Optimal Geometry of Elliptical Target Localization

This letter unifies the optimal geometry analysis for elliptical target localization by a new notion called virtual agents (VAs), which allows the conversion of a bi-static time-of-arrival (TOA) measurement to a direct TOA measurement with equivalent Fisher information. Using the notion of VAs, we determine the optimal geometries with different types of measurements based on D-optimality. In particular, the optimal geometry is attained when the angles between transmitter-to-target and target-to-agent directions are ±π/3 for the TOA case, or the agents have an equal angular spacing around the target with equal ranging information intensity (RII) for the angle-of-arrival (AOA) case. Moreover, we also show that for the TOA/AOA fusion case, the optimal geometry occurs if the transmitter, agents, and target are collinear under both single-agent with arbitrary RII and multi-agent with identical RII between two measurements conditions. Finally, numerical results are given to validate our theoretical analysis.