Competitive linear MMSE estimation under structured data uncertainties

In this paper, we consider the linear estimation problem under structured data uncertainties. A robust algorithm is presented under bounded uncertainties under the mean square error (MSE) criterion. The performance of the linear estimator is defined relative to the performance of the linear minimum MSE (MMSE) estimator tuned to the underlying unknown data uncertainties, i.e., the introduced algorithm has a competitive framework. Then, using this relative performance measure, we find the estimator that minimizes this cost for the worst-case system model. We show that finding this estimator can equivalently be cast as a semidefinite programming (SDP) problem. Numerical examples are provided to illustrate the theoretical results.