Weiss–Weinstein Lower Bounds for Markovian Systems. Part 1: Theory

Abstract

Being essentially free from regularity conditions, the Weiss-Weinstein estimation error lower bound can be applied to a larger class of systems than the well-known Crameacuter-Rao lower bound. Thus, this bound is of special interest in applications involving hybrid systems, i.e., systems with both continuously and discretely distributed parameters, which can represent, in practice, fault-prone systems. However, the requirement to know explicitly the joint distribution of the estimated parameters with all the measurements makes the application of the Weiss-Weinstein lower bound to Markovian dynamic systems cumbersome. A sequential algorithm for the computation of the Crameacuter-Rao lower bound for such systems has been recently reported in the literature. Along with the marginal state distribution, the algorithm makes use of the transitional distribution of the Markovian state process and the distribution of the measurements at each time step conditioned on the appropriate states, both easily obtainable from the system equations. A similar technique is employed herein to develop sequential Weiss-Weinstein lower bounds for a class of Markovian dynamic systems. In particular, it is shown that in systems satisfying the Crameacuter-Rao lower bound regularity conditions, the sequential Weiss-Weinstein lower bound derived herein reduces, for a judicious choice of its parameters, to the sequential Crameacuter-Rao lower bound