenith tropospheric delays in support of numerical weather prediction applications publication-title: Adv. Space Res. doi: 10.1016/j.asr.2014.02.021 – ident: 10.1016/j.asr.2015.07.020_b0015 doi: 10.1109/ITSC.2008.4732683 – volume: 83 start-page: 191 issue: 3–4 year: 2009 ident: 10.1016/j.asr.2015.07.020_b0025 article-title: The international GNSS service in a changing landscape of global navigation satellite systems publication-title: J. Geod. doi: 10.1007/s00190-008-0300-3 |
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| SubjectTerms | Algorithms Ambiguity Backward smoothing Dynamical systems GNSS Kalman filter Mathematical models Precise Point Positioning Robustness Smoothing Stability Stations |
| Title | Backward smoothing for precise GNSS applications |
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