An Alternating Minimization Algorithm for 3-D Target Localization Using 1-D AOA Measurements

State-of-the-art studies on angle of arrival (AOA)-based 3-D localization methods require both azimuth and elevation angles, which means the planar arrays are necessary, but in some limited environments, only linear arrays are available. In this letter, the problem of 3-D target localization based on 1-D AOA is considered. Different from the azimuth or elevation angle, the 1-D angle used in this letter is the angle between the ray pointing to the target and the array orientation, which could be obtained directly by each sensor. A nonlinear least square problem is formulated and an alternating minimization algorithm is derived as a fast algorithm for solving the nonlinear problem. The Cramer-Rao lower bound (CRLB) is derived to verify the feasibility of the model and as a benchmark compared with the proposed algorithm. Simulation results show that the proposed method can attain the CRLB accuracy at a moderate noise level. Further more, the proposed algorithm has better positioning performance and higher convergence probability compared with Gauss-Newton method.