Rate-Distortion Analysis of Pose Estimation via Multi-Aspect Scattering Data

A Hidden Markov Model (HMM) provides an efficient means of modeling multiaspect scattering data, with each HMM state representing a contiguous set of target-sensor orientations over which the wave physics is approximately stationary. The HMM-estimated state sequence gives a good approximation of the target pose. Rate-distortion theory is used to develop an error bound for estimating the state sequence (pose), as a function of the number of codes employed by the discrete HMM. The rate is defined as the number of discrete-HMM codes used to quantize the data, and the distortion is the probability of error in estimating the state of each measurement in the sequence. The rate-distortion function is calculated via the Blahut algorithm, considering example scattering data from an underwater elastic target. The performance of a discrete HMM using Lloyd quantization is compared with the rate-distortion bound, and is found to be far from optimal. Bayes-VQ is then applied in the context of HMM-based pose estimation, demonstrating significant performance improvement when good prior information about the target is available. This context-based quantizer accounts for the Bayes risk of pose estimation.