Analytic and Unambiguous Phase-Based Algorithm for 3-D Localization of a Single Source with Uniform Circular Array
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Department of Microwave Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China
2
School of Electrical and Electronic Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798, Singapore
*
Author to whom correspondence should be addressed.
Sensors 2018, 18(2), 484; https://doi.org/10.3390/s18020484
Received: 16 December 2017
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Revised: 31 January 2018
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Accepted: 3 February 2018
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Published: 6 February 2018
(This article belongs to the Section Sensor Networks)
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.
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Keywords:
three-dimensional (3-D) localization estimation; uniform circular array (UCA); phase ambiguity; Fourier transform
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MDPI and ACS Style
Zuo, L.; Pan, J.; Ma, B. Analytic and Unambiguous Phase-Based Algorithm for 3-D Localization of a Single Source with Uniform Circular Array. Sensors 2018, 18, 484. https://doi.org/10.3390/s18020484
AMA Style
Zuo L, Pan J, Ma B. Analytic and Unambiguous Phase-Based Algorithm for 3-D Localization of a Single Source with Uniform Circular Array. Sensors. 2018; 18(2):484. https://doi.org/10.3390/s18020484
Chicago/Turabian StyleZuo, Le, Jin Pan, and Boyuan Ma. 2018. "Analytic and Unambiguous Phase-Based Algorithm for 3-D Localization of a Single Source with Uniform Circular Array" Sensors 18, no. 2: 484. https://doi.org/10.3390/s18020484
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