Estimation of constrained parameters with guaranteed MSE improvement

We address the problem of estimating an unknown parameter vector x in a linear model y = Cx+v subject to the a priori information that the true parameter vector x belongs to a known convex polytope . The proposed estimator has the parametrized structure of the maximum a posteriori probability (MAP) estimator with prior Gaussian distribution, whose mean and covariance parameters are suitably designed via a linear matrix inequality approach so as to guarantee, for any x , an improvement of the mean-squared error (MSE) matrix over the least-squares (LS) estimator. It is shown that this approach outperforms existing “superefficient” estimators for constrained parameters based on different parametrized structures and/or shapes of the parameter membership region.