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The realization and evaluation of mixed GPS/BDS PPP ambiguity resolution

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Abstract

Aiming at shortening convergence time and improving positioning accuracy, multi-GNSS precise point positioning (PPP) ambiguity resolution (PPP-AR) has been an important issue in the past decade. In this paper, a mixed (or inter-system) GPS and BDS PPP-AR model with inter-system biases considered is proposed. Datasets from the IGS MGEX network are utilized in the study to evaluate the proposed model. As a critical correction in multi-GNSS PPP-AR, the inter-system bias (ISB) can be treated as a fixed constant or unknown estimate. The effects of various ISB processing methods on other key corrections for PPP-AR, such as fractional cycle bias (FCB) and inter-system phase bias (ISPB), are analyzed. Experimental results indicate that fixing or estimating ISB approaches will not affect GPS FCB estimations. However, various ISB dealing methods will have a significant influence on some BDS FCB and ISPB estimations at some stations because of the limited BDS tracking satellites over long periods of observation. Regardless of the presence of unstable FCB products on some BDS satellites, narrow-lane FCBs on other satellites are time-continuous, and their daily changes are within the range of 0.3 cycle. And in aspect of the time to first fix (TTFF), fixing ISB is superior to estimating it. The performance of the mixed GPS and BDS PPP-AR is evaluated. Experimental results indicate that compared with the intra-system PPP-AR, the mixed method has no superiority when ISB is estimated. While it has a slight improvement in TTFF, i.e., from 969.64 to 897.96 s, however, the total fixed rate decreases from 86.5 to 85.56% when ISB is fixed as a constant. In addition, the mixed PPP-AR shows significant improvement over the intra-system PPP-AR under circumstances with limited satellite visibility.

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References

  • Afifi A, El-Rabbany A (2015) Performance analysis of several GPS/Galileo precise point positioning models. Sensors 15(6):14701–14726

    Article  Google Scholar 

  • Bisnath S, Gao Y (2009) Current state of precise point positioning and future prospects and limitations. In: Sideris MG (ed) Observing our Changing Earth. International Association of Geodesy Symposia, vol 133. Springer, Berlin, pp 615–623

    Chapter  Google Scholar 

  • Cai C, Gao Y (2007) Performance analysis of precise point positioning based on combined GPS and GLONASS. In: Proceedings of ION GNSS 2007, pp 858–865

  • Cai C, Gao Y (2013) Modeling and assessment of combined GPS/GLONASS precise point positioning. GPS Solut 17(2):223–236

    Article  Google Scholar 

  • Cheng S, Wang J, Peng W (2017) Statistical analysis and quality control for GPS fractional cycle bias and integer recovery clock estimation with raw and combined observation models. Adv Space Res 60(12):2648–2659

    Article  Google Scholar 

  • Choi BK, Yoon H (2018) Positioning stability improvement with inter-system biases on multi-GNSS PPP. J Appl Geodesy 12(3):239–248

    Article  Google Scholar 

  • Collins P, Lahaye F, He´rous P, Bisnath S (2008) Precise point positioning with ambiguity resolution using the decoupled clock model. In: Proceedings of ION GNSS 2008. Institute of Navigation, Savannah, GA, 16–19 Sept, pp 1315–1322

  • Dach R, BrockMann E, Schaer S, Beutler G, Meindl M, Prange L, Bock H, Jäggi A, Ostini L (2009) GNSS processing at CODE: status report. J Geod 83(3):353–365

    Article  Google Scholar 

  • Dilssner F, Springer T, Schönemann E, Enderle W (2014) Estimation of satellite antenna phase center corrections for BeiDou. IGS Workshop 2014, Pasadena, California, USA, June 23–27

  • Frei E, Beutler G (1990) Rapid static positioning based on the fast ambiguity resolution approach FARA: theory and first results. Manuscripta Geodaetica 15:325–356

    Google Scholar 

  • 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 Geod 82(7):389–399

    Article  Google Scholar 

  • Geng J, Shi C (2017) Rapid initialization of real-time PPP by resolving undifferenced GPS and GLONASS ambiguities simultaneously. J Geod 91:361–374

    Article  Google Scholar 

  • Geng J, Meng X, Dodson AH, Ge M, Teferle FN (2010) Rapid re-convergences to ambiguity-fixed solutions in precise point positioning. J Geod 84(12):705–714

    Article  Google Scholar 

  • Geng J, Teferle FN, Meng X, Dodson AH (2011) Towards PPP-RTK: ambiguity resolution in real-time precise point positioning. Adv Space Res 47(10):1664–1673

    Article  Google Scholar 

  • Guo F, Li X, Liu W (2016) Mitigating BeiDou satellite-induced code bias: taking into account the stochastic model of corrections. Sensors 16(6):909

    Article  Google Scholar 

  • Khodabandeh A, Teunissen PJG (2016) PPP-RTK and inter-system biases: the ISB look-up table as a means to support multi-system PPP-RTK. J Geod 90(9):837–851

    Article  Google Scholar 

  • Kubo N, Tokura H, Pullen S (2018) Mixed GPS–BeiDou RTK with inter-systems bias estimation aided by CSAC. GPS Solut 22(1):5

    Article  Google Scholar 

  • Landau H, Brandl M, Chen X, Drescher R, Glocker M, Nardo A, Nitschke M, Salazar D, Weinbach U, Zhang F (2013) Towards the inclusion of Galileo and BeiDou/compass satellites in trimble centerpoint RTX. In: Proceedings of the 26th international technical meeting of the satellite division of the institute of navigation (ION GNSS + 2013), Nashville, pp 1215–1223

  • Laurichesse D, Mercier F (2009) Integer ambiguity resolution on undifferenced GPS phase measurements and its application to PPP. Navigation 56(2):135–149

    Article  Google Scholar 

  • Leick A, Rapoport L, Tatarnikov D (2015) GPS satellite surveying, 4th edn. Wiley, Hoboken

    Google Scholar 

  • Li X, Ge M, Zhang H, Wickert J (2013) A method for improving uncalibrated phase delay estimation and ambiguity-fixing in real-time precise point positioning. J Geod 87(5):405–416

    Article  Google Scholar 

  • Li X, Ge M, Douša J, Wickert J (2014) Real-time precise point positioning regional augmentation for large GPS reference networks. GPS Solut 18(1):61–71

    Article  Google Scholar 

  • Li P, Zhang X, Guo F (2017) Ambiguity resolved precise point positioning with GPS and BeiDou. J Geod 91(1):25–40

    Article  Google Scholar 

  • Li X, Li X, Yuan Y, Zhang K, Zhang X, Wickert J (2018) Multi-GNSS phase delay estimation and PPP ambiguity resolution: GPS, BDS, GLONASS, Galileo. J Geod 92:579–608

    Article  Google Scholar 

  • Liu Y, Ye S, Song W, Lou Y, Chen D (2017) Integrating GPS and BDS to shorten the initialization time for ambiguity-fixed PPP. GPS Solut 21(2):333–343

    Article  Google Scholar 

  • Nadarajah N, Khodabandeh A, Wang K, Choudhury M, Teunissen PJG (2018) Multi-GNSS PPP-RTK: From Large-to Small-Scale Networks. Sensors 18(4):1078

    Article  Google Scholar 

  • Niell AE (1996) Global mapping functions for the atmosphere delay at radio wavelengths. J Geophys Res 101(B2):3227–3246

    Article  Google Scholar 

  • Odijk D, Teunissen PJG (2013) Characterization of between-receiver GPS-Galileo inter-system biases and their effect on mixed ambiguity resolution. GPS solut 17(4):521–533

    Article  Google Scholar 

  • Odijk D, Zhang B, Teunissen PJG (2015) Multi-GNSS PPP and PPP-RTK: some GPS + BDS results in Australia. In: Proceedings of the China Satellite Navigation Conference (CSNC) 2015, Vol 2. Springer, Berlin, pp 613–623

  • Odijk D, Khodabandeh A, Nadarajah N, Choudhury M, Zhang B, Li W, Teunissen PJG (2017) PPP-RTK by means of S-system theory: Australian network and user demonstration. J Spat Sci 62(1):3–27

    Article  Google Scholar 

  • Saastamoinen J (1973) Contribution to the theory of atmospheric refraction. Bull Geodesique 107:13–34

    Article  Google Scholar 

  • Takasu T, Yasuda A (2010) Kalman-filter-based integer ambiguity resolution strategy for long-baseline RTK with ionosphere and troposphere estimation. In: Proceedings of the ION GNSS, Portland, OR, USA, 21–24 Sept 2010, pp 161–171

  • Teunissen PJG (1995) The least-squares ambiguity decorrelation adjustment: a method for fast GPS integer ambiguity estimation. J Geod 70(1–2):65–82

    Article  Google Scholar 

  • Teunissen PJG (1998) Success probability of integer GPS ambiguity rounding and bootstrapping. J Geod 72(72):606–612

    Article  Google Scholar 

  • Teunissen PJG, Khodabandeh A (2015) Review and principles of PPP–RTK methods. J Geod 89(3):217–240

    Article  Google Scholar 

  • Teunissen PJG, Verhagen S (2009) GNSS carrier phase ambiguity resolution: challenges and open problems. In: Sideris MG (ed) Observing our changing Earth. Springer, Berlin, pp 785–792

    Google Scholar 

  • Teunissen PJG, Joosten P, Tiberius C (1999) Geometry-free ambiguity success rates in case of partial fixing. In: Proceedings of the 1999 national technical meeting of The Institute of Navigation. SanDiego, CA, pp 201–207

  • Yi W, Song YW, Lou Y, Shi C, Yao Y, Guo H, Chen M, Wu J (2017) Improved method to estimate undifferenced satellite fractional cycle biases using network observations to support PPP ambiguity resolution. GPS Solut 21(3):1369–1378

    Article  Google Scholar 

  • Zhang B, Teunissen PJG, Odijk D (2011) A novel un-differenced PPP-RTK concept. J Navig 64(S1):S180–S191

    Article  Google Scholar 

  • Zou X, TangW Shi C, Liu J (2015) Instantaneous ambiguity resolution for URTK and its seamless transition with PPP-AR. GPS Solut 19(4):559–567

    Article  Google Scholar 

  • Zumberge JF, Heflin MB, Jefferson DC (1997) Precise point positioning for the efficient and robust analysis of GPS data from large networks. J Geophys Res 102(B3):5005–5017

    Article  Google Scholar 

Download references

Acknowledgements

This work has been supported by National Natural Science Foundation of China (Grant No. 41504027).

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Correspondence to Chaoqian Xu.

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Yao, Y., Peng, W., Xu, C. et al. The realization and evaluation of mixed GPS/BDS PPP ambiguity resolution. J Geod 93, 1283–1295 (2019). https://doi.org/10.1007/s00190-019-01245-x

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  • DOI: https://doi.org/10.1007/s00190-019-01245-x

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