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Integer-estimable FDMA model as an enabler of GLONASS PPP-RTK

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Abstract

PPP-RTK extends the precise point positioning (PPP) concept by incorporating the idea of integer ambiguity resolution underlying the real-time kinematic (RTK) technique, making rapid initialization and high accuracy attainable with a standalone receiver. While PPP-RTK has been well achieved by using global navigation satellite system code division multiple access observables, GLONASS PPP-RTK is nonetheless challenging due to the nature of frequency division multiple access (FDMA) observables. In this work, we present a GLONASS PPP-RTK concept that takes advantage of the integer-estimable FDMA (IE-FDMA) model recently proposed in Teunissen (in GPS Solut 23(4):1–19, 2019. https://doi.org/10.1007/s10291-019-0889-0) to guarantee rigorous integer ambiguity resolution and simultaneously takes care of the presence of the inter-frequency biases (IFBs) in homogeneous and heterogeneous network configurations. When conducting GLONASS PPP-RTK based on a network of homogeneous receivers, code and phase observation equations are used to construct the IE-FDMA model, in which the IFBs are implicitly eliminated through reparameterization. For a network consisting of heterogeneous receivers, we exclude the code observables and develop a phase-only IE-FDMA model instead, thereby circumventing the adverse effects of IFBs. For verification purposes, we collect a set of five-day global positioning system (GPS) and GLONASS data from two regional networks: one equipped with homogeneous receivers and another with heterogeneous receivers. The results show that the GLONASS-specific network corrections, including satellite clocks, satellite phase biases, and ionospheric delays estimated by the two networks, are as precise as those of their GPS-specific counterparts. Via satellite clock and phase bias corrections, we succeed in fixing both GPS and GLONASS ambiguities, shortening the convergence time to 5 (12) min, compared to 11 (18) min of ambiguity-float positioning in the case of a homogeneous (heterogeneous) network with a data sampling rate of 30 s. For ambiguity-fixed positioning, the convergence time defined in this work also indicates the time to first fix since the positioning error converges to the centimeter level once successful integer ambiguity resolution is achieved. Adding ionospheric corrections further speeds up the initialization in the two networks, with the convergence time being reduced to 0.5 (3) min. Compared with GPS-only positioning, the integration of GPS and GLONASS yields an improvement of 8–34% in accuracy and leads to a reduction of 25–50% in convergence.

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Data availability

The RINEX data acquired from the National Geodetic Survey (NGS) CORS network in the USA can be downloaded at ftp://geodesy.noaa.gov/cors/.

References

  • Al-Shaery A, Zhang S, Rizos C (2013) An enhanced calibration method of GLONASS inter-channel bias for GNSS RTK. GPS Solutions 17(2):165–173

    Article  Google Scholar 

  • Baarda W (1973) S-transformations and criterion matrices. In: Publications on geodesy, 18 (vol 5, no 1), Netherlands Geodetic Commission, Delft, The Netherlands

  • Banville S, Collins P, Lahaye F (2013a) Concepts for undifferenced GLONASS ambiguity resolution. In: Proceedings of the 26th international technical meeting of the satellite division of the institute of navigation (ION GNSS+ 2013). Nashville, Tennessee, 16–20 September, pp 1186–1197

  • Banville S, Collins P, Lahaye F (2013b) GLONASS ambiguity resolution of mixed receiver types without external calibration. GPS Solut 17(3):275–282

    Article  Google Scholar 

  • Banville S et al (2021) Enabling ambiguity resolution in CSRS-PPP. NAVIG J Inst Navig 68(2):433–451

    Article  Google Scholar 

  • Blewitt G (1990) An automatic editing algorithm for GPS data. Geophys Res Lett 17(3):199–202

    Article  Google Scholar 

  • Bona P (2000) Precision, cross correlation, and time correlation of GPS phase and code observations. GPS Solut 4(2):3–13

    Article  Google Scholar 

  • Brack A, Männel B, Schuh H (2020) GLONASS FDMA data for RTK positioning: a five-system analysis. GPS Solut 25(1):1–13. https://doi.org/10.1007/s10291-020-01043-5

    Article  Google Scholar 

  • Collins P, Bisnath S, Lahaye F, Héroux P (2010) Undifferenced GPS ambiguity resolution using the decoupled clock model and ambiguity datum fixing. NAVIG J Inst Navig 57(2):123–135

    Article  Google Scholar 

  • Ge M, Gendt G, Ma R, 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, Bock Y (2016) GLONASS fractional-cycle bias estimation across inhomogeneous receivers for PPP ambiguity resolution. J Geod 90(4):379–396

    Article  Google Scholar 

  • Hou P, Zhang B, Liu T (2020) Integer-estimable GLONASS FDMA model as applied to Kalman-filter-based short-to long-baseline RTK positioning. GPS Solut 24(4):1–14. https://doi.org/10.1007/s10291-020-01008-8

    Article  Google Scholar 

  • Hu J, Zhang X, Li P, Ma F, Pan L (2020) Multi-GNSS fractional cycle bias products generation for GNSS ambiguity-fixed PPP at Wuhan University. GPS Solut 24(1):1–13. https://doi.org/10.1007/s10291-019-0929-9

    Article  Google Scholar 

  • Khodabandeh A (2021) Single-station PPP-RTK: correction latency and ambiguity resolution performance. J Geod 95(4):1–24. https://doi.org/10.1007/s00190-021-01490-z

    Article  Google Scholar 

  • Khodabandeh A, Teunissen P (2015) An analytical study of PPP-RTK corrections: precision, correlation and user-impact. J Geod 89(11):1109–1132

    Article  Google Scholar 

  • Khodabandeh A, Teunissen P (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 

  • Kozlov D, Tkachenko M, Tochilin A (2000) Statistical characterization of hardware biases in GPS+ GLONASS receivers. In: Proceedings of the 13th international technical meeting of the Satellite Division of The Institute of Navigation (ION GPS 2000). Salt Lake City, UT, 19–22 September, pp 817–826

  • 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(2):135–149

    Article  Google Scholar 

  • Leandro R, Santos M, Langley R UNB neutral atmosphere models: development and performance. In: Proceedings of the 2006 national technical meeting of the institute of navigation. pp 564–573

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

    Book  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(6):579–608

    Article  Google Scholar 

  • Liu Y, Song W, Lou Y, Ye S, Zhang R (2017) GLONASS phase bias estimation and its PPP ambiguity resolution using homogeneous receivers. GPS Solut 21(2):427–437

    Article  Google Scholar 

  • Odijk D (2002) Fast precise GPS positioning in the presence of ionospheric delays. In: Publications on geodesy, 52, Netherlands Geodetic Commission, Delft, The Netherlands

  • Odijk D, Teunissen PJG, Zhang B (2012) Single-frequency integer ambiguity resolution enabled GPS precise point positioning. J Surv Eng 138(4):193–202

    Article  Google Scholar 

  • Odijk D, Zhang B, Khodabandeh A, Odolinski R, Teunissen PJG (2016) On the estimability of parameters in undifferenced, uncombined GNSS network and PPP-RTK user models by means of S-system theory. J Geod 90(1):15–44

    Article  Google Scholar 

  • Reussner N, Wanninger L (2011) GLONASS inter-frequency biases and their effects on RTK and PPP carrier-phase ambiguity resolution. In: Proceedings of ION GNSS 24th international technical meeting of the Satellite Division (ION GNSS 2011). Portland, OR, 19–23 September pp 712–716

  • Rocken C et al (1993) Sensing atmospheric water vapor with the Global Positioning System. Geophys Res Lett 20(23):2631–2634

    Article  Google Scholar 

  • Schönemann E, Becker M, Springer T (2011) A new approach for GNSS analysis in a multi-GNSS and multi-signal environment. J Geod Sci 1(3):204–214

    Google Scholar 

  • Sleewagen J (2012) Demystifying GLONASS inter-frequency carrier phase biases. Inside GNSS 7(3):57–61

    Google Scholar 

  • Takasu T, Yasuda A (2009) Development of the low-cost RTK-GPS receiver with an open source program package RTKLIB. In: International symposium on GPS/GNSS. Jeju, Korea, 4–6 November

  • Teunissen PJG (1985) Generalized inverses, adjustment the datum problem and S-transformations. In: Grafarend EW, Sanso F (eds) Optimization and design of geodetic networks. Springer, Berlin,

  • 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 P (1998) The ionosphere-weighted GPS baseline precision in canonical form. J Geodesy 72(2):107–111

    Article  Google Scholar 

  • Teunissen PJG (2019) A new GLONASS FDMA model. GPS Solut 23(4):1–19. https://doi.org/10.1007/s10291-019-0889-0

    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, Khodabandeh A (2019) GLONASS ambiguity resolution. GPS Solut 23(4):1–11. https://doi.org/10.1007/s10291-019-0890-7

    Article  Google Scholar 

  • Teunissen PJG, Montenbruck O (2017) Springer handbook of global navigation satellite systems. Springer, Berlin

    Book  Google Scholar 

  • Teunissen PJG, Odijk D, Zhang B (2010) PPP-RTK: results of CORS network-based PPP with integer ambiguity resolution. J Aeronaut Astronaut Aviat Ser A 42(4):223–230

    Google Scholar 

  • Tian Y, Ge M, Neitzel F (2015) Particle filter-based estimation of inter-frequency phase bias for real-time GLONASS integer ambiguity resolution. J Geod 89(11):1145–1158

    Article  Google Scholar 

  • Wang K, Khodabandeh A, Teunissen P (2017) A study on predicting network corrections in PPP-RTK processing. Adv Space Res 60(7):1463–1477

    Article  Google Scholar 

  • Wanninger L (2012) Carrier-phase inter-frequency biases of GLONASS receivers. J Geod 86(2):139–148

    Article  Google Scholar 

  • Wübbena G, Schmitz M, Bagge A (2005) PPP-RTK: precise point positioning using state-space representation in RTK networks. In: Proceedings of the 18th international technical meeting of the satellite division of the institute of navigation (ION GNSS 2005). Long Beach, CA, 13–16 September, pp 13–16

  • Yamada H, Takasu T, Kubo N, Yasuda A (2010) Evaluation and calibration of receiver inter-channel biases for RTK-GPS/GLONASS. In: Proceedings of the 23rd international technical meeting of the satellite division of the institute of navigation (ION GNSS 2010). Portland, OR, 21–24 September, pp 1580–1587

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

    Article  Google Scholar 

  • Zhang B, Hou P, Liu T, Yuan Y (2020) A single-receiver geometry-free approach to stochastic modeling of multi-frequency GNSS observables. J Geod 94(4):1–21. https://doi.org/10.1007/s00190-020-01366-8

    Article  Google Scholar 

Download references

Acknowledgements

This work was partially funded by the National Natural Science Foundation of China (Grant Nos. 42022025, 41774042) and the Scientific Instrument Developing Project of the Chinese Academy of Sciences (Grant No. YJKYYQ20190063). The corresponding author is supported by the CAS Pioneer Hundred Talents Program.

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Authors and Affiliations

  1. State Key Laboratory of Geodesy and Earth’s Dynamics, Innovation Academy for Precision Measurement Science and Technology, Chinese Academy of Sciences, Wuhan, China

    Baocheng Zhang, Pengyu Hou, Jiuping Zha & Teng Liu

  2. College of Earth and Planetary Sciences, University of Chinese Academy of Sciences, Beijing, China

    Pengyu Hou & Jiuping Zha

Authors
  1. Baocheng Zhang
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  2. Pengyu Hou
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  3. Jiuping Zha
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  4. Teng Liu
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Contributions

BZ proposed the method, designed the research, and wrote the manuscript. PH developed the software, processed the data, and wrote the manuscript. JZ helped process the data. TL revised the manuscript. All authors contributed to the analysis, interpretation, and discussion of the results.

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Correspondence to Baocheng Zhang.

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Zhang, B., Hou, P., Zha, J. et al. Integer-estimable FDMA model as an enabler of GLONASS PPP-RTK. J Geod 95, 91 (2021). https://doi.org/10.1007/s00190-021-01546-0

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