A note on sensor arrangement for long-distance target localization

We considered a sensor formation problem for target localization based on the time difference of arrival (TDOA) data. It is assumed that the target is located far off from the sensors while the sensors are relatively close to each other. The estimators of the target location expressed in terms of the spherical coordinates are found to be uncorrelated when the sensors are arranged in a concentric ring formation. The proposed optimal formation of sensors is in the concentric ring formation and is shown to change in accordance with sensors' angular positions with respect to the line-of-sight vector from the reference sensor to the target. The proposed optimal sensor formations are compared in the context of estimation accuracy both in theory and by numerical experiments. They are shown optimal in general through refined numerical experiments.