Three-Dimensional Source Localization Based on 1-D AOA Measurements: Low-Complexity and Effective Estimator

Three-dimensional (3-D) source localization based on 1-D angles of arrival (AOA) measurements from multiple linear arrays have attracted much attention due to the low cost of linear arrays and the easy access to 1-D AOAs. However, most existing methods are restricted to specific array deployments, and the convex optimization methods applicable to the linear array with arbitrary deployments have drawbacks such as high computational complexity and nonportability to small industrial equipment. In this article, we propose two 1-D AOA-based source localization methods. The first method uses the iterative reweighted least square (IRLS) to obtain a coarse solution and a deviation refinement (DR) procedure to refine the estimation. Each step in IRLS-DR has a closed-form solution; thus, it is computationally efficient. Moreover, it applies to arbitrary interarray deployments, and theoretical analysis shows that its performance can approach the Cramér–Rao lower bound (CRLB) at small noise levels. The second method addresses the maximum likelihood estimation (MLE). A modified Levenberg–Marquardt (MLM) method is proposed, which focuses on designing a new selection strategy of the regularization parameter to realize a high convergence probability and localization accuracy. Experiments based on computer simulations and SWellEx96-S59 ocean acoustic measurements are carried out to verify the performance and advantages of the proposed methods.