Combined Cramer-Rao/Weiss-Weinstein Bound for Tracking Target Bearing

Abstract

A recursive Bayesian Cramer-Rao/Weiss-Weinstein bound for the discrete-time nonlinear filtering problem for the special case when the state-space model consists of a linear process model and a general (nonlinear) measurement model is developed. This type of model arises in many applications including target tracking. It is often the case that the recursive Bayesian Cramer-Rao bound (BCRB) developed by Tichavsky et al is a good predictor of mean-square error performance for some of the state vector parameters, but is a weak bound for other components. The recursive Weiss-Weinstein bound (WWB) developed by Rapoport & Oshman and Reece & Nicholson offers a potentially higher bound but is generally more difficult to derive and implement, and its evaluation involves choosing "test points" in the parameter space. It becomes equal to the BRCB in the limiting case when the test points equal zero. A bound which combines the BCRB with the WWB using non-zero test points only for a subset of the state-vector components can provide as tight a bound as the WWB while keeping the complexity manageable. We first derive the recursive bound for the linear process/nonlinear measurement model, then apply the bound to the problem of tracking the bearing and bearing rate of a narrowband source using observations from a sparse linear array. The bound is compared to the recursive BCRB and to simulated tracking performance. The BCRWWB provides a tighter bound than the BCRB for the bearing tracking error, which is subject to ambiguities