Cramér-Rao Bound Analysis of Passive Localization in Collaborative Environment of Surface Ships

Although Cramér-Rao Bounds (CRB) for angle-of-arrival (AOA) based position estimation have been extensively studied for decades, the existing works mainly focused on target direction finding errors, neglecting the deviations of mutual measurements in collaborative environment of surface ships. The deviations of mutual direction-finding and ranging between cooperative ships should be taken into account for source localization using mutual measurements in collaborative environment of surface ships. In this paper, we derive quantitative expressions of the CRB on the positioning accuracy while considering the deviations of mutual measurements, and calculate the lower bound on the circular error probability (CEP) of the cooperative localization system. The derived bounds are simple to evaluate and provide a good prediction of the actual AOA based cooperative localization system performance in collaborative environment of surface ships. Numerical examples illustrate our theoretical results.