Posterior Cramér-Rao Bounds for Nonlinear Dynamic System with Colored Noises

A mean squared error lower bound for the discrete-time nonlinear filtering with colored noises is derived based on the posterior version of the Cramér-Rao inequality. The colored noises are characterized by the auto-regressive model including the auto-correlated process noise and autocorrelated measurement noise simultaneously. Moreover, the proposed lower bound is also suitable for a general model of nonlinear high order auto-regressive systems. Finally, the lower bound is evaluated by a typical example in target tracking. It shows that the new lower bound can assess the achievable performance of suboptimal filtering techniques, and the colored noise has a significantly effect on the lower bound and the performance of filters.