Optimal deployment of vehicles with circular formation for bearings-only multi-target localization

This paper focuses on the optimal deployment problem of multiple mobile vehicles with circular formation for multi-target localization using bearings-only sensors. Initially, a general closed-form formula of geometric dilution of precision (GDOP) is derived based on the Cramer–Rao lower bound (CRLB) for bearings-only localization. By this generalized formula, the analytical formula of GDOP for multiple vehicles containing the same observation noise variance with circular formation is then deduced directly. Next, the necessary and sufficient condition for sensor placement optimality with the minimization of GDOP is presented, which guarantees what are the best positions where the vehicles should be in the desired observation circumference with the given radius centered at the target. The optimal deployment positions as well as the global minimum of GDOP are then proposed with analytical expressions. Furthermore, an efficient optimal deployment algorithm is developed to deploy the vehicles to approach the best positions as precisely as possible for practical multi-target localization. Finally, an illustrative example is used to demonstrate the effectiveness of the proposed approach.