A Numerical Procedure for Approximating Overbounds on Navigation Systems Error Distributions

G. Phanomchoeng, D. Gebre-Egziabher, J.H. Rife

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 overbounding 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.
Published in:	Proceedings of the 19th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS 2006) September 26 - 29, 2006 Fort Worth Convention Center Fort Worth, TX
Pages:	1614 - 1619
Cite this article:	Phanomchoeng, G., Gebre-Egziabher, D., Rife, J.H., "A Numerical Procedure for Approximating Overbounds on Navigation Systems Error Distributions," Proceedings of the 19th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS 2006), Fort Worth, TX, September 2006, pp. 1614-1619.
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