Novel Techniques for the Design of Robust State Estimators

Abstract We present a characterization of the class of all stable unbiased observers of the state of linear dynamic systems. Itlis characterization is parameterized by a single stable transfer function and the state estimation error is shown to be an affine function of this transfer function. Based on this characterization, we show how different optimization criteri a Ciin be employed to design filters which are optimal with respect to various criteria. In particular we address L 1 , L 2 and L ∞ optimization prucedures. The techniques are illustrated by it specific example. For this example, a variety of optimal filters are derived corresponding to L 1 , L 2 and L ∞ opimization as well as various combinations of these criteria. we argue that, depending upon the assumptions one makes about the noise and distllrbances, these filters have advantages over the commonly L 2 criterion filters.