A fresh look at Bayesian Cram??r-Rao bounds for discrete-time nonlinear filtering

In this paper, we aim to relate different Bayesian Cramér-Rao bounds which appear in the discrete-time nonlinear filtering literature in a single framework. A comparative theoretical analysis of the bounds is provided in order to relate their tightness. The results can be used to provide a lower bound on the mean square error in nonlinear filtering. The findings are illustrated and verified by numerical experiments where the tightness of the bounds are compared.