Closed-Form Rectilinear Emitters Localization With Multiple Sensor Arrays: Phase Alignment and Optimal Weighted Least-Square Method

Position determination algorithms of rectilinear emitters (also called strictly second-order noncircular emitters) with multiple sensor arrays (SAs) allow for higher localization accuracy and more achievable degrees of freedom compared to the conventional version with circular emitters. However, it also brings additional computational complexity and noise. In this article, we develop a position determination algorithm of rectilinear emitters in closed-form on the basis of phase alignment and optimal weighted least square (OWLS), which is termed the PAOWLS method. First, we utilize the polynomial root-finding method to obtain the angle of arrival (AOA) and estimate rectilinear phases to align AOA. Then, we construct a least-square (LS) constraint to estimate the positions of emitters directly (termed the PALS method). Finally, we construct a weighted LS constraint and deduce the optimal weight to compensate for the position estimation bias. Extensive numerical results verify the outstanding performance of the proposed algorithm in terms of localization accuracy, resolution capability, and computational complexity.