Juan Blanch, Xinwei Liu, and Todd Walter, Stanford University

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We describe a method to determine symmetric and unimodal pair overbounding distributions that are key to the determination of strict Gaussian bounds used in GNSS integrity. The method works by casting the search of the symmetric and unimodal bounding distribution as a linear program. We then use the proposed method to compute a set of Gaussian bounds with varying bias (for a given sample distribution) and to determine the approximate optimal choice for a given application. As an application, we apply the method to determine optimal Gaussian bounds for GPS clock and ephemeris errors.