Bayesian Cramér-Rao Bound for nonlinear filtering with dependent noise processes

The Bayesian Cramér Rao Bound (BCRB) is derived for nonlinear state space models with dependent process and measurement noise processes. It generalizes the previously BCRB for the case of dependent noise. Two different dependence structures appearing in literature are considered, leading to two different recursions for BCRB. The special cases of Gaussian noise, and linear models are presented separately. Simulations demonstrate that correct treatment of dependencies is important for both filtering algorithms and the BCRB.