Cramer-Rao Bounds for Target Tracking Problems Involving Colored Measurement Noise

Abstract

Recursive formulas are derived for computing the Cramer-Rao lower bound on the error covariance matrix associated with estimating the state vector of a moving target from a sequence of biased and temporally correlated measurements. The discussion is limited to deterministic motion with no process noise. Furthermore, the nonlinear mapping from the target state space to the observation space is assumed to be corrupted by additive noise. When the measurement noise process becomes temporally decorrelated, the recursive relation for computing the Cramer-Rao lower bound reduces to that originally obtained by Taylor [1]. Specific noise models are examined, and results are illustrated using an example. For the special case of the random walk process, it is shown that the recursive formula for the Cram?Rao lower bound reduces to the error covariance propagation equations of the prewhitening filter of Bryson and Henrikson [2].