POSTERIOR CRAMER-RAO BOUNDS FOR DISCRETE-TIME NONLINEAR FILTERING

A mean-square error lower hound for the discrete-time nonlinear filter ing problem is derived based on the Van Trees (posterior) version of t he Cramer-Rao inequality. This lower bound is applicable to multidimen sional nonlinear, possibly mon-Gaussian, dynamical systems and is more general than the previous bounds in the literature. The case af singu lar conditional distribution of the one-step-ahead state vector given the present state is considered. The bound is evaluated for three impo rtant examples: the recursive estimation of slowly varying parameters of an autoregressive process, tracking a slowly varying frequency of a single cisoid in noise, and tracking parameters of a sinusoidal frequ ency with sinusoidal phase modulation.