  This paper analytically characterizes optimal sensor placements for target
localization and tracking in 2D and 3D. Three types of sensors are considered:
bearing-only, range-only, and received-signal-strength. The optimal placement
problems of the three sensor types are formulated as an identical parameter
optimization problem and consequently analyzed in a unified framework. Recently
developed frame theory is applied to the optimality analysis. We prove
necessary and sufficient conditions for optimal placements in 2D and 3D. A
number of important analytical properties of optimal placements are further
explored. In order to verify the analytical analysis, we present a gradient
control law that can numerically construct generic optimal placements.
