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

Abstract

Performance verification of GNSS-based safety-of-life systems requires demonstration that theprobability 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 integrityperformance of navigation systems at high confidence levels.

Overbounding False-Alarm Probability for a Chi-Square Monitor with Natural Biases

“…then P fa ≥ P fa , as can be seen by substituting (4) and (12) into (10). The important detail is that the negative sign in front of P gx2 means that a lower bound for the integral P gx2 results in an upper bound for P fa .…”

“…Within the navigation field, the process of developing rigorous risk bounds is called overbounding. Overbounding position-error distributions has been the subject of intense prior research [2][3][4][5][6][7][8][9][10]. In recent years, a particular emphasis has been placed on overbounding for integrity monitors, too, with the goal of obtaining rigorous bounds for false-alarm and missed-detection risks [11][12][13][14].…”

Troposzferikus maradék ellentmondások becslése az életbiztonságra veszélyes GNSS-alkalmazások esetén

“…Van Leeuwen et al (2004) is tanulmányozták a fent említett modellt Hollandia területén, ami alapján arra a megállapításra jutottak, hogy az túlságosan konzervatív. Ez alapján tehát úgy tűnik, hogy valós igény mutatkozhat egy új, kevésbé konzervatív, azonban a biztonságot nem kompromittáló modell kifejlesztésére.…”

“…Annak érdekében, hogy az eloszlás szárnyainak jellegét is figyelembe vegyük, a maradék hibák vizsgálatához az extrémérték-elemzést hívtuk segítségül. Ez a matematikai eljárás széles körben használt például árvízi vízszintek becslésénél, de újabban a GNSS és a hozzá tartozó kiegészítő rendszerek vizsgálatára is alkalmazzák (Ober 2014).…”

Comparing Geometric Approximations of Heavy-Tail Effects for Chi-Square Integrity Monitors

“…Here, the term heavy‐tails refers to PDFs exhibiting a higher‐than‐expected probability of occurrence for large errors . Heavy‐tails are commonly observed in analyzing GNSS signals , including SDM signals . The influence of heavy tails on the characterization of confidence bounds for GNSS position estimates, also known as protection levels , has been carefully studied .…”