GPS Solutions

, 23:22 | Cite as

A triple-frequency cycle slip detection and correction method based on modified HMW combinations applied on GPS and BDS

  • Dongsheng Zhao
  • Gethin Wyn Roberts
  • Craig M. HancockEmail author
  • Lawrence Lau
  • Ruibin Bai
Original Article


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°.


GPS BDS Triple frequency Cycle slips 



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.


  1. 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 145–154Google Scholar
  2. Blewitt G (1990) An automatic editing algorithm for GPS data. Geophys Res Lett 17(3):199–202CrossRefGoogle Scholar
  3. 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):247–260CrossRefGoogle Scholar
  4. Dai Z (2012) MATLAB software for GPS cycle slip processing. GPS Solut 16(2):267–272CrossRefGoogle Scholar
  5. 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 1060–1066Google Scholar
  6. Dai Z, Knedlik S, Loffeld O (2009) Instantaneous triple-frequency GPS cycle slip detection and repair. Int J Navig Obs 2009:1–15Google Scholar
  7. 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):527–542CrossRefGoogle Scholar
  8. de Lacy MC, Reguzzoni M, Sansò F (2012) Real-time cycle slip detection in triple-frequency GNSS. GPS Solut 16(3):353–362CrossRefGoogle Scholar
  9. Feng Y (2008) GNSS three carrier ambiguity resolution using ionosphere-reduced virtual signals. J Geod 82(12):847–862CrossRefGoogle Scholar
  10. 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 1213–1231Google Scholar
  11. Hofmann-Wellenhof B, Lichtenegger H, Collins J (2001) Global positioning system: theory and practice, 5th edn. Springer, New York. CrossRefGoogle Scholar
  12. 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):840–847Google Scholar
  13. 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):761–769CrossRefGoogle Scholar
  14. 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):689CrossRefGoogle Scholar
  15. 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):927–943CrossRefGoogle Scholar
  16. Liu Z (2011) A new automated cycle slip detection and repair method for a single dual-frequency GPS receiver. J Geod 85(3):171–183CrossRefGoogle Scholar
  17. 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):427CrossRefGoogle Scholar
  18. Melbourne WG (1985) The case for ranging in GPS-based geodetic systems. In: Proc. positioning with GPS-1985, NGS, Rockville, MD, pp 373–386Google Scholar
  19. 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 20:289–297CrossRefGoogle Scholar
  20. 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 19–26Google Scholar
  21. 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):144–149CrossRefGoogle Scholar
  22. 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 403–412Google Scholar
  23. 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 22:6CrossRefGoogle Scholar
  24. Xu G (2007) GPS: theory, algorithms and applications, 2nd edn. Springer, BerlinGoogle Scholar
  25. Zhang X, Li X (2012) Instantaneous re-initialization in real-time kinematic PPP with cycle slip fixing. GPS Solut 16(3):315–327CrossRefGoogle Scholar
  26. Zhang X, Li P (2016) Benefits of the third frequency signal on cycle slip correction. GPS Solut 20:451–460CrossRefGoogle Scholar
  27. 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):589–599CrossRefGoogle Scholar
  28. 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):381–391CrossRefGoogle Scholar
  29. 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):1929CrossRefGoogle Scholar
  30. 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 4046–4054Google Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Civil EngineeringThe University of Nottingham Ningbo ChinaNingboChina
  2. 2.International Doctoral Innovation CenterThe University of Nottingham Ningbo ChinaNingboChina
  3. 3.Faculty of Natural Sciences and Technology, University of the Faroe IslandsTórshavnFaroe Islands
  4. 4.School of Computer ScienceThe University of Nottingham Ningbo ChinaNingboChina

Personalised recommendations