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The presence of cycle slips corrupts the carrier phase measurement which is critical for high precision global navigation satellite system static or kinematic positioning. The process of cycle slips is comprised of detecting the slips, estimating its exact integer and making a repair. In this paper, a novel approach to cycle slip detection and repair based on Bayesian compressive sensing is proposed, in order to reduce the noise effects on the performances of cycle slip detection and repair. Unlike traditional cycle slip detection and repair methods, we exploit the sparse property of the cycle slip signal, aiming to obtain the perception matrix and establish the sparse cycle slip detection model. Then in order to estimate and repair the value of cycle slips, the residuals of carrier phase double difference and the interference noise between multiple satellites, when more than one satellite has cycle slips, are taken into consideration, which is used as prior information to obtain the likelihood expression for cycle slip signal. Finally, we use the prior information about signals based on relevance vector machine principle derived from sparse Bayesian learning to predict cycle slip distribution and then estimate the value of cycle slips. The novel approach is tested with the actual collection of satellite data in the experiment. It is shown that the novel approach proposed in this paper can effectively estimate cycle slips and achieve better performance than orthogonal matching pursuit and l1 norm based algorithm when the redundancy of carrier phase is large enough. In the case of single frequency carrier phase observation, when redundancy is not less than 7, the novel approach can completely detect and repair cycle slips; in the case of dual-frequency carrier phase observation, when cycle slips happen in four of the eight satellites, 97.6% probability of accuracy is accomplished by the new approach.
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Keywords:
- cycle slip detection and repair /
- compressive sensing /
- sparse Bayesian learning /
- relevance vector machine
[1] Cai C S, Liu Z Z, Xia P F, Dai W J 2013 GPS Solutions 17 247
[2] Parkins A 2011 GPS Solutions 15 391
[3] Ji S Y, Wang Z J, Chen W, Weng D J, Xu Y, Fan S J, Huang B H, Sun G Y, Wang H Q, He Y W 2014 Survey Rev. 46 104
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[5] Dai Z, Knedlik S, Loffeld O 2008 Proceedings of 5th Workshop on Positioning, Navigation and Communication Hannover, Germany, March 27-27, 2008 p37
[6] Dai Z 2012 GPS Solutions 16 267
[7] Liu Z Z 2011 J. Geodesy. 85 171
[8] Henkel P, Oku N 2015 International Association of Geodesy Symposia 142 291
[9] De Lacy M C, Reguzzoni M, Sansò F 2012 GPS Solutions 16 353
[10] Zhao Q L, Sun B Z, Dai Z Q, Hu Z G, Shi C, Liu J N 2015 GPS Solutions 19 381
[11] Yao Y F, Gao J X, Wang J, Hu H, Li Z K 2016 Survey Rev. 48 367
[12] Sun B Q, Ou J K, Sheng C Z, Liu J H 2010 Geomat. Inform. Sci. Wuhan Univ. 10 1157 (in Chinese)[孙保琪, 欧吉坤, 盛传贞, 刘吉华2010武汉大学学报 10 1157]
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[14] Gao Y, Huang G Y, Zhang X H, Xu H W, Zhang L Q 2015 The 27th Chinese Control and Decision Conference Qingdao, China, May 23-25, 2015 p3627
[15] Donoho D L 2006 IEEE Trans. Inform. Theory 52 1289
[16] Candes E J, Romberg J K, Tao T 2006 Commun. Pure and Appl. Math. 59 1207
[17] Duarte M F, Baraniuk R G 2013 Appl. Comput. Harmon. Anal. 35 111
[18] Foucart S, Rauhut H 2013 A Mathematical Introduction to Compressive Sensing (Vol. 1) (New York:Springer) p61
[19] Leick A, Rapoport L, Tatarnikov D J 2015 GPS Satellite Surveying (Vol. 4) (New Jersey:John Wiley & Sons) p681
[20] Sharma A, Paliwal K K, Imoto S, Miyano S 2013 Int. J. Mach. Learn. Cyb. 4 679
[21] Kang R Z, Tian P W, Yu H Y 2014 Acta Phys. Sin. 63 200701 (in Chinese)[康荣宗, 田鹏武, 于宏毅2014 63 200701]
[22] Candès E J, Romberg J, Tao T 2006 IEEE Trans. Inform. Theory 52 489
[23] Candès E J 2008 Comptes Rendus Mathematique 346 589
[24] Wen F Q, Zhang G, Fen D 2015 Acta Phys. Sin. 64 070201 (in Chinese)[文方青, 张弓, 贲德2015 64 070201]
[25] Tropp J A, Gilbert A C 2007 IEEE Trans. Inform. Theory 53 4655
[26] Ji S H, Xue Y, Carin L 2008 IEEE Trans. Signal Process. 56 2346
[27] Wipf D P, Rao B D 2004 IEEE Trans. Signal Process. 52 2153
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[1] Cai C S, Liu Z Z, Xia P F, Dai W J 2013 GPS Solutions 17 247
[2] Parkins A 2011 GPS Solutions 15 391
[3] Ji S Y, Wang Z J, Chen W, Weng D J, Xu Y, Fan S J, Huang B H, Sun G Y, Wang H Q, He Y W 2014 Survey Rev. 46 104
[4] Xu G C 2007 GPS:Theory, Algorithms and Applications (Vol. 2) (Berlin:Springer Science & Business Media) p167
[5] Dai Z, Knedlik S, Loffeld O 2008 Proceedings of 5th Workshop on Positioning, Navigation and Communication Hannover, Germany, March 27-27, 2008 p37
[6] Dai Z 2012 GPS Solutions 16 267
[7] Liu Z Z 2011 J. Geodesy. 85 171
[8] Henkel P, Oku N 2015 International Association of Geodesy Symposia 142 291
[9] De Lacy M C, Reguzzoni M, Sansò F 2012 GPS Solutions 16 353
[10] Zhao Q L, Sun B Z, Dai Z Q, Hu Z G, Shi C, Liu J N 2015 GPS Solutions 19 381
[11] Yao Y F, Gao J X, Wang J, Hu H, Li Z K 2016 Survey Rev. 48 367
[12] Sun B Q, Ou J K, Sheng C Z, Liu J H 2010 Geomat. Inform. Sci. Wuhan Univ. 10 1157 (in Chinese)[孙保琪, 欧吉坤, 盛传贞, 刘吉华2010武汉大学学报 10 1157]
[13] Rapoport L 2014 ION GNSS2014 Tampa, USA, September 8-12, 2014 p2602
[14] Gao Y, Huang G Y, Zhang X H, Xu H W, Zhang L Q 2015 The 27th Chinese Control and Decision Conference Qingdao, China, May 23-25, 2015 p3627
[15] Donoho D L 2006 IEEE Trans. Inform. Theory 52 1289
[16] Candes E J, Romberg J K, Tao T 2006 Commun. Pure and Appl. Math. 59 1207
[17] Duarte M F, Baraniuk R G 2013 Appl. Comput. Harmon. Anal. 35 111
[18] Foucart S, Rauhut H 2013 A Mathematical Introduction to Compressive Sensing (Vol. 1) (New York:Springer) p61
[19] Leick A, Rapoport L, Tatarnikov D J 2015 GPS Satellite Surveying (Vol. 4) (New Jersey:John Wiley & Sons) p681
[20] Sharma A, Paliwal K K, Imoto S, Miyano S 2013 Int. J. Mach. Learn. Cyb. 4 679
[21] Kang R Z, Tian P W, Yu H Y 2014 Acta Phys. Sin. 63 200701 (in Chinese)[康荣宗, 田鹏武, 于宏毅2014 63 200701]
[22] Candès E J, Romberg J, Tao T 2006 IEEE Trans. Inform. Theory 52 489
[23] Candès E J 2008 Comptes Rendus Mathematique 346 589
[24] Wen F Q, Zhang G, Fen D 2015 Acta Phys. Sin. 64 070201 (in Chinese)[文方青, 张弓, 贲德2015 64 070201]
[25] Tropp J A, Gilbert A C 2007 IEEE Trans. Inform. Theory 53 4655
[26] Ji S H, Xue Y, Carin L 2008 IEEE Trans. Signal Process. 56 2346
[27] Wipf D P, Rao B D 2004 IEEE Trans. Signal Process. 52 2153
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