Probability-constrained approach to estimation of random Gaussian parameters

The problem of estimating a random signal vector x observed through a linear transformation H and corrupted by an additive noise is considered. A linear estimator that minimizes the mean squared error (MSE) with a certain selected probability is derived under the assumption that both the additive noise and random signal vectors are zero mean Gaussian with known covariance matrices. Our approach can be viewed as a robust generalization of the Wiener filter. It simplifies to the recently proposed robust minimax estimator in some special cases.