The Cramér-Rao estimation error lower bound computation for deterministic nonlinear systems

For continuous-time nonlinear deterministic system models with discrete nonlinear measurements in additive Ganssian white noise, the extended Kalman filter (EKF) convariance propagation equations linearized about the true unknown trajectory provide the Cramér-Rao lower bound to the estimation error covariance matrix. A useful application is establishing the optimum filter performance for a given nonlinear estimation problem by developing a simulation of the nonlinear system and an EKF linearized about the true trajectory.