Zuo Le, Pan Jin, Ma Boyuan
Department of Microwave Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China.
School of Electrical and Electronic Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798, Singapore.
Sensors (Basel). 2018 Feb 6;18(2):484. doi: 10.3390/s18020484.
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.
本文提出了一种用于估计单个源在均匀圆形阵列（UCA）干涉仪下三维（3-D）定位的解析算法。利用傅里叶变换来扩展单个源的相位分布，并将定位问题重新表述为等效频谱处理问题。在傅里叶域中，三维参数被解耦到不同的频谱中。建立了三维定位参数与傅里叶频谱之间的代数关系。傅里叶采样定理确保了使用均匀圆形阵列对单个源进行三维定位所需的最小阵元数为五个。精度分析为三维定位算法提供了数学见解，即更多的阵元会带来更高的估计精度。此外，发现并利用了均匀圆形阵列基于相位的高阶差分不变性（HODI）特性来实现相位范围压缩。在相位范围压缩之后，通过均匀圆形阵列的HODI来解决模糊度分辨问题。该算法的一个主要优点是模糊度分辨和三维定位估计都是解析性的，并且可以同时进行处理，因此计算效率高。提供了数值模拟和实验结果来验证所提出的三维定位算法的有效性。
