Bounding Integrity Risk in the Presence of Parametric Time Correlation Uncertainty

S. Langel, S. Khanafseh, B. Pervan

Abstract:	State estimation of linear dynamical systems with time correlation uncertainty in the measurement noise is considered. The presence of random noise introduces a state estimate error that is defined in terms of a probability distribution. For safety-of-life aviation applications, the integrity risk associated with the state estimate error must be explicitly quantified. This paper focuses on developing a methodology to compute upper bounds on integrity risk subject to a parametric uncertainty structure on the measurement noise autocorrelation function. Using well known results from linear algebra, we derive a concise formula which describes how the autocorrelation uncertainty maps from the measurement domain to the position domain. This formula allows the integrity risk to be written directly in terms of the unknown parameters. For autocorrelation functions described by a 1st order Gauss-Markov model, the integrity risk bounding problem is formulated as a polynomial optimization problem with non-linear inequality constraints. An efficient numerical algorithm is developed to obtain the global optimum, hence guaranteeing that the computed integrity risk will always upper bound the true risk.
Published in:	Proceedings of the 2012 International Technical Meeting of The Institute of Navigation January 30 - 1, 2012 Marriott Newport Beach Hotel & Spa Newport Beach, CA
Pages:	1666 - 1680
Cite this article:	Langel, S., Khanafseh, S., Pervan, B., "Bounding Integrity Risk in the Presence of Parametric Time Correlation Uncertainty," Proceedings of the 2012 International Technical Meeting of The Institute of Navigation, Newport Beach, CA, January 2012, pp. 1666-1680.
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