Abstract
Cycle slip determination plays an important role in continuous real-time kinematic (RTK) positioning. Since cycle slips should be processed at each epoch, a fast determination method is needed for high-speed RTK applications, such as autopilot and airborne positioning, in which case high-sampling-rate GNSS data (such as 50 HZ) are required to be processed in real time. The geometry-free (GF) phase combination is one of the most commonly used combinations to deal with the cycle slips. However, the GF phase combination cannot distinguish the frequency on which cycle slips occur. Therefore, other methods, such as the Hatch–Melbourne–Wübbena (HMW) combination, are usually adopted to determine the frequency and the size of the cycle slips. Since noisy code pseudorange measurements are introduced, it is difficult to identify the small cycle slips, especially when cycle slips occur in multiple satellites and multiple frequencies simultaneously. In this contribution, a modified geometry-free (MGF) phase-only linear combination is proposed to quickly determine cycle slips for high-sampling-rate multi-GNSS RTK. The MGF algorithm utilizes the decimal part of the time difference GF phase combination to determine cycle slips satellite by satellite. It can directly estimate the cycle slips on a specific frequency, rather than a combined cycle slip as in the GF combination. The MGF method is tested against airborne and other kinematic situations. The results show that the MGF method can quickly determine the small cycle slips on each frequency even when all carrier phases suffer from cycle slips simultaneously. Compared with the combined method of GF and HMW and using a 24-h 1-Hz GPS/BDS dataset, the MGF method is 144 times faster and reduces the number of incorrectly repaired cycle slips from 4005 to 141.
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References
Baselga S (2011) Nonexistence of rigorous tests for multiple outlier detection in least-squares adjustment. J Surv Eng 137(3):109–112
Bastos L, Landau H (1988) Fixing cycle slips in dual-frequency kinematic GPS-applications using Kalman filtering. Manuscr Geodaet 13(4):249–256
Blewitt G (1990) An automatic editing algorithm for GPS data. Geophys Res Lett 17(3):199–202
Cai C, Liu Z, Xia P, Dai W (2013) Cycle slip detection and repair for undifferenced GPS observations under high ionospheric activity. GPS Solut 17(2):247–260
Chang G, Xu T, Yao Y, Wang Q (2018) Adaptive Kalman filter based on variance component estimation for the prediction of ionospheric delay in aiding the cycle slip repair of GNSS triple-frequency signals. J Geod 92(11):1241–1253. https://doi.org/10.1007/s00190-018-1116-4
Collin F, Warnant R (1995) Application of the wavelet transform for GPS cycle slip correction and comparison with Kalman filter. Manuscr Geodaet 20(3):161–172
de Lacy MC, Reguzzoni M, Sansò F, Venuti G (2008) The Bayesian detection of discontinuities in a polynomial regression and its application to the cycle-slip problem. J Geod 82(9):527–542. https://doi.org/10.1007/s00190-007-0203-8
Euler HJ, Schaffrin B (1991) On a measure for the discernibility between different ambiguity solutions in the static-kinematic GPS-mode. In: Schwarz KP, Lachapelle G (eds) Kinematic systems in geodesy, surveying, and remote sensing. International Association of Geodesy Symposia, vol 107. Springer, New York, pp 285–295
Gao Y, Li Z (1999) Cycle slip detection and ambiguity resolution algorithms for dual-frequency GPS data processing. Mar Geod 22(3):169–181
Goad C (1985) Precise positioning with the global positioning system. In: Proceedings of 3rd international symposium on inertial technology for surveying and geodesy, pp 745–756
Hatch R (1982) The synergism of GPS code and carrier measurements. In: Proceedings of the third international symposium on satellite Doppler positioning at physical sciences. Laboratory of New Mexico State University, 8–12 Feb, vol 2, pp 1213–1231
Hu GR, Khoo HS, Goh PC, Law CL (2003) Development and assessment of GPS virtual reference stations for RTK positioning. J Geod 77(5–6):292–302. https://doi.org/10.1007/s00190-003-0327-4
Jazaeri S, Amiri-Simkooei AR, Sharifi MA (2012) Fast integer least-squares estimation for GNSS high-dimensional ambiguity resolution using lattice theory. J Geod 86(2):123–136. https://doi.org/10.1007/s00190-011-0501-z
Ji S, Chen W, Zhao C, Ding X, Chen Y (2007) Single epoch ambiguity resolution for Galileo with the CAR and LAMBDA methods. GPS Solut 11(4):259–268
Ju B, Gu D, Chang X, Herring TA, Duan X, Wang Z (2017) Enhanced cycle slip detection method for dual-frequency BeiDou GEO carrier phase observations. GPS Solut 21(3):1227–1238
Kleusberg A, Georgiadou Y, van den Heuvel F, Heroux P (1993) GPS data preprocessing with DIPOP 3.0. Internal technical memorandum, Department of Surveying Engineering, University of New Brunswick, Fredericton, New Brunswick, Canada
Knight NL, Wang J, Rizos C (2010) Generalized measures of reliability for multiple outliers. J Geod 84(10):625–635
Li B, Qin Y, Li Z, Lou L (2016) Undifferenced cycle slip estimation of triple-frequency BeiDou signals with ionosphere prediction. Mar Geod 39(5):348–365
Lichtenegger H, Hofmann-Wellenhof B (1990) GPS-data preprocessing for cycle-slip detection. Proceedings of global positioning system: an overview, IAG symposium 102:57–68
Liu Z (2011) A new automated cycle slip detection and repair method for a single dual-frequency GPS receiver. J Geod 85(3):171–183. https://doi.org/10.1007/s00190-010-0426-y
Liu W, Jin X, Wu M, Hu J, Wu Y (2018) A new real-time cycle slip detection and repair method under high ionospheric activity for a triple-frequency GPS/BDS receiver. Sensors 18(2):427
Mader GL (1986) Dynamic positioning using GPS carrier phase measurements. Manuscr Geodaet 11:272–277
Malys S, Jensen PA (1990) Geodetic point positioning with GPS carrier beat phase data from the CASA UNO experiment. Geophys Res Lett 17(5):651–654
Melbourne WG (1985) The case for ranging in GPS based geodetic systems. In: Proceedings of the 1st international symposium on precise positioning with the global positioning system, Rockville, MD, USA, 15–19 April, pp 373–386
Odijk D, Verhagen S (2007) Recursive detection, identification and adaptation of model errors for reliable high-precision GNSS positioning and attitude determination. In: 3rd international conference on recent advances in space technologies, RAST 2007. Istanbul, Turkey, pp 624–629. DOI: 10.1109/RAST.2007.4284068.
Rizos C (2007) Alternatives to current GPS-RTK services and some implications for CORS infrastructure and operations. GPS Solut 11(3):151–158
Sükeová L, Santos MC, Langley RB, Leandro RF, Nnani O, Nievinski F (2007) GPS L2C signal quality analysis. In: Proceedings of the 63rd annual meeting of the institute of navigation, Cambridge, MA, April 2007, pp 232–241
Teunissen PJG (1990) Quality control in integrated navigation systems. IEEE Aerosp Electron Syst Mag 5(7):35–41. https://doi.org/10.1109/62.134219
Teunissen PJG (1998) Success probability of integer GPS ambiguity rounding and bootstrapping. J Geod 72(10):606–612
Teunissen PJG (1999a) Minimal detectable biases of GPS data. J Geod 72(4):236–244
Teunissen PJG (1999b) An optimality property of the integer least-squares estimator. J Geod 73(11):587–593
Teunissen PJG, Odijk D (2003) Rank defect integer estimation and phase-only modernized GPS ambiguity resolution. J Geod 76(9–10):259–268
Wu Y, Jin S, Wang Z, Liu J (2010) Cycle slip detection using multi-frequency GPS carrier phase observations: a simulation study. Adv Space Res 46(2):144–149
Wübbena G (1985) Software developments for geodetic positioning with GPS using TI 4100 code and carrier measurements. In: Proceedings of 1st international symposium on precise positioning with the global positioning system. Rockville, MD, USA, 15–19 April, pp 403–412
Ye S, Liu Y, Song W, Lou Y, Yi W, Zhang R, Jiang P, Xiang Y (2016) A cycle slip fixing method with GPS+GLONASS observations in real-time kinematic PPP. GPS Solut 20(1):101–110
Zhao D, Roberts GW, Hancock CM, Lau L, Bai R (2019a) A triple-frequency cycle slip detection and correction method based on modified HMW combinations applied on GPS and BDS. GPS Solut 23(1):22. https://doi.org/10.1007/s10291-018-0817-8
Zhao L, Zhu K, Zhang S (2019b) Study on integrated cycle slip handling using GPS/Galileo combined observations. GPS Solut 23(3):77. https://doi.org/10.1007/s10291-019-0867-6
Zumberge JF, Heflin MB, Jefferson DC, Watkins MM (1997) Precise point positioning for the efficient and robust analysis of GPS data from large networks. J Geophys Res 102(B3):5005–5017
Acknowledgements
This work is supported by the National Natural Science Foundation of China (Nos. 41704028, 41374032) and the Fundamental Research Funds for the Central Universities (2682017CX086). The two airborne datasets of the kinematic experiments are from the National Oceanic and Atmospheric Administration (NOAA) and GAMIT data examples. All this support is gratefully acknowledged. Our special thanks go to all the anonymous reviewers for their constructive and valuable comments.
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Feng, W., Zhao, Y., Zhou, L. et al. Fast cycle slip determination for high-rate multi-GNSS RTK using modified geometry-free phase combination. GPS Solut 24, 42 (2020). https://doi.org/10.1007/s10291-020-0956-6
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DOI: https://doi.org/10.1007/s10291-020-0956-6