LAUSR

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.