Abstract
Integer ambiguity resolution is critical for achieving positions of high precision and reliability of precise point positioning (PPP). However, as an important error source in global navigation satellite system (GNSS), multipath interference limits the ability of PPP in high-accuracy GNSS positioning applications. Thus, to guarantee the performance of PPP ambiguity resolution techniques in a multipath environment, a sidereal filtering technique based on sparsity promoting regularization is adopted to mitigate the multipath error. The key idea of the proposed strategy emphasizes the use of the L1 norm to extract multipath from noisy carrier phase residuals. The classical single-difference between-satellites method is used to fix PPP with the estimated phase clocks/bias products for obtaining carrier phase residuals in the previous period. Two GPS datasets are adopted to assess the denoising effect of the multipath model and the performance of the proposed strategy. The carrier phase residuals of static PPP ambiguity resolution and the positioning accuracy of kinematic float PPP after the application of the multipath model are used to reflect the final filtering performance. Results show that the multipath model based on first-order regularization can improve the RMS of carrier phase residuals by approximately 49.8% compared with the solution without multipath mitigation. In kinematic float PPP, a mean coordinate improvement of 49.7% for day of year (DOY) 273 and 57.8% for DOY 275 in 2017 could be achieved.
Similar content being viewed by others
References
Alkan RM, Saka MH, Ozulu İM, İlçi V (2017) Kinematic precise point positioning using GPS and GLONASS measurements in marine environments. Measurement 109:36–43. https://doi.org/10.1016/j.measurement.2017.05.054
Atkins C, Ziebart M (2015) Effectiveness of observation-domain sidereal filtering for GPS precise point positioning. GPS Solut 20:1. https://doi.org/10.1007/s10291-015-0473-1
Beck A, Teboulle M (2009) A fast iterative shrinkage-thresholding algorithm for linear inverse problems. SIAM J Imaging Sci 2:183–202. https://doi.org/10.1137/080716542
Bilich A, Cassidy JF, Larson KM (2008) GPS seismology: application to the 2002 Mw 7.9 Denali Fault earthquake. Bull Seismol Soc Am 98:593–606. https://doi.org/10.1785/0120070096
Blewitt G (1989) Carrier phase ambiguity resolution for the global positioning system applied to geodetic baselines up to 2000 km. J Geophys Res Solid Earth 94:10187–10203. https://doi.org/10.1029/jb094ib08p10187
Bock Y (1991) Continuous monitoring of crustal deformation. GPS World 2:40–47
Boyd S, Parikh N, Chu E, Peleato B, Eckstein J (2011) Distributed optimization and statistical searning via the alternating direction method of multipliers. Found Trends Mach Learn 3(1):1–122. https://doi.org/10.1561/2200000016
Chang GB, Chen C, Yang YX, Xu TH (2018) Tikhonov regularization based modeling and sidereal filtering mitigation of GNSS multipath errors. Remote Sens 10:1801. https://doi.org/10.3390/rs10111801
Chen C, Chang GB, Zheng NS, Xu TH (2019) GNSS multipath error modeling and mitigation by using sparsity-promoting regularization. IEEE Access 7:24096–24108. https://doi.org/10.1109/access.2019.2899622
Choi K, Bilich A, Larson KM, Axelrad P (2004) Modified sidereal filtering: implications for high-rate GPS positioning. Geophys Res Lett 31:178–198(121). https://doi.org/10.1029/2004gl021621
Collins P, Lahaye F, Héroux P, Bisnath S (2008) Precise point positioning with ambiguity resolution using the decoupled clock model. Paper presented at the Proceedings of ION GNSS 2008, Institute of Navigation, Savannah, Georgia, US, Sept 16–19
Dai W, Huang D, Cai C (2014) Multipath mitigation via component analysis methods for GPS dynamic deformation monitoring. GPS Solut 18:417–428. https://doi.org/10.1007/s10291-013-0341-9
Daubechies I, Devore R, Fornasier M (2010) Iteratively reweighted least squares minimization for sparse recovery. Commun Pure Appl Math 63:1–38. https://doi.org/10.1002/cpa.20303
Efron B, Tibshirani R (1993) An introduction to the Bootstrap. Chapman and Hall, London. https://doi.org/10.1007/978-1-4899-4541-9
Elósegui P, Davis JL, Oberlander D, Baena R, Ekström G (2006) Accuracy of high-rate GPS for seismology. Geophys Res Lett 33:L11308. https://doi.org/10.1029/2006gl026065
Fan X, Lian Q, Shi B (2017) Compressed sensing MRI with phase noise disturbance based on adaptive tight frame and total variation. IEEE Access 5:19311–19321. https://doi.org/10.1109/ACCESS.2017.2749381
Ge M, Gendt G, Rothacher M, Shi C, Liu J (2008) Resolution of GPS carrier-phase ambiguities in precise point positioning (PPP) with daily observations. J Geodesy 82:389–399
Geng J, Teferle FN, Shi C, Meng X, Dodson AH, Liu J (2009) Ambiguity resolution in precise point positioning with hourly data. GPS Solut 13:263–270. https://doi.org/10.1007/s10291-009-0119-2
Geng J, Chen X, Pan Y, Mao S, Li C, Zhou J, Zhang K (2019a) PRIDE PPP-AR: an open-source software for GPS PPP ambiguity resolution. GPS Solut 23:91. https://doi.org/10.1007/s10291-019-0888-1
Geng J, Chen X, Pan Y, Zhao Q (2019b) A modified phase clock/bias model to improve PPP ambiguity resolution at Wuhan University. J Geod 93:2053–2067. https://doi.org/10.1007/s00190-019-01301-6
Genrich JF, Bock Y (1992) Rapid resolution of crustal motion at short ranges with the global positioning system. J Geophys Res Solid Earth 97:3261–3269
Holland PW, Welsch RE (1977) Robust regression using iteratively reweighted least-squares. Commun Stat 6:813–827. https://doi.org/10.1080/03610927708827533
Hung HK, Rau RJ (2013) Surface waves of the 2011 Tohoku earthquake: observations of Taiwan’s dense high-rate GPS network. J Geophys Res Solid Earth 118:332–345. https://doi.org/10.1029/2012JB009689
Jian W, Wang J, Roberts C (2013) Reducing GPS carrier phase errors with EMD-wavelet for precise static positioning. Emp Surv Rev 41:152–161. https://doi.org/10.1179/003962609x390067
Kouba J, Héroux P (2001) Precise point positioning using IGS orbit and clock products. GPS Solut 5:12–28. https://doi.org/10.1007/PL00012883
Larson KM, Bilich A, Axelrad P (2007) Improving the precision of high-rate GPS. J Geophys Res Solid Earth 112:1–11. https://doi.org/10.1029/2006JB004367
Lau L (2017) Wavelet packets based denoising method for measurement domain repeat-time multipath filtering in GPS static high-precision positioning. GPS Solut 21:461–474. https://doi.org/10.1007/s10291-016-0533-1
Laurichesse D, Mercier F, Berthias JP, Broca P, Cerri L (2009) Integer ambiguity resolution on undifferenced GPS phase measurements and its application to PPP and satellite precise orbit determination. Navigation 56:135–149. https://doi.org/10.1002/j.2161-4296.2009.tb01750.x
Li X, Xin L, Yuan Y, Zhang K, Zhang X, Wickert J (2017) Multi-GNSS phase delay estimation and PPP ambiguity resolution: GPS, BDS, GLONASS, Galileo. J Geod 92:1–30. https://doi.org/10.1007/s00190-017-1081-3
Moulborne W (1985) The case for ranging in GPS-based geodetic systems. Paper presented at the Proceedings first international symposium on precise positioning with the global positioning system, Rockville, 15–19 April
O’Brien CM (2016) Statistical learning with sparsity: the lasso and generalizations. Int Stat Rev 84:156–157. https://doi.org/10.1111/insr.12167
Pugliano G, Robustelli U, Rossi F, Santamaria R (2015) A new method for specular and diffuse pseudorange multipath error extraction using wavelet analysis. GPS Solut 20:499–508. https://doi.org/10.1007/s10291-015-0458-0
Ragheb AE, Clarke PJ, Edwards SJ (2007) GPS sidereal filtering: coordinate- and carrier-phase-level strategies. J Geod 81:325–335. https://doi.org/10.1007/s00190-006-0113-1
Reuveni Y, Kedar S, Owen SE, Moore AW, Webb FH (2012) Improving sub-daily strain estimates using GPS measurements. Geophys Res Lett 39:623. https://doi.org/10.1029/2012GL051927
Rudin LI, Osher S, Fatemi E (1992) Nonlinear total variation based noise removal algorithms. In: Eleventh international conference of the Center for nonlinear studies on experimental mathematics: computational issues in nonlinear science. https://doi.org/10.1016/0167-2789(92)90242-f
Schwarz CR, Snay RA, Soler T (2009) Accuracy assessment of the National Geodetic Survey’s OPUS-RS utility. GPS Solut 13:119–132
Shi J (2012) Precise point positioning integer ambiguity resolution with decoupled clocks. University of Calgary, Calgary
Su M, Zheng J, Yang Y, Qiang W (2018) A new multipath mitigation method based on adaptive thresholding wavelet denoising and double reference shift strategy. GPS Solut 22:40. https://doi.org/10.1007/s10291-018-0708-z
Takasu T (2006) High-rate precise point positioning: observation of crustal deformation by using 1-Hz GPS data. Paper presented at the GPS/GNSS symposium, Tokyo
Teunissen PJG (1995) The least-squares ambiguity decorrelation adjustment: a method for fast GPS integer ambiguity estimation. J Geod 70:65–82. https://doi.org/10.1007/BF00863419
Teunissen PJG (1998) Success probability of integer GPS ambiguity rounding and bootstrapping. J Geod 72:606–612. https://doi.org/10.1007/s001900050199
Teunissen PJG (1999) An optimality property of the integer least-squares estimator. J Geod 73:587–593. https://doi.org/10.1007/s001900050269
Teunissen PJG (2001) Integer estimation in the presence of biases. J Geod 75:399–407. https://doi.org/10.1007/s001900100191
Teunissen PJG, Khodabandeh A (2015) Review and principles of PPP-RTK methods. J Geod 89:217–240. https://doi.org/10.1007/s00190-014-0771-3
Wang D, Meng X, Gao C, Pan S, Chen Q (2017) Multipath extraction and mitigation for bridge deformation monitoring using a single-difference model. Adv Space Res 60:2882–2895. https://doi.org/10.1016/j.asr.2017.01.007
Wang M, Wang J, Dong D, Li H, Han L, Chen W (2018) Comparison of three methods for estimating GPS multipath repeat time. Remote Sens 10:6. https://doi.org/10.3390/rs10020006
Wohlberg B, Rodriguez P (2008) An iteratively reweighted norm algorithm for minimization of total variation functionals. IEEE Signal Process Lett 14:948–951. https://doi.org/10.1109/LSP.2007.906221
Wübbena G (1985) Software developments for geodetic positioning with GPS using TI-4100 code and carrier measurements. Paper presented at the Proceedings of first international symposium on precise positioning with the global positioning system, Rockville, 15–19 April
Yu K, Wei B, Zhang X, Yu X (2015) Snow depth estimation based on multipath phase combination of GPS triple-frequency signals. IEEE Trans Geosci Remote Sens 53:5100–5109. https://doi.org/10.1109/tgrs.2015.2417214
Zhang QZ, Yang W, Zhang SB, Liu X (2018) Characteristics of BeiDou navigation satellite system multipath and its mitigation method based on Kalman filter and Rauch–Tung–Striebel smoother. Sensors 18:198. https://doi.org/10.3390/s18010198
Zheng DW, Zhong P, Ding XL, Chen W (2005) Filtering GPS time-series using a Vondrak filter and cross-validation. J Geod 79:363–369. https://doi.org/10.1007/s00190-005-0474-x
Zheng K et al (2019) Mitigation of unmodeled error to improve the accuracy of multi-GNSS PPP for crustal deformation monitoring. Remote Sens 11:2232. https://doi.org/10.3390/rs11192232
Zumberge JF, Heflin MB, Jefferson DC, Watkins MM, Webb FH (1997) Precise point positioning for the efficient and robust analysis of GPS data from large networks. J Geophys Res Solid Earth 102:5005–5017. https://doi.org/10.1029/96jb03860
Acknowledgements
This work is partially sponsored by the National Natural Science Foundation of China (Grant Numbers 41604006, 41874006, 41674008, and 41774005) and partially sponsored by the Natural Science Foundation of Jiangsu Province (Grant Number BK20160247). The authors are grateful for the open-source software: PRIDE PPP-AR. The authors are also grateful to two anonymous reviewers for providing many valuable comments which help improving the manuscript significantly.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Yang, L., Gao, J., Chang, G. et al. Effectiveness of L1-norm regularization sidereal filtering for precise point positioning. Acta Geod Geophys 55, 593–607 (2020). https://doi.org/10.1007/s40328-020-00308-2
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s40328-020-00308-2