Cooperative Source Positioning Based on 1D AOA and Depth Measurements: A Closed-Form Solution

Three dimensional (3D) source positioning techniques based on linear arrays have garnered significant attention from scholars in recent years, which use multiple one-dimensional angles of arrival (1D AOA) to localize sources. Existing 1D AOA-based 3D source positioning techniques are not directly applicable to cooperative positioning systems, particularly in scenarios involving cooperative sources such as underwater environments, the depth of the source is usually observable. This paper presents a novel cooperative positioning model that integrates 1D AOA and depth information, proposing a two-stage weighted least squares (TWLS) closed-form solution method. Furthermore, the Cramér-Rao lower bound (CRLB) for 1D AOAs and depth measurements is derived. The simulation experimental results demonstrate the feasibility of the proposed positioning scheme and the advantages of the TWLS method.