A numerical procedure for approximating overbounds on navigation systems error distributions

Gridsada Phanomchoeng, Demoz Gebre Egziabher, Jason H. Rife

Research output: Contribution to conferencePaperpeer-review

4 Scopus citations

Abstract

Algorithms used in commercial aviation navigation systems must meet stringent reliability requirements. In particular, they must provide bounds on the probability with which hazardous navigation errors occur. This paper proposes a method called polynomial overbounding which allows numerically approximating such bounds. Polynomial overbounding extends the approach of previous methods which bound navigation system output errors by over-bounding the worst case cumulative distribution function of input sensor errors. However, unlike previous methods, the overbound used are polynomials. A conservative polynomial fit to the worst case cumulative distribution function is generated. A derivative of the fitted polynomial provides the overbounding probability density function used to generate the final overbounds on the navigation state error distributions. This involves evaluating multi-dimensional integrals. A numerical procedures for evaluating these integrals efficiently is presented. It is shown that this approach has the potential of removing some of the unnecessary conservatism built into approaches such as Gaussian overbounding.

Original languageEnglish (US)
Pages1614-1619
Number of pages6
StatePublished - Dec 1 2006
EventInstitute of Navigation - 19th International Technical Meeting of the Satellite Division, ION GNSS 2006 - Fort Worth, TX, United States
Duration: Sep 26 2006Sep 29 2006

Other

OtherInstitute of Navigation - 19th International Technical Meeting of the Satellite Division, ION GNSS 2006
CountryUnited States
CityFort Worth, TX
Period9/26/069/29/06

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