Optimal sensor placement for target localisation and tracking in 2D and 3D

This paper analytically characterises optimal sensor placements for target localisation 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 optimisation problem and consequently analysed 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.