An Asymptotically Efficient Estimator in Closed-Form for 3-D AOA Localization Using a Sensor Network

Locating a signal source using angles of arrival (AOAs) in a wireless sensor network is attractive because it does not require synchronization of the distributed receivers as in the time-based localization. A challenge for AOA positioning is that the solution tends to have a large amount of bias compared with the maximum-likelihood estimator when using the computationally attractive pseudolinear formulation. AOA localization has been well studied for the 2-D situation, and relatively few developments are for the more practical 3-D scenario. This paper proposes a closed-form solution for 3-D localization using AOAs that can handle the presence of sensor position errors, achieves asymptotically the CRLB performance, and maintains a bias level close to the maximum-likelihood estimator. Theoretical analysis and simulation studies corroborate the performance of the proposed estimator.