Analytical Algorithm for 3-D Localization of a Single Source With Uniform Circular Array

This letter presents an analytical algorithm for estimating three-dimensional (3-D) localization of a single source with uniform circular arrays (UCAs). Fourier transforms are exploited to expand the phase distribution of a single source, and the localization problem is reformulated as an equivalent spectrum manipulation problem. 3-D parameters are decoupled to different spectrums in the Fourier domain. Algebraic relations are established between 3-D parameters and Fourier spectrums. Fourier sampling theorem ensures that the minimum element number for 3-D localization with a UCA is five. Accuracy analysis provides mathematical insights into the function of a center sensor. Numerical simulations and experimental results verify the effectiveness and appealing performance of the proposed 3-D localization algorithm.