This paper addresses the problem of Bayesian estimation in the presence of signal distribution mismatch. A new estimator is derived based on the minimum mean-square error (MMSE) criterion with constraints on the first and second order statistics of the parameters of interest. The resulting constrained MMSE (CMMSE) estimator is found to be robust to signal distribution mismatch, since it incorporates statistical information on the parameters of interest. The performance of the CMMSE estimator under different mismatch conditions is studied via simulations using several examples. It is shown that the CMMSE estimator outperforms the MMSE in the presence of signal distribution mismatch. With no distribution mismatch, the CMMSE performance is slightly lower than the MMSE.
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