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A procedure for the significance testing of unmodeled errors in GNSS observations

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Abstract

It is a crucial task to establish a precise mathematical model for global navigation satellite system (GNSS) observations in precise positioning. Due to the spatiotemporal complexity of, and limited knowledge on, systematic errors in GNSS observations, some residual systematic errors would inevitably remain even after corrected with empirical model and parameterization. These residual systematic errors are referred to as unmodeled errors. However, most of the existing studies mainly focus on handling the systematic errors that can be properly modeled and then simply ignore the unmodeled errors that may actually exist. To further improve the accuracy and reliability of GNSS applications, such unmodeled errors must be handled especially when they are significant. Therefore, a very first question is how to statistically validate the significance of unmodeled errors. In this research, we will propose a procedure to examine the significance of these unmodeled errors by the combined use of the hypothesis tests. With this testing procedure, three components of unmodeled errors, i.e., the nonstationary signal, stationary signal and white noise, are identified. The procedure is tested by using simulated data and real BeiDou datasets with varying error sources. The results show that the unmodeled errors can be discriminated by our procedure with approximately 90% confidence. The efficiency of the proposed procedure is further reassured by applying the time-domain Allan variance analysis and frequency-domain fast Fourier transform. In summary, the spatiotemporally correlated unmodeled errors are commonly existent in GNSS observations and mainly governed by the residual atmospheric biases and multipath. Their patterns may also be impacted by the receiver.

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Acknowledgements

This study is sponsored by the National Natural Science Foundation of China (41574023, 41622401, 41504022), the Technology Innovation Action Plan of Shanghai Science and Technology Committee (17511109501), the National Key Research and Development Program of China (2016YFB0501802), and the Fundamental Research Funds for the Central Universities. The authors are grateful to the editor and three reviewers for giving constructive comments, which greatly improved this paper.

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Authors and Affiliations

  1. College of Surveying and GeoInformatics, Tongji University, Shanghai, 200092, China

    Bofeng Li, Zhetao Zhang, Yunzhong Shen & Ling Yang

  2. State Key Laboratory of Geodesy and Earth’s Dynamics, Institute of Geodesy and Geophysics, Chinese Academy of Sciences, Wuhan, China

    Bofeng Li

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  1. Bofeng Li
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  2. Zhetao Zhang
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Correspondence to Bofeng Li or Zhetao Zhang.

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Li, B., Zhang, Z., Shen, Y. et al. A procedure for the significance testing of unmodeled errors in GNSS observations. J Geod 92, 1171–1186 (2018). https://doi.org/10.1007/s00190-018-1111-9

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