A Tool for GNSS Integrity Verification Based on Statistical Extreme Value Theory

H. Veerman, A. van Kleef, F. Wokke, B. Ober, C. Tiberius, S. Verhagen, A. Bos, A. Mieremet

Abstract:	With the advent of augmentation systems such as WAAS and EGNOS, satellite navigation gets more and more used for so-called Safety of Life (SoL) applications, with civil aviation being the most prominent example. For SoL applications reliability performance of the system is typically expressed in terms of accuracy, availability, continuity of service and integrity. Especially the integrity of the position solution resulting from the satellite navigation signals is crucial. In general integrity performance requirements are exceedingly demanding, and therefore compliance is difficult to test. For example, the GNSS integrity performance requirement for ICAO LPV (Localizer Performance with Vertical Guidance) approach procedures is 2 x 10-7 per approach position error probability of exceedance of the corresponding protection level, where an approach is defined as of 150 seconds duration. In particular, it is required to assess and verify the probability that the position error (PE) of a GNSS user exceeds the alert limit, while no alert is raised within the time-to-alert associated with the operation. Testing a GNSS system's integrity by collecting Misleading Information (MI) events not only is impractical given the low event rate - on average only one event is expected to occur every 20 years - but also the low yield is considered inadequate for a precise statistical assessment. It should be noted that although no MI events are observed the system can be unsafe, because of the fact that the probability of MI is higher than its integrity function, implemented through protection levels, promises: in this case we speak of misleading integrity information (MII). Thus MI is misleading actual position information, which is almost never present in the data, while we are looking for MII: for example SBAS PL’s or Galileo’s Integrity Risk given by the system that on average are too small. Nevertheless, for SoL verification it is important to verify GNSS integrity performance within a limited time duration. This is especially the case for ‘difficult’ locations and/or conditions, e.g. near the border of the SBAS' service area or under adverse environmental conditions or system modes, e.g. during a violent ionospheric storm. In order to overcome this problem statistically sound techniques can be applied to GNSS integrity verification, based on the Extreme Value Theory (EVT), which enable extrapolation of the observed distribution's tail into the non-integrity domain [20]. Early investigations [19] based on EVT algorithms developed in Matlab using real SBAS data proved that results from this approach were not only correct, accurate and reproducible, but also very promising due to the limited measurement time duration that was required for obtaining statistically relevant results. Based on GPS/EGNOS data collection over a period of a few months MI probabilities both in the position domain as well as in the signal range domain could be obtained taking into account 2s confidence levels for MI probabilities Due to the fact that confidence intervals are both related to the minimally needed data collection time period and the capability to prove compliance, optimal determination of confidence levels is important and thus was given special attention. Two approaches of confidence level estimation were studied: using the Gauss-Newton algorithm and the bootstrapping re-sampling approach. Determining confidence levels by both approaches using a few sequences of EGNOS data, it is shown that confidence intervals based on the Gauss-Newton approach are overly optimistic, while the bootstrapping re-sampling approach provides more conservative confidence intervals that is considered adequate. These promising results positively motivated the Netherlands Space Office to fund the development of a software tool, named GIMAT - GNSS Integrity Monitoring and Analysis Tool, based on these EVT algorithms. GIMAT is developed by a Dutch consortium composed of Delft University of Technology, Integricom, National Aerospace Laboratory NLR and Science & Technology. GIMAT is now close to its completion. Its first operational application will support the implementation of an EGNOS-based LPV procedure near the Eelde airfield in The Netherlands, testing local GNSS integrity compliance with ICAO SARPs (Standards and Recommended Practices) later this year. Furthermore, plans are currently being made to test GNSS position solution integrity at a location in the North of Scandinavia, near the boundary of the EGNOS service Area, using GIMAT. The paper presents a short introduction to the mathematical theory of the EVT, the consecutive steps that are made in the software tool to address MI probability estimation and proof of range error distribution overbounding. Full details can be found in [1]. Finally some early results obtained by GIMAT are presented.
Published in:	Proceedings of the 2012 International Technical Meeting of The Institute of Navigation January 30 - 1, 2012 Marriott Newport Beach Hotel & Spa Newport Beach, CA
Pages:	1655 - 1665
Cite this article:	Veerman, H., van Kleef, A., Wokke, F., Ober, B., Tiberius, C., Verhagen, S., Bos, A., Mieremet, A., "A Tool for GNSS Integrity Verification Based on Statistical Extreme Value Theory," Proceedings of the 2012 International Technical Meeting of The Institute of Navigation, Newport Beach, CA, January 2012, pp. 1655-1665.
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