Comment on “Bayesian MMSE Estimation of a Gaussian Source in the Presence of Bursty Impulsive Noise”

In the above-titled letter by Alam et al. (see ibid., vol.22, no.9, p.1846-49, September 2018), the authors claimed to derive the minimum-mean-squared-error (MMSE) estimator for a scalar Gaussian source in the presence of correlated noise, modeled by a two-state Gauss-Markov process. In the proposed approach, first, the state of the noise process at time epoch k is determined according to the maximum a posteriori (MAP) decision rule based on the whole sequence of observations. Then, given the hard decision on the noise state, the corresponding MMSE estimator (i.e., conditional mean) is employed to estimate the source signal at time epoch k. However, performing estimation based on the hard decision of the MAP detector is not optimal in terms of minimizing the mean-squared-error (MSE). In this comment, we show that the optimal MMSE estimator for the considered problem is obtained as a weighted average of the MMSE estimators corresponding to distinct states of the noise probable at time epoch k and the weights are equal to the a posteriori probabilities of the noise state computed based on the whole sequence of observations.