Two lower bounds on the covariance for nonlinear estimation problems

Two Convariance lower bounds for nonlinear state estimation problems are presented. These bounds are based upon the Cramer-Rao bound for treating nuisance parameters and they can be applied to filtering, smoothing, and prediction problems. The tightness of these bounds are examined using a nonlinear system where the recursive equation for covariance computation can be obtained. These results are also compared with the bound of Bobrovsky and Zakai.