On state-estimation of a two-state hidden Markov model with quantization

We consider quantization from the perspective of minimizing filtering error when quantized instead of continuous measurements are used as inputs to a nonlinear filter, specializing to discrete-time two-state hidden Markov models (HMMs) with continuous-range output. An explicit expression for the filtering error when continuous measurements are used is presented. We also propose a quantization scheme based on maximizing the mutual information between quantized observations and the hidden states of the HMM.