Ambiguity Resolution for Passive 2-D Source Localization with a Uniform Circular Array

This paper proposes two novel phase-based algorithms for the passive localization of a single source with a uniform circular array (UCA) under the case of measuring phase ambiguity based on two phase difference observation models, which are defined as the unambiguous-relative phase observation model (UARPOM) and the ambiguous-relative phase observation model (ARPOM). First, by analyzing the varying regularity of the phase differences between the adjacent array elements of a UCA, the corresponding relationship between the phase differences and the azimuth and elevation angle of the signal is derived. Based on the two phase observation models, two corresponding novel algorithms, namely, the phase integral accumulation and the randomized Hough transform (RHT), are addressed to resolve the phase ambiguity. Then, by using the unambiguous phase differences, the closed-form estimates of the azimuth and elevation angles are determined via a least squares (LS) algorithm. Compared with the existing phase-based methods, the proposed algorithms improve the estimation accuracy. Furthermore, our proposed algorithms are more flexible for the selection of an array radius. Such an advantage could be applied more broadly in practice than the previous methods of ambiguity resolution. Simulation results are presented to verify the effectiveness of the proposed algorithm.