Abstract
The China’s BeiDou system is the first global satellite navigation system to broadcast the three frequency signals for full constellation. A lot of studies have been done recently for positioning and navigation by using BeiDou three frequency signals, but mostly based on the GPS-like empirical stochastic model. This paper aims to study the stochastic modelling of BeiDou observations and then analyze its impact on the ambiguity resolution and precision positioning. To generalize the stochastic model, the satellite-dependent precisions, cross correlations between arbitrary two frequencies and time correlations for each frequency are set up. The results indicate that comparing with empirical stochastic model, the realistic stochastic model can improve the ambiguity resolution and positioning precision. Besides, the derived variance matrix of parameters with realistic stochastic model can objectively reflect the actual precisions of parameter estimates, which is rather important for solution evaluation in real applications.
Keywords
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He H, Li J, Yang Y, Xu J, Guo H, Wang A (2014) Performance assessment of single- and dual-frequency BeiDou/GPS single-epoch kinematic positioning. GPS Solut 18(3):393–403
Koch K (1999) Parameter estimation and hypothesis testing in linear models, 2nd edn. Springer, Berlin
Li B (2016) Stochastic modeling of triple-frequency BeiDou signals: estimation, assessment and impact analysis. J Geod. doi:10.1007/s00190-016-0896-7
Li B, Shen Y, Xu P (2008) Assessment of stochastic models for GPS measurements with different types of receivers. Chi Sci Bull 53(20):3219–3225
Li B, Shen Y, Lou L (2011) Efficient estimation of variance and covariance components: a case study for GPS stochastic model evaluation. IEEE Trans Geosci Remote Sens 49(1):203–210
Li B, Verhagen S, Teunissen PJG (2014) Robustness of GNSS integer ambiguity resolution in the presence of atmospheric biases. GPS Solut 18:283–296
Liu X (2002) A comparison of stochastic models for GPS single differential kinematic positioning. In: ION GPS 2002, Portland
Shi C, Zhao Q, Hu Z, Liu J (2013) Precise relative positioning using real tracking data from COMPASS GEO and IGSO satellites. GPS Solut 17(1):103–119
Teunissen PJG (1995) The least-squares ambiguity decorrelation adjustment: a method for fast GPS integer ambiguity estimation. J Geod 70:65–82
Teunissen PJG (1999) An optimality property of the integer least-squares estimator. J Geod 73(11):587–593
Teunissen PJG, Amiri-Simkooei AR (2008) Least-squares variance component estimation. J Geod 82:65–82
Teunissen PJG, Jonkman NF, Tiberius CCJM (1998) Weighting GPS dual frequency observations: bearing the cross of cross-correlation. GPS Solut 2(2):28–37
Tiberius C, Kenselaar F (2000) Estimation of the stochastic model for GPS code and phase observation. Surv Rev 35(277):441–454
Verhagen S, Li B, Teunissen PJG (2013) Ps-LAMBDA: ambiguity success rate evaluation software for interferometric applications. Comput Geosci 54:361–376
Wang K, Rothacher M (2013) Ambiguity resolution for triple-frequency geometry-free and ionosphere-free combination tested with real data. J Geod 87(6):539–553
Wang J, Satirapod C, Rizos C (2002) Stochastic assessment of GPS carrier phase measurements for precise static relative positioning. J Geod 76(2):95–104
Acknowledgements
This work is supported by the National Natural Science Foundations of China (41574023, 41374031), the China Special Fund for Surveying, Mapping and Geoinformation Research in the Public Interest (HY14122136) and the Fund of Youth 1000-Plan Talent Program.
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Li, B., Hao, Q. (2016). Towards Reliable and Precise BeiDou Positioning with Stochastic Modelling. In: Freymueller, J.T., Sánchez, L. (eds) International Symposium on Earth and Environmental Sciences for Future Generations. International Association of Geodesy Symposia, vol 147. Springer, Cham. https://doi.org/10.1007/1345_2016_225
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DOI: https://doi.org/10.1007/1345_2016_225
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-69169-5
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