Stochastic model reliability in GNSS baseline solution

Abstract

GNSS observations stochastic model influences all subsequent stages of data processing, from the possibility to reach the optimal parameters estimation, to the reliability and quality control of the solution. Nowadays, an uncontrolled use of GNSS stochastic models is common for both data processing and simulation missions, especially in commercial GNSS software packages. As a result, the variance–covariance matrices that are derived in the processing are inadequate and cause incorrect interpretations of the results. A proper method to evaluate the reliability of the stochastic model is needed to reflect the confidence level in statistic testing and simulation mission efforts. In this contribution, a novel method for evaluating the statistical nature of GNSS stochastic model is presented. The method relies on the deterministic nature of the integer ambiguity variable to examine and express the expected multinormal distribution of the double-difference adjustment results. The suggested method was used with a controlled experiment and 24 h of observations data to investigate how the statistical nature of the stochastic model is affected by different baseline lengths. The results indicate that as the baseline length increases, the stochastic model is less predictable and exposed to irregularities in the observation’s precision. Additionally, the reliability of the integer ambiguity resolution success rate (SR) was tested as part of the stochastic model evaluation. The results show a dramatic degradation in the SR prediction level when using an inadequate stochastic model, which suggests using extra caution when handling this parameter unless high-confidence reliable stochastic model is available.

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Availability of data and materials

All data analyzed during this study are included in this published article and its supplementary information files.

Code availability

The code generated during the current study is available from the corresponding author on reasonable request.

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Authors

Contributions

A.B. and G.E.T contributed to methodology. A.B. performed formal analysis and investigation. A.B. contributed to writing—original draft preparation. G.E.T contributed to writing—review and editing. G.E.T was involved in supervision.

Corresponding author

Correspondence to Aviram Borko.

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Borko, A., Even-Tzur, G. Stochastic model reliability in GNSS baseline solution. J Geod 95, 20 (2021). https://doi.org/10.1007/s00190-021-01472-1

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Keywords

  • Global navigation satellite system (GNSS)
  • Stochastic modeling
  • Reliability testing
  • Integer ambiguity resolution
  • Success rate