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Multi-frequency phase-only PPP-RTK model applied to BeiDou data

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Abstract

Typically, navigation software processes global navigation satellite system (GNSS) phase observables along with the code observables to achieve high-precision positioning. However, the unmodeled code-related errors, typically multipath effects, may deteriorate the positioning performance. Such effects are well known for the second generation BeiDou navigation satellite system (BDS-2). To prevent this adverse effect on the state-of-the-art positioning technique, namely integer ambiguity resolution-enabled precise point positioning (PPP-RTK), we propose a multi-frequency phase-only PPP-RTK model. This model excludes the code observables and addresses the rank deficiency problem underlying the phase observation equations at the undifferenced and uncombined level. To verify the model, we collect five-day triple-frequency BDS 30-s data from a network of seven reference stations (about 112 km apart) to estimate the products on the network side. Based on these products, we conduct simulated dynamic positioning at a user station to test the phase-only PPP-RTK model and compare it with the customary code-plus-phase (CPP) model. The results show that the satellite phase biases, existing only at the third frequency, have a precision of better than two centimeters, while the precision of the satellite clock and ionospheric delay is better than eight centimeters. Due to the strong correlation between individual corrections, it is necessary to assess the quality of combined products, including the satellite clock, satellite phase bias and ionospheric delay, the precision of which is several millimeters to two centimeters, which is sufficiently precise for user positioning. Regarding BDS-2 positioning, the time-to-first-fix (TTFF) of the CPP PPP-RTK is 12 epochs, while it is only three epochs for the phase-only PPP-RTK. The reason why the CPP model underperforms the phase-only model is that the BDS-2 data collected are subject to notable code multipath. We show that the code multipath in the third-generation BDS (BDS-3) data is mild, so the CPP PPP-RTK achieves instantaneous centimeter-level positioning with a TTFF of one epoch. The BDS-3 phase-only PPP-RTK obtains virtually the same positioning results, but the TTFF is two epochs. When combining BDS-2 with BDS-3, the TTFF of both models remains unchanged compared to that of the BDS-3 solutions, implying that ambiguity resolution based on the stronger dual-system CPP model is robust to the BDS-2 code multipath. However, the ambiguity-float solution of the CPP PPP-RTK is adversely affected by the code multipath and requires 43 epochs to convergence, while its phase-only counterpart needs 36 epochs.

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Data availability

The datasets that support the findings of this research are available from the corresponding author on reasonable request.

Abbreviations

BDS:

BeiDou navigation satellite system

CDMA:

Code division multiple access

CLK:

Clock

CPP:

Code-plus-phase

DOY:

Day of year

FDMA:

Frequency division multiple access

GEO:

Geostationary orbit

GNSS:

Global navigation satellite system

GPS:

Global positioning system

IGSO:

Inclined geosynchronous orbit

ION:

Ionosphere

MEO:

Medium orbit

PPP-RTK:

Integer ambiguity resolution-enabled precise point positioning

RMS:

Root-mean-square

RTK:

Real-time kinematic

SPB:

Satellite phase bias

STD:

Standard deviation

TTFF:

Time-to-first-fix

References

  • Amiri-Simkooei A (2013) Application of least squares variance component estimation to errors-in-variables models. J Geodesy 87(10):935–944

    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 et al. (2021) Enabling ambiguity resolution in CSRS-PPP. Navigation 68(2):433–451

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

    Article  Google Scholar 

  • Byun SH, Hajj GA, Young LE (2002) Development and application of GPS signal multipath simulator. Radio Sci 37(6):1–23

    Article  Google Scholar 

  • Chang X-W, Guo Y (2005) Huber’s M-estimation in relative GPS positioning: computational aspects. J Geodesy 79(6):351–362

    Article  Google Scholar 

  • Chu F-Y, Yang M, Wu J (2016) A new approach to modernized GPS phase-only ambiguity resolution over long baselines. J Geodesy 90(3):241–254

    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. Navigation 57(2):123–135

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Eueler HJ, Goad CC (1991) On optimal filtering of GPS dual frequency observations without using orbit information. Bulletin Géodésique 65(2):130–143

    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 Geodesy 82(7):389–399

    Article  Google Scholar 

  • Hassibi A, Boyd S (1998) Integer parameter estimation in linear models with applications to GPS. IEEE Trans Signal Proc 46(11):2938–2952

    Article  Google Scholar 

  • Hauschild A, Montenbruck O, Sleewaegen J-M, Huisman L, Teunissen PJ (2012) Characterization of compass M-1 signals. GPS Solutions 16(1):117–126

    Article  Google Scholar 

  • Hou P, Zhang B, Yuan Y (2021) Combined GPS+ BDS instantaneous single- and dual-frequency RTK positioning: stochastic modelling and performance assessment. J Spat Sci 66(1):3–26

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Khodabandeh A, Amiri-Simkooei A, Sharifi M (2012) GPS position time-series analysis based on asymptotic normality of M-estimation. J Geodesy 86(1):15–33

    Article  Google Scholar 

  • Khodabandeh A, Zaminpardaz S, Nadarajah N (2021) A study on multi-GNSS phase-only positioning. Meas Sci Technol 32(9):095005

    Article  Google Scholar 

  • 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 

  • Leick A, Rapoport L, Tatarnikov D (2015) GPS Satellite Surveying. Wiley, Hoboken

    Book  Google Scholar 

  • Lu R, Chen W, Dong D, Wang Z, Zhang C, Peng Y, Yu C (2021) Multipath mitigation in GNSS precise point positioning based on trend-surface analysis and multipath hemispherical map. GPS Solutions 25(3):1–14

    Google Scholar 

  • Montenbruck O, Hauschild A, Steigenberger P, Hugentobler U, Teunissen P, Nakamura S (2013) Initial assessment of the COMPASS/BeiDou-2 regional navigation satellite system. GPS Solutions 17(2):211–222

    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

  • Pan L, Guo F, Ma F (2018) An improved BDS satellite-induced code bias correction model considering the consistency of multipath combinations. Remote Sensing 10(8):1189

    Article  Google Scholar 

  • Remondi BW, Brown G (2000) Triple differencing with Kalman filtering: making it work. GPS Solutions 3(3):58–64

    Article  Google Scholar 

  • Strode PR, Groves PD (2016) GNSS multipath detection using three-frequency signal-to-noise measurements. GPS Solutions 20(3):399–412

    Article  Google Scholar 

  • 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

    Google Scholar 

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

    Article  Google Scholar 

  • Teunissen P (2001) Integer estimation in the presence of biases. J Geodesy 75(7):399–407

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Teunissen PJG, Amiri-Simkooei AR (2008) Least-squares variance component estimation. J Geodesy 82(2):65–82

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Teunissen PJG, Kleusberg A (2012) GPS for Geodesy. Springer, Berlin

    Google Scholar 

  • Teunissen PJG, Montenbruck O (2017) Springer Handbook of Global Navigation Satellite Systems. Springer, Berlin

    Book  Google Scholar 

  • Teunissen P, Odijk D (2003) Rank-defect integer estimation and phase-only modernized GPS ambiguity resolution. J Geodesy 76(9):523–535

    Article  Google Scholar 

  • Teunissen P, De Jonge P, Tiberius C (1997) The least-squares ambiguity decorrelation adjustment: its performance on short GPS baselines and short observation spans. J Geodesy 71(10):589–602

    Article  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 

  • Wang K, Chen P, Teunissen PJ (2018) Fast phase-only positioning with triple-frequency GPS. Sensors 18(11):3922

    Article  Google Scholar 

  • Wanninger L, Beer S (2015) BeiDou satellite-induced code pseudorange variations: diagnosis and therapy. GPS Solutions 19(4):639–648

    Article  Google Scholar 

  • Wübbena G, Schmitz M, Bagge A (2005) PPP-RTK: precise point positioning using state-space representation in RTK networks. In: Proc. ION GNSS 2005, The Institute of Navigation, 2005. Long Beach, CA, September 13–16, pp 13–16

  • Yang Y, Gao W (2006) An optimal adaptive Kalman filter. J Geodesy 80(4):177–183

    Article  Google Scholar 

  • Yang Y, Li J, Xu J, Tang J, Guo H, He H (2011) Contribution of the compass satellite navigation system to global PNT users. Chin Sci Bull 56(26):2813–2819

    Article  Google Scholar 

  • Zha J, Zhang B, Liu T, Hou P (2021) Ionosphere-weighted undifferenced and uncombined PPP-RTK: theoretical models and experimental results. GPS Solutions 25(4):1–12

    Article  Google Scholar 

  • Zhang X, He X, Liu W (2017a) Characteristics of systematic errors in the BDS Hatch–Melbourne–Wübbena combination and its influence on wide-lane ambiguity resolution. GPS Solutions 21(1):265–277

    Article  Google Scholar 

  • Zhang X, Wu M, Liu W, Li X, Yu S, Lu C, Wickert J (2017b) Initial assessment of the COMPASS/BeiDou-3: New-generation navigation signals. J Geodesy 91(10):1225–1240

    Article  Google Scholar 

  • Zhang B, Hou P, Zha J, Liu T (2021) Integer-estimable FDMA model as an enabler of GLONASS PPP-RTK. J Geodesy 95(8):1–21. https://doi.org/10.1007/s00190-021-01546-0

    Article  Google Scholar 

Download references

Acknowledgements

This work was partially funded by the National Natural Science Foundation of China (Grant Nos. 42022025, 41774042), the Key Research and Development Plan of Hubei Province (Grant No. 2020BHB014), and the Scientific Instrument Developing Project of the Chinese Academy of Sciences (Grant No. YJKYYQ20190063). The CAS Pioneer Hundred Talents Program supports the second author.

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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

    Pengyu Hou, Baocheng Zhang, Teng Liu & Jiuping Zha

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

    Pengyu Hou

  3. State Key Laboratory of Satellite Navigation System and Equipment Technology, The 54Th Research Institute of China Electronics Technology Group Corporation, Shijiazhuang, China

    Baocheng Zhang

  4. Institute of Solar-Terrestrial Physics SB RAS, Lermontov str., p/o box 291,126a, Irkutsk, Russia, 664033

    Yury V. Yasyukevich

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  1. Pengyu Hou
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  2. Baocheng Zhang
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  3. Yury V. Yasyukevich
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  4. Teng Liu
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  5. Jiuping Zha
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Correspondence to Baocheng Zhang.

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Hou, P., Zhang, B., Yasyukevich, Y.V. et al. Multi-frequency phase-only PPP-RTK model applied to BeiDou data. GPS Solut 26, 76 (2022). https://doi.org/10.1007/s10291-022-01263-x

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