Recursive Joint Cramér-Rao Lower Bound for Nonlinear Parametric Systems with Colored Noise

The performance evaluation for joint state and parameter estimation (JSPE) is of great significance. Joint Cramér-Rao lower bound (JCRLB) has been widely studied for JSPE of nonlinear parametric systems with white noise. However, in practice, the noise is often colored due to high measurement frequency and bandlimited signal channels. In this paper, a recursive JCRLB is developed for JSPE of nonlinear parametric systems with colored noise, characterized by auto-regressive (AR) models. First, we propose a unified recursive JCRLB for JSPE of general nonlinear parametric systems with higher-order autocorrelated process noises and autocorrelated measurement noise simultaneously. Then its relationship with the posterior Cramér-Rao lower bound (PCRLB) for filtering of nonlinear systems with colored noise and the hybrid Cramér-Rao lower bound (HCRLB) for JSPE of regular parametric systems with white noise are provided. Illustrative examples in radar target tracking verify the effectiveness of the proposed JCRLB for the performance evaluation for JSPE of nonlinear parametric systems with colored noise.