Abstract
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.
Highlights
Source localization using an array of sensors is an important topic for wireless communication, radar, and sonar, etc
In order to compare with the closed-form algorithm [1], assuming only sampling noises exist, a uniform circular array (UCA) consisting of 16 elements with a radius of ρ0 = 0.25λ is exemplified
The root mean square errors (RMSEs) of elevation angle, azimuth angle, and range were estimated for performance evaluation
Summary
Source localization using an array of sensors is an important topic for wireless communication, radar, and sonar, etc. In this paper, we propose an analytic and unambiguous phase-based algorithm for 3-D localization of a single source with a UCA. Accuracy analysis is addressed in the Fourier domain to provide mathematical insights into the proposed algorithm. The high-order difference invariance (HODI) property of a UCA is addressed to compress the phase range and thereby realizing ambiguity resolution. The estimation algorithm sufficiently exploits the centro-symmetry and periodicity of a circular aperture by Fourier transforms and has established algebraic relations between 3-D localization parameters and phase samples on the circumference of a UCA.
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