A cramér-rao bound for multidimensional discrete-time dynamical systems

In this note a mean-square error lower bound for the discrete-time nonlinear filtering problem is derived based on Cramér-Rao theory. The lower bound is applicable to multidimensional nonlinear dynamical systems and is tighter than others that have appeared in the literature. The case of singular process noise covariance is considered. A smoothing lower bound for the multidimensional case is also obtained. It is shown that all lower bounds derived can be conveniently evaluated by Monte Carlo simulation techniques.