Abstract
By taking advantage of the additional combined signals introduced by triple-frequency GNSS, we propose a cycle slip detection and correction method based on the traditional extra-wide-lane Hatch–Melbourne–Wübbena (HMW) combination and also modified HMW combinations. Instead of using the combined code signals directly in the traditional HMW combination, the modified HMW combination adopts the original code signals and one combined phase signal with corrected cycle slips to eliminate the ionospheric bias and reduce the effect of the noise induced by the code measurement. To determine the optimally combined signals and the corresponding coefficients in the modified HMW combination, four constrained conditions are proposed based on the maximum acceptable ionospheric bias and measurement noise of the combination in the process of cycle slip detection. Two optimally combined signals are selected; however, the second best signal cannot maintain a 100% success rate when epoch intervals are increased, due to the effect of the remaining ionospheric bias. To solve this problem, a scale factor is introduced to balance the corrected percentage of the ionospheric bias and the amplification of the measurement noise. These selected signals are further tested with real triple-frequency GPS and BDS observations. Results show that the proposed method can provide a 100% success rate in detecting cycle slips in the observations with large epoch intervals (up to 30 s) from medium earth orbit satellites with elevation angles above 5°, as well as inclined geosynchronous orbit and geostationary orbit satellites with elevation angles above 20°.
Similar content being viewed by others
References
Bisnath SB, Langley RB (2000) Efficient, automated cycle slip correction of dual-frequency kinematic GPS data. In: Proc. ION GPS 2000, Institute of Navigation, Salt Lake City, UT, USA, September 19–22, pp 145–154
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
Dai Z (2012) MATLAB software for GPS cycle slip processing. GPS Solut 16(2):267–272
Dai Z, Knedlik S, Loffeld O (2008) Cycle slip detection, determination, and validation for triple-frequency GPS. In: 2008 IEEE/ION position, location and navigation symposium, Monterey, CA, pp 1060–1066
Dai Z, Knedlik S, Loffeld O (2009) Instantaneous triple-frequency GPS cycle slip detection and repair. Int J Navig Obs 2009:1–15
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
de Lacy MC, Reguzzoni M, Sansò F (2012) Real-time cycle slip detection in triple-frequency GNSS. GPS Solut 16(3):353–362
Feng Y (2008) GNSS three carrier ambiguity resolution using ionosphere-reduced virtual signals. J Geod 82(12):847–862
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, Feb. 8–12, vol 2, pp 1213–1231
Hofmann-Wellenhof B, Lichtenegger H, Collins J (2001) Global positioning system: theory and practice, 5th edn. Springer, New York. https://doi.org/10.1007/978-3-7091-6199-9
Huang L, Zhai G, Ouyang Y, Lu X, Wu T, Deng K (2015) Triple-frequency TurboEdit cycle slip processing method of weakening ionospheric activity. Acta Geodaetica Cartogr Sin 44(8):840–847
Huang L, Lu Z, Zhai G, Ouyang Y, Huang M, Lu X, Wu T, Li K (2016) A new triple-frequency cycle slip detecting algorithm validated with BDS data. GPS Solut 20(4):761–769
Jan S-S, Tao A-L (2016) Comprehensive comparisons of satellite data, signals, and measurements between the BeiDou navigation satellite system and the global positioning system. Sensors 16(5):689
Li M, Qu L, Zhao Q, Guo J, Su X, Li X (2014) Precise point positioning with the BeiDou navigation satellite system. Sensors 14(1):927–943
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
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
Melbourne WG (1985) The case for ranging in GPS-based geodetic systems. In: Proc. positioning with GPS-1985, NGS, Rockville, MD, pp 373–386
Nadarajah N, Khodabandeh A, Teunissen PJG (2016) Assessing the IRNSS L5-signal in combination with GPS, Galileo, and QZSS L5/E5a-signals for positioning and navigation. GPS Solut 20:289–297
Roberts GW, Meng X, Dodson AH (2002) Using adaptive filtering to detect multipath and cycle slips in GPS/accelerometer bridge deflection monitoring data. In: FIG XXII international congress, Washington, DC, pp 19–26
Wu Y, Jin SG, Wang ZM, Liu JB (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 first international symposium on precise positioning with the global positioning system, Rockville, 15–19 April, MD, USA, pp 403–412
Xiao G, Mayer M, Heck B, Sui L, Zeng T, Zhao D (2018) Improved time-differenced cycle slip detect and repair for GNSS undifferenced observations. GPS Solut 22:6
Xu G (2007) GPS: theory, algorithms and applications, 2nd edn. Springer, Berlin
Zhang X, Li X (2012) Instantaneous re-initialization in real-time kinematic PPP with cycle slip fixing. GPS Solut 16(3):315–327
Zhang X, Li P (2016) Benefits of the third frequency signal on cycle slip correction. GPS Solut 20:451–460
Zhao Q, Dai Z, Hu Z, Sun B, Shi C, Liu J (2014) Three-carrier ambiguity resolution using the modified TCAR method. GPS Solut 19(4):589–599
Zhao Q, Sun B, Dai Z, Hu Z, Shi C, Liu J (2015) Real-time detection and repair of cycle slips in triple-frequency GNSS measurements. GPS Solut 19(3):381–391
Zhao D, Roberts GW, Lau L, Hancock CM, Bai R (2016) A theoretical and empirical integrated method to select the optimal combined signals for geometry-free and geometry-based three-carrier ambiguity resolution. Sensors 16(11):1929
Zhao D, Roberts GW, Hancock CM, Lau L, Bai R (2017) Cycle slip detection for triple-frequency GPS observations under ionospheric scintillation. In: Proc. ION GNSS 2017, Institute of Navigation, Portland, OR, USA, September 25–29, pp 4046–4054
Acknowledgements
The authors gratefully acknowledge Jet Propulsion Laboratory and the Curtin GNSS Research Center for providing GNSS products and data, respectively. This work was carried out at the International Doctoral Innovation Center (IDIC). The authors acknowledge the financial support from Ningbo Education Bureau, Ningbo Science and Technology Bureau, China’s MOST and The University of Nottingham. The work is also partially supported by the Ningbo Science and Technology Bureau as part of the International Academy for the Marine Economy and Technology (IAMET) Project “Structural Health Monitoring of Infrastructure in the Logistics Cycle” (2014A35008), Young Scientist program of Natural Science Foundation of China (NSFC) with a project code 41704024, Zhejiang Provincial Natural Science Foundation of China under Grant no. LY16D040001 and ‘the Open Foundation of Key Laboratory of Precise Engineering and Industry Surveying of National Administration of Surveying, Mapping and Geoinformation’ (PF2017-6). The authors would like to acknowledge Dr. Lingyong Huang, from China Aerospace Surveying and Mapping Satellite Center, Beijing 102102, China, due to his help during the developing of the algorithm.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Zhao, D., Roberts, G.W., Hancock, C.M. et al. A triple-frequency cycle slip detection and correction method based on modified HMW combinations applied on GPS and BDS. GPS Solut 23, 22 (2019). https://doi.org/10.1007/s10291-018-0817-8
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s10291-018-0817-8