Asymptotic error probability expressions for multihypothesis testing using multisensor data

Existing upper bounds to the error probability in testing between m>2 hypotheses, and H. Chernoff's (1952) asymptotically correct error probability expression for m=2 hypotheses, as the number of observations n to infinity , are discussed. The multidimensional version of Chernoff's bound and its relationship to large deviation theory is presented. Large deviation theory is used to develop new bounds. The new bounds are asymptotically exact, in the sense that as n to infinity , they converge to the correct asymptotic rate, which is guaranteed to be the optimum one by the large deviation theorem. Necessary and sufficient conditions are determined so that asymptotic convergence of the error rates to zero is sustained in the presence of mismatch, which occurs when inaccurate versions of the true probability density functions are utilized in the maximum-likelihood decision rule. The conditions are expressed in terms of informational divergence distances, for Markov chain data and Gaussian multivariate stationary random processes. The results for multisensor data are generalized.<
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