Probability of error analysis for hidden Markov model filtering with random packet loss

This paper studies the probability of error for maximum a posteriori (MAP) estimation of hidden Markov models, where measurements can be either lost or received according to another Markov process. Analytical expressions for the error probabilities are derived for the noiseless and noisy cases. Some relationships between the error probability and the parameters of the loss process are demonstated via both analysis and numerical results. In the high signal-to-noise ratio (SNR) regime, approximate expressions which can be more easily computed than the exact analytical form for the noisy case are presented.