Optimal Sensor Placement for Target Localization and Tracking in 2D and 3D

TL;DR

This paper provides a unified analytical framework for optimal sensor placement in 2D and 3D for target localization and tracking, using frame theory to derive conditions for various sensor types.

Contribution

It introduces a unified formulation for optimal sensor placement across different sensor types and applies frame theory to derive necessary and sufficient conditions for optimality.

Findings

Derived necessary and sufficient conditions for optimal placements in 2D and 3D.

Unified analytical framework for different sensor types.

Presented a gradient control law for numerical construction of optimal placements.

Abstract

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.