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 mod
els (HMMs) with continuous-range output. An explicit expression for the fil
tering error when continuous measurements are used is presented. We also pr
opose a quantization scheme based on maximizing the mutual information betw
een quantized observations and the hidden states of the HMM.