Optimal placement of bearing-only sensors for target localization

We investigate optimal placements of multiple bearing-only sensors for target localization in both 2D and 3D spaces. The target is assumed to be static, and sensortarget ranges are arbitrary but fixed. The Fisher information matrix is used to characterize the localization uncertainty. By employing frame theory, we show that there are two types of optimal sensor placements, regular and irregular. Necessary and sufficient conditions of optimal placements are presented. It is proved that an irregular optimal placement can be converted to a regular one in a lower dimensional space. We furthermore propose explicit algorithms to construct some important specific regular optimal placements.