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Proceedings Paper

Lognormal approximation for quantifying performance of Bayesian target classifier in presence of pose uncertainty
Author(s): William W. Irving; Robert B. Washburn; Robert R. Tenney
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Paper 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.

Paper Details

Date Published: 10 June 1996
PDF: 8 pages
Proc. SPIE 2757, Algorithms for Synthetic Aperture Radar Imagery III, (10 June 1996); doi: 10.1117/12.242060
Show Author Affiliations
William W. Irving, Alphatech, Inc. (United States)
Robert B. Washburn, Alphatech, Inc. (United States)
Robert R. Tenney, Alphatech, Inc. (United States)

Published in SPIE Proceedings Vol. 2757:
Algorithms for Synthetic Aperture Radar Imagery III
Edmund G. Zelnio; Robert J. Douglass, Editor(s)

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