Ambiguity Analysis and Resolution for Phase-Based 3D Source Localization under Given UCA

Under uniform circular array, by employing some algebraic schemes to exploit the phase information of receiving data and further estimate the source’s three-dimensional (3D) parameters (azimuth angle, elevation angle, and range), a series of novel phase-based algorithms with low computational complexity have been proposed recently. However, when the array diameter is larger than source’s half-wavelength, these algorithms would suffer from phase ambiguity problem. Even so, there always exist certain positions, where the source’s parameters can still be determined with nonambiguity. Therefore, this paper first investigates the zone of ambiguity-free source 3D localization using phase-based algorithms. For the ambiguous zone, a novel ambiguity resolution algorithm named ambiguity traversing and cosine matching (ATCM) is presented. In ATCM, the phase differences of centrosymmetric sensors under different ambiguities are utilized to match a cosine function with sensor number-varying, and the source’s unambiguous rough angles can be derived from amplitude and initial phase of the cosine function. Then, the unambiguous angles are employed to resolve the phase ambiguity of the phase-based 3D parameter estimation algorithm, and the source’s range as well as more precise angles can be achieved. Theoretical analyses and numerical examples show that, apart from array diameter and source’s frequency, the sensor number and spacing of employed sensors are two key factors determining the unambiguous zone. Moreover, simulation results demonstrate the effectiveness and satisfactory performance of our proposed ambiguity resolution algorithm.