Mixed H^2/H^∞ Estimation: Preliminary Analytic Characterization And A Numerical Solution

We introduce and motivate the problem of mixed H^2/H∞ estimation by studying the stochastic and deterministic approaches of H^2 and H^∞ estimation. Mixed H^2/H^∞ estimators have the property that they have the best average performance over all estimators that achieve a certain worst-case performance bound. They thus allow a tradeoff between average and worst-case performances. In the finite horizon case, we obtain a numerical solution (based on convex optimization methods) for the optimal mixed H^2/H^∞ estimator. We also give some analytic characterizations, both on this optimal solution, and on the set of all estimators achieving a guaranteed worst-case bound. A numerical example is also provided.