GNSS Integrity Achievement by using Extreme Value Theory

J-M. Azais, S. Gadat, J-C. Lévy, B. Rols, C. Mercadier, C. Jordan, N. Suard

Abstract:	The demonstration of the GNSS integrity requirement (10-7/150 sec range) for SBAS services as for future systems like GALILEO is a key issue either in the development/acceptance phase or in the operational one. Currently, for SBAS as EGNOS or WAAS, a lot of simulations coupled with data collections were done before the operation or service commissioning and a permanent data collection network is used to monitor, among other parameters, the integrity (or more precisely the absence of a Loss Of Integrity (LOI) in case of misleading information). The demonstration needs to assess a 10-7 order of magnitude which is a tricky issue: the classical methods require several tens years of observations and such LOI are generally not observed among the data because of their scarcity. To make possible the extrapolation of the error distributions into the tails, CNES and TAS have established a research action with French Universities of Lyon I and Toulouse III to use the Extreme Value Theory (EVT). Recent developments in quantile estimation have allowed the application of EVT in numerous domains regardless of the underlying error distributions of the measurement data, and avoid the questionable assumption of Gaussian error distributions. Indeed, a model from the Gaussian distribution may not be adapted: the tail can decrease more slowly (for instance). With the EVT theory, the properties of the tails of the error distributions can be derived from the measurement data. This allows to meaningfully extrapolate the data into the region of misleading information, even when no (or very limited amounts of) sample values in this region are available. Different observables have been defined in position or range domains and, based on different EGNOS releases several data sets were elaborated covering different situations regarding the integrity level. Since the integrity is concluded from the computation of a very large quantile, these data sets have been analysed with a prototype tool implemented from the EVT theory. A goodness-of-fit test has been used to verify the a priori assumptions. We computed different quantile estimations in order to be more efficient: from maximum likelihood or moment estimators as POT, Hill, De Dekkers or Pickands estimators ([9], [10], [11], [12]). Finally, confidence intervals have been derived from both Bootstrap and Central Limit Theorem. It has to be kept in mind for the interpretation of the results that the observables encompass different sources for misleading information: the information broadcast by the system, the data that have been collected and the associated accuracy, but also the tools used to prepare the different observables. The paper presents - the applied approach - the different observables and the way they were computed - the test and associated results - the observations obtained on EGNOS system, on the data collection environment and on the tools used to prepare the observables ?? some recommendations to use this technique for future assessment of such demanding GNSS integrity requirement
Published in:	Proceedings of the 22nd International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS 2009) September 22 - 25, 2009 Savannah International Convention Center Savannah, GA
Pages:	1281 - 1287
Cite this article:	Azais, J-M., Gadat, S., Lévy, J-C., Rols, B., Mercadier, C., Jordan, C., Suard, N., "GNSS Integrity Achievement by using Extreme Value Theory," Proceedings of the 22nd International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS 2009), Savannah, GA, September 2009, pp. 1281-1287.
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