Abstract: We analyze a class of Bayesian, binaryhypothesis-testing problems relevant to theclassification of targets in the presence of poseuncertainty. When hypothesis H$-1$/ is true, we observeone of N$-1$/ possible complex-valued signal vectors,immersed in additive, white complex Gaussian noise;when hypothesis H$-2$/ occurs, we observe one of N$-2$/ other possible signal vectors, again immersed innoise. Given prior probabilities for H$-1$/ and H$-2$/,and also prior conditional probabilities for thepresence of each of the signal vectors, the problem isto determine both a decision rule that minimizes theerror probability and also the associated minimalproblem is to determine both a decision rule thatminimizes the error probability and also the associatedminimal error probability. The optimal decision rulehere is well-known to be a likelihood ratio test havinga straightforward analytical form; however, theperformance of this optimal test is intractableanalytically, and thus approximations are required tocalculate the probability of error. We devise anapproximation based on the observation that both thenumerator and denominator of the likelihood ratio teststatistic consist of sums of lognormal randomvariables. Previous work has shown that such sums arewell approximated as themselves having a lognormaldistribution; we exploit this fact to obtain a simple,approximate error probability expression. For aspecific problem, we then compare the resulting errorprobability numbers with ones obtained via Monte Carlosimulation, demonstrating good agreement between thetwo methods. !4
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