Application of Spatial Statistics to Ionosphere Estimation for WAAS

Juan Blanch and Todd Walter

Abstract:	Now that the Wide Area Augmentation System (WAAS) has finalized the algorithms providing Lateral Navigation/Vertical Navigation (LNAV/VNAV) service, an increasing level of attention is being given to the feasibility of a GNSS Landing System (GLS) service. This would reduce the required Vertical Alarm Limit (VAL) from 50 meters to 20 meters or below. One of the algorithms that would be required to increase performance substantially is the ionospheric correction algorithm. WAAS incorporates information from reference stations to create a correction map of the ionosphere. More importantly, this map contains confidence bounds describing the integrity of the corrections. The confidence bounds must be large enough to describe the error in the correction but tight enough to allow the operation to proceed. The difficulty in generating these corrections is that the reference station measurements are not co-located with the aviation user measurement. For any estimation algorithm, a very sensitive parameter in the real time estimation of the ionospheric delay is the quality of the coverage by the Ionospheric Pierce Points (IPPs) measurements. Because the IPPs are scattered irregularly over the region of interest, the measure of coverage, or metric, is not an easy parameter to define, and has lead to many difficulties in the current WAAS system. Geostatistics, a field that was originally developed for ore reserve estimation and is part of the broader field known as spatial statistics, has created a number of models and techniques to treat estimation problems involving spatial data. In particular the method called kriging is nowadays popular in many fields of science and industry where there is a need for evaluating spatially or temporally correlated data. After summarizing the geostatistical method, this paper examines the worthiness of kriging for ionospheric estimation. It is explained in particular how to generate a family of metrics measuring the quality of sampling of a given region, useful for any estimation method. Extensive validation of the algorithms presented, using past WAAS ionospheric measurements for both quiet and disturbed periods, suggest that kriging provides useful insights and solutions to the ionospheric estimation problem, and could help WAAS to achieve GLS capability.
Published in:	Proceedings of the 2002 National Technical Meeting of The Institute of Navigation January 28 - 30, 2002 The Catamaran Resort Hotel San Diego, CA
Pages:	719 - 724
Cite this article:	Blanch, Juan, Walter, Todd, "Application of Spatial Statistics to Ionosphere Estimation for WAAS," Proceedings of the 2002 National Technical Meeting of The Institute of Navigation, San Diego, CA, January 2002, pp. 719-724.
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