Analytic and Unambiguous Phase-Based Algorithm for 3-D Localization of a Single Source with Uniform Circular Array

• Main Authors: Zuo, Le, Pan, Jin, Ma, Boyuan
• Other Authors: School of Electrical and Electronic Engineering
• Format: Article
• Language: English
• Published: 2018
• Subjects: Three-dimensional (3-D) Localization Estimation; Uniform Circular Array (UCA)
• Online Access: https://hdl.handle.net/10356/88045; http://hdl.handle.net/10220/44516
• Institution: Nanyang Technological University

This paper presents an analytic algorithm for estimating three-dimensional (3-D) localization of a single source with uniform circular array (UCA) interferometers. 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. The 3-D parameters are decoupled to different spectrums in the Fourier domain. Algebraic relations are established between the 3-D localization parameters and the Fourier spectrums. Fourier sampling theorem ensures that the minimum element number for 3-D localization of a single source with a UCA is five. Accuracy analysis provides mathematical insights into the 3-D localization algorithm that larger number of elements gives higher estimation accuracy. In addition, the phase-based high-order difference invariance (HODI) property of a UCA is found and exploited to realize phase range compression. Following phase range compression, ambiguity resolution is addressed by the HODI of a UCA. A major advantage of the algorithm is that the ambiguity resolution and 3-D localization estimation are both analytic and are processed simultaneously, hence computationally efficient. Numerical simulations and experimental results are provided to verify the effectiveness of the proposed 3-D localization algorithm.