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Real-time cascading PPP-WAR based on Kalman filter considering time-correlation

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Abstract

Precise point positioning (PPP) with wide-lane ambiguity resolution (PPP-WAR) can quickly achieve decimeter-level positioning accuracy, which is an essential improvement for real-time PPP in terms of reliability and accuracy. However, current implementations of PPP-WAR are based only on the standard Kalman filter (KF) under the assumption of uncorrelated measurements. As Global Navigation Satellite System measurements are often contaminated by colored noises, a KF considering the time-correlation of measurements (CKF) has the potential to improve the performance of PPP-WAR. In this paper, we proposed a real-time cascading PPP-WAR technique based on the CKF model. A real-time kinematic vehicle experiment is conducted to assess the performance of the proposed real-time PPP-WAR method. On the one hand, we analyze and compare the efficiency of CKF-based cascading PPP-WAR with that of KF-based PPP-WAR. The filter output analysis shows that the proposed CKF method is, overall more efficient than the standard KF method in terms of performance indicators, such as wide-lane ambiguity fix-rate, time-to-first-fix, ambiguity residual statistics and correctness of the filter’s stochastic model. On the other hand, we evaluate the convergence time and positioning accuracy of CKF-based PPP-WAR by comparing it with KF-based PPP-WAR. The results show that the fix-rate of the CKF method increased by 26% compared with the KF-based WAR method. Moreover, the CKF-PPP-WAR can achieve 0.5 m (sub-meter) level with 1–4 s faster, 0.2 m level with 2–20 s faster, 0.1 m level with 5–60 s faster compared with float PPP. On average, CKF-PPP-WAR can achieve decimeter-level accuracy by reducing the convergence time 20% than KF-PPP-WAR, and 25% than float PPP. After convergence, the average positioning accuracy of CKF-PPP-WAR is 2–6 cm better with 25% improvement over float PPP and 1–4 cm better with a 23% improvement over KF-PPP-WAR.

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Data availability

The datasets generated and analyzed during the current study are available from the corresponding author on reasonable request.

References

  • Abdel-Salam MAT (2005) Precise point positioning using un-differenced code and carrier phase observations. Dissertation, University of Calgary, Canada. UCGE reports no. 20229

  • Ashby N (2004) The sagnac effect in the global positioning system. In: Rizzi G, Ruggiero ML (eds) Relativity in rotating frames. Kluwer Academic Publishers, Dordrecht The Netherlands, pp 11–28

    Chapter  Google Scholar 

  • Banville S, Collins P, Zhang W, Langley RB (2014) Global and regional ionospheric corrections for faster PPP convergence. Navig J Inst Navig 61(2):115–124

    Article  Google Scholar 

  • Boehm J, Niell A, Tregoning P, Schuh H (2006) Global mapping function (GMF): a new empirical mapping function based on numerical weather model data. Geophys Res Lett 33:L07304. https://doi.org/10.1029/2005GL025546

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Cai C, Gao Y, Pan L, Zhu J (2015) Precise point positioning with quad-constellations: GPS, BeiDou, GLONASS and Galileo. Adv Space Res 56(1):133–143

    Article  Google Scholar 

  • Chang G (2014) On Kalman filter for linear system with colored measurement noise. J Geodesy 88(12):1163–1170

    Article  Google Scholar 

  • Collins P, Lahaye F, Héroux P, Bisnath S (2008) Precise point positioning with ambiguity resolution using the decoupled clock model. ION GNSS 2008, Savannah, USA, September 2008, pp 1315–1322

  • Committee R S (2016) RTCM standard 10403.3 differential GNSS (global navigation satellite systems) services-version 3. RTCM Special Committee No.104, USA

  • El-Mowafy A, Deo M, Kubo N (2017) Maintaining real-time precise point positioning during outages of orbit and clock corrections. GPS Solut 21(3):937–947

    Article  Google Scholar 

  • Estey LH, Meertens CM (1999) TEQC: the multi-purpose toolkit for GPS/GLONASS data. GPS Solut 3(1):42–49

    Article  Google Scholar 

  • Gao Y, Chen K (2004) Performance analysis of precise point positioning using real-time orbit and clock products. J Global Position Syst 3(1–2):95–100

    Article  Google Scholar 

  • Gao Y, Gao Y, Liu B, Du Y, Wang J (2019) A robust approach to model colored noise for Low-cost high-precision Positioning. In: Proceedings of ION GNSS+ 2019, Institute of Navigation, Miami, USA, pp 3686–3694

  • Gao Y, Yang J, Gao Y, Huang G (2021) A linear Kalman filter-based integrity monitoring considering colored measurement noise. GPS Solut 25(2):1–13

    Article  Google Scholar 

  • Ge M, Gendt G, Rothacher M, a, Shi C, Liu J, (2008) Resolution of GPS carrier-phase ambiguities in precise point positioning (PPP) with daily observations. J Geodesy 82(7):389–399

    Article  Google Scholar 

  • Geng J, Bock Y (2013) Triple-frequency GPS precise point positioning with rapid ambiguity resolution. J Geodesy 87(5):449–460

    Article  Google Scholar 

  • Geng J, Guo J (2020) Beyond three frequencies: An extendable model for single-epoch decimeter-level point positioning by exploiting Galileo and BeiDou-3 signals. J Geodesy 94(1):1–15

    Article  Google Scholar 

  • Geng J, Guo J, Chang H, Li X (2019) Toward global instantaneous decimeter-level positioning using tightly coupled multi-constellation and multi-frequency GNSS. J Geodesy 93(7):977–991

    Article  Google Scholar 

  • Geng J, Guo J, Meng X, Gao K (2020) Speeding up PPP ambiguity resolution using triple-frequency GPS/BeiDou/Galileo/QZSS data. J Geodesy 94(1):1–15

    Article  Google Scholar 

  • Goode M, Edwards S, Moore P, de Jong K (2013) Time correlation in GNSS precise point positioning. In: ION GNSS+ 2013, Nashville, USA, September 2013, pp 1207–1214

  • Kouba J (2009b) A simplified yaw-attitude model for eclipsing GPS satellites. GPS Solut 13(1):1–12

    Article  Google Scholar 

  • Kouba J (2009a) A guide to using international GNSS service (IGS) products. IGS Central Bureau, Jet Propulsion Laboratory, Pasadena

  • Laurichesse D (2015) Phase biases for ambiguity resolution: from an undifferenced to an uncombined formulation. http://www.ppp-wizard.net/Articles/WhitePaperL5.pdf

  • 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 

  • Laurichesse D, Mercier F, Berthias J-P (2010) Real-time PPP with undifferenced integer ambiguity resolution, experimental results. ION GNSS 2010, Portland, USA, September 2010, pp 2534–2544

  • 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

    Article  Google Scholar 

  • Melbourne W (1985) The case for ranging in GPS-based geodetic systems. In: Proceedings of the 1st international symposium on precise positioning with GPS, pp 373–386

  • Nie Z, Liu F, Gao Y (2020) Real-time precise point positioning with a low-cost dual-frequency GNSS device. GPS Solut 24(1):9

    Article  Google Scholar 

  • Petovello MG, O’Keefe K, Lachapelle G, Cannon ME (2009) Consideration of time-correlated errors in a Kalman filter applicable to GNSS. J Geodesy 83(1):51–56

    Article  Google Scholar 

  • Saastamoinen J (1972) Atmospheric correction for the troposphere and stratosphere in radio ranging satellites. In: The use of artificial satellites for geodesy, vol 15, pp 247–251

  • Shi J, Gao Y (2014) A comparison of three PPP integer ambiguity resolution methods. GPS Solut 18(4):519–528

    Article  Google Scholar 

  • Shi J, Xu C, Guo J, Gao Y (2014) Local troposphere augmentation for real-time precise point positioning. Earth Planets Space 66(1):30

    Article  Google Scholar 

  • Shirazian M (2013) Incorporation of the GPS satellite ephemeris covariance matrix into the precise point positioning. J Geodetic Sci 3(3):143–150

    Article  Google Scholar 

  • Teunissen P, Odolinski R, Odijk D (2014) Instantaneous BeiDou+ GPS RTK positioning with high cut-off elevation angles. J Geodesy 88(4):335–350

    Article  Google Scholar 

  • Wang K, Li Y, Rizos C (2012) Practical approaches to Kalman filtering with time-correlated measurement errors. IEEE Trans Aerosp Electron Syst 48(2):1669–1681

    Article  Google Scholar 

  • Wang K, Khodabandeh A, Teunissen PJ (2018) Five-frequency Galileo long-baseline ambiguity resolution with multipath mitigation. GPS Solut 22(3):75

    Article  Google Scholar 

  • Wubbena G (1985) Software developments for geodetic positioning with GPS using TI 4100 code and carrier measurements. In: Proceedings 1st international symposium on precise positioning with the global positioning system. US Department of Commerce, pp 403–412

  • Xiang Y, Gao Y, Li Y (2020) Reducing convergence time of precise point positioning with ionospheric constraints and receiver differential code bias modeling. J Geodesy 94(1):1–13

    Article  Google Scholar 

  • Xu G, Xu Y (2007) GPS: theory, algorithms and applications. Springer, Berlin

    Google Scholar 

  • Zhou F, Dong D, Li W, Jiang X, Wickert J, Schuh H (2018) GAMP: an open-source software of multi-GNSS precise point positioning using undifferenced and uncombined observations. GPS Solut 22(2):33

    Article  Google Scholar 

  • Zhou P, Yang H, Xiao G, Du L, Gao Y (2019) Estimation of GPS LNAV based on IGS products for real-time PPP. GPS Solut 23(1):27

    Article  Google Scholar 

  • Zhou P, Wang J, Nie Z, Gao Y (2020) Estimation and representation of regional atmospheric corrections for augmenting real-time single-frequency PPP. GPS Solut 24(1):7

    Article  Google Scholar 

  • Zumberge J, Heflin M, Jefferson D, Watkins M, Webb F (1997) Precise point positioning for the efficient and robust analysis of GPS data from large networks. J Geophys Res Solid Earth 102(B3):5005–5017

    Article  Google Scholar 

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Acknowledgements

The financial support from the Natural Sciences and Engineering Research Council of Canada (NSERC) and the Chinese Scholarship Council (CSC) are greatly acknowledged.

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Authors and Affiliations

  1. Department of Geomatics Engineering, University of Calgary, Calgary, Canada

    Yang Jiang, Yuting Gao, Peiyuan Zhou & Yang Gao

  2. College of Geology Engineering and Geomatics, Chang’an University, Xi’an, China

    Guanwen Huang

Authors
  1. Yang Jiang
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  2. Yuting Gao
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  3. Peiyuan Zhou
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  4. Yang Gao
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  5. Guanwen Huang
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Contributions

YJ and YG designed the processing strategy and the experiments, developed the algorithms, performed the analysis of the experiments and wrote the paper. PZ, YG, GH supervised the project and contributed to the final version of the manuscript.

Corresponding author

Correspondence to Yuting Gao.

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Jiang, Y., Gao, Y., Zhou, P. et al. Real-time cascading PPP-WAR based on Kalman filter considering time-correlation. J Geod 95, 69 (2021). https://doi.org/10.1007/s00190-021-01520-w

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