The Error Lower Bound of Target State Estimation in Passive Localization by Bearing-only Sensors

Error analysis of passive positioning based on bearing-only sensor network is crucial to improve the accuracy and reliability of state estimation in various applications such as target tracking and autonomous driving. However, the theoretical research on the lower bound of target state estimation error (LBSEE) by bearing-only sensor is very limited. This paper analyzes and provides the LBSEE of bearings-only sensors under random noise conditions. Initially, in the passive positioning model of a pair of bearing-only sensors, the random state variables of the target are reasonably transformed. Then, based on the mean square error of the transformed random state variables, a rigorous theoretical derivation is performed to establish the LBSEE. Finally, five scenarios are designed for parameter impact analysis under different constraints such as angle of measurement, baseline distance, line of sight separation angle, and heterogeneous component structure. The corresponding simulation examples verify the theoretical LBSEE and prove its effectiveness for sensor control applications. This study not only enriches the state estimation theory of passive sensors, but also provides a scientific basis for practical applications and promotes the development of sensor networks and collaborative positioning technology.