Bayesian MMSE Estimation of a Gaussian Source in the Presence of Bursty Impulsive Noise

In this letter, we derive the minimum mean square error (MMSE) optimal Bayesian estimation (OBE) for a Gaussian source, in the presence of bursty impulsive noise, as essentially encountered within power substations. Clearly, it is observed that the presence of bursty impulsive noise makes the input-output characteristics of MMSE OBE non-linear. To handle the non-linearity, we propose a novel MMSE estimator, based on the detection of the unobservable states of the noise process, using the maximum a posteriori (MAP) detector. Resultantly, the proposed MAP-based MMSE estimator is shown to achieve the lower bound derived for the proposed scenario and outperform the various MMSE estimators that neglect the noise memory.