Cramer-Rao lower bounds for bearings-only maneuvering target tracking with incomplete measurements

Abstract

The theoretical Cramer-Rao lower bound (CRLB) for bearings-only maneuvering target tracking is derived in the case where the observation measurements are lost in a random fashion. Two binary variables are introduced to model two events respectively, one which the target maneuvers or not and another that the target is detected or missed. The corresponding recursive formula for theoretical CRLB is then derived based on the sequential version of the CRLB for general nonlinear systems. The theoretical formula suffers from heavy calculation load of the Fisher information matrix (FIM) while the constant probability of detection is less than unity. An approximation of the theoretical bound is proposed. In addition, a detection reduction factor bound is presented and proved to be less than the theoretical CRLB. The results are illustrated with a numerical example.