The cooperative localization of submerged autonomous underwater vehicles (AUVs) using the Time Difference of Arrival (TDOA) measurements of surface AUV sensors is an effective method for many applications of AUVs. Proper positioning of the sensors to maximize the observability of the AUVs is very critical for cooperative localization. In this paper, a novel method for obtaining the optimal formation of sensor AUVs has been presented for the three-dimensional (3D) cooperative localization of targets using the TDOA technique. An evaluation function for estimating the optimal formation has been derived based on Fisher Information Matrix (FIM) theory for a single target as well as multiple-target cooperative localization systems. An iterative stepping algorithm has been followed to solve the evaluation function and obtain the optimal positions of the sensors. The algorithm ensured that the computation complexity should remain limited, even when the number of sensor AUVs is increased. Various simulation examples are then presented to calculate the optimal formation for different systems/situations. The effect of the position of the reference sensor and operating depth of the target AUVs on the optimal formation of the sensors has also been studied, and conclusions are drawn. For implementation of the proposed method for more practical scenarios, a simulation example is also presented for cases when the target's position is only known with uncertainty.
Keywords: Fisher Information Matrix; Time Difference of Arrival (TDOA); autonomous underwater vehicles (AUVs); cooperative localization; optimal formation.