Robust MSE estimation for linear Gaussian model with uncertainties

This paper considers a robust mean-square-error (MSE) estimate problem with model uncertainties. When the statistics about the signal and the observations are available imperfectly, we need to take the model error into account. Here, we consider finding the best estimator minimizing the MSE for the least favorable model within a neighborhood of the nominal model. The neighborhood is formed by placing a bound on the Kullback-Leibler (KL) divergence between the actual and nominal models. We use the strong Lagrangian duality theory to transform the minmax problem into a min-min problem, then the robust MSE estimator can be obtained numerically.