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A Hidden Markov Model (HMM) provides an efficient way to model multi-aspect measurements, with each state representing a contiguous set of target orientations. The state sequence estimated by the Viterbi algorithm gives a good estimation of the target pose. In this paper, rate distortion theory is used to develop a bound for the state sequence (pose) estimated by a discrete HMM. A model for the classification process is detailed, facilitating the application of rate distortion theory. Here the rate is defined as the number of codes used in a discrete HMM, and the distortion is the probability of error in estimating the state sequence. The rate distortion function is calculated for an underwater acoustic target using the Blahut algorithm. The performance of a discrete HMM with a different number of codes is compared with the bound and found to be far from optimal. Possible approaches to improve the performance are discussed.