Recursive Weiss-Weinstein lower bounds for discrete-time nonlinear filtering

Being essentially free from regularity conditions, the Weiss-Weinstein lower bound can be applied to a larger class of systems than the well-known Cramer-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 renders the application of the Weiss-Weinstein lower bound to Markovian dynamic systems impractical. A new algorithm is presented in this paper for the recursive computation of the Weiss-Weinstein lower bound for a wide class of Markovian dynamic systems. 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. For systems satisfying the Cramer-Rao lower bound regularity conditions, and for a particular choice of its parameters, it is shown that the recursive Weiss-Weinstein lower bound reduces to the recently introduced recursive Cramer-Rao lower bound. Moreover, it is shown that several recently reported lower bounds, derived for systems with fault-prone measurements, are special cases of the proposed recursive Weiss-Weinstein lower bound.