Lognormal approximation for quantifying performance of Bayesian target classifier in presence of pose uncertainty

William W. Irving; Robert B. Washburn; Robert R. Tenney

doi:10.1117/12.242060

10 June 1996 Lognormal approximation for quantifying performance of Bayesian target classifier in presence of pose uncertainty

William W. Irving, Robert B. Washburn, Robert R. Tenney

Author Affiliations +

Proceedings Volume 2757, Algorithms for Synthetic Aperture Radar Imagery III; (1996) https://doi.org/10.1117/12.242060
Event: Aerospace/Defense Sensing and Controls, 1996, Orlando, FL, United States

Abstract

We analyze a class of Bayesian, binary hypothesis-testing problems relevant to the classification of targets in the presence of pose uncertainty. When hypothesis H₁ is true, we observe one of N₁ possible complex-valued signal vectors, immersed in additive, white complex Gaussian noise; when hypothesis H₂ occurs, we observe one of N₂ other possible signal vectors, again immersed in noise. Given prior probabilities for H₁ and H₂, and also prior conditional probabilities for the presence of each of the signal vectors, the problem is to determine both a decision rule that minimizes the error probability and also the associated minimal problem is to determine both a decision rule that minimizes the error probability and also the associated minimal error probability. The optimal decision rule here is well-known to be a likelihood ratio test having a straightforward analytical form; however, the performance of this optimal test is intractable analytically, and thus approximations are required to calculate the probability of error. We devise an approximation based on the observation that both the numerator and denominator of the likelihood ratio test statistic consist of sums of lognormal random variables. Previous work has shown that such sums are well approximated as themselves having a lognormal distribution; we exploit this fact to obtain a simple, approximate error probability expression. For a specific problem, we then compare the resulting error probability numbers with ones obtained via Monte Carlo simulation, demonstrating good agreement between the two methods.

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William W. Irving, Robert B. Washburn, and Robert R. Tenney "Lognormal approximation for quantifying performance of Bayesian target classifier in presence of pose uncertainty", Proc. SPIE 2757, Algorithms for Synthetic Aperture Radar Imagery III, (10 June 1996); https://doi.org/10.1117/12.242060

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KEYWORDS

Error analysis

Monte Carlo methods

Interference (communication)

Automatic target recognition

Binary data

Statistical analysis

Analytical research

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