Title: A MATLAB Toolset to Determine Strict Gaussian Bounding Distributions of a Sample Distribution
Author(s): Juan Blanch, Todd Walter, Per Enge
Published in: Proceedings of the 30th International Technical Meeting of The Satellite Division of the Institute of Navigation (ION GNSS+ 2017)
September 25 - 29, 2017
Oregon Convention Center
Portland, Oregon
Pages: 4236 - 4247
Cite this article: Blanch, Juan, Walter, Todd, Enge, Per, "A MATLAB Toolset to Determine Strict Gaussian Bounding Distributions of a Sample Distribution," Proceedings of the 30th International Technical Meeting of The Satellite Division of the Institute of Navigation (ION GNSS+ 2017), Portland, Oregon, September 2017, pp. 4236-4247.
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Abstract: The integrity analysis of systems like Satellite-Based Augmentation Systems (SBAS), Ground-based Augmentation Systems (SBAS), Receiver Autonomous Integrity Monitoring (RAIM), or Advanced RAIM (ARAIM) requires proving that the actual distribution of errors can be replaced by a simpler distribution, often a gaussian distribution. Two key results have been used to generate these overbounding distributions: cdf bounding and paired overbounding. Although these two results are very powerful, each of them has a weakness that limits their direct application. The goal of this paper is to overcome some of these weaknesses. We will first present a method to determine gaussian overbounding distributions that combines cdf bounding and paired overbounding. This method is based on the determination of an intermediate overbounding distribution that is symmetric and unimodal. Then, we present a modification of the paired overbounding theorem that relaxes the cdf paired overbounding requirement mentioned above. These techniques are the basis of a MATLAB toolset that computes rigorous gaussian overbounding distributions for any sample distribution.