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We consider the problem of estimating the pose of a target based on a sequence of scattered waveforms measured at multiple target-sensor orientations. Using a hidden Markov model (HMM) representation of the scattered-waveform sequence, pose estimation reduces to estimating the underlying HMM states from a sequence of observations. It is assumed that each scattered waveform must be quantized via an encoding procedure. A distortion D is defined as the error in estimating the underlying HMM states, and the rate R represents the size of the discrete-HMM codebook. Rate-distortion theory is applied to define the minimum rate required to achieve a desired distortion, denoted as R(D). After deriving the rate-distortion function R(D), we demonstrate that discrete-HMM performance based on Lloyd encoding is far from this bound. Performance is improved via block coding, based on Bayes VQ. Results are presented for a canonical HMM problem, and then for multiaspect acoustic scattering from underwater elastic targets. Although the examples presented here are for multiaspect scattering and pose estimation, the results are of general applicability to discrete-HMM state estimation.