Joint Cramér-Rao Lower Bound for Nonlinear Parametric Systems With Cross-Correlated Noises

Joint state and parameter estimation (JSPE) has a surge of interest due to its dual purposes in many fields, such as sensor registration and signal processing. In this letter, a recursive joint Cramér-Rao lower bound (JCRLB) is developed for JSPE of nonlinear parametric systems with cross-correlated process and measurement noises at the same time. The JCRLBs for two special cases of such systems with additive Gaussian noises are also studied. Illustrative examples show the effectiveness of the JCRLB for the performance evaluation of JSPE of nonlinear parametric systems with cross-correlated noises at the same time.