Empirical Integrity Verification of GNSS and SBAS Based on the Extreme Value Theory

Pieter Bastiaan Ober, Davide Imparato, Sandra Verhagen, Christian Tiberius, Henk Veerman, Arnaud Van Kleef, Frank Wokke, André Bos, and Arjan Mieremet

Peer Reviewed

Abstract: Performance verification of GNSS-based safety-of-life systems requires demonstration that the probability of an excessive positioning error is as small as 10–7 or even smaller. Integrity concepts are based on the requisite that the system provides conservative performance estimates for alert generation. The GNSS Integrity Monitoring and Analysis Tool (GIMAT) developed by the authors focuses on data-based analyses to verify whether this is indeed the case. Since the tails of the error distributions must be investigated, it is impractical to simply use observed cases of performance over-estimation. Such events are – by design – extremely rare and would require many decades of data collection. Nevertheless, system verification requires assessment of a system’s integrity performance within limited time. GIMAT therefore exploits Extreme Value Theory (EVT), which enables extrapolation of the observed distribution’s tail into the misleading information domain. The paper presents a short introduction into the mathematical theory of EVT in the context of integrity verification, and contains real-life results that are obtained from the analysis of EGNOS data. Based on two months of data, it is shown that EGNOS is compliant with ICAO requirements for this period, and that EVT is successful in predicting integrity performance of navigation systems at high confidence levels.
Published in: NAVIGATION: Journal of the Institute of Navigation, Volume 61, Number 1
Pages: 23 - 38
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