A comparison between optimal and Kalman filtering for hidden Markov processes

This paper gives sufficient conditions for specifying the optimal linear filters for a hidden Markov process (HMP) and compares its performance with the optimal (i.e., minimum conditional variance) filter derived from the corresponding hidden Markov model using a simulation. The optimal filter performs much better at high signal-to-noise ratio (SNR) but the performance loss using the linear filter reduces as the SNR decreases.