We present a second-order statistics (SOS)-based algorithm for three-dimensional (3-D) localization of multiple near-field sources using an uniform circular array (UCA). Based on the centro-symmetric property of UCA steering vectors, a particular diagonal matrix, which only includes two-dimensional (2-D) direction of arrival (DOA) is constructed by utilizing the rotational relationship of the different UCA outputs. By exploiting the subspace of an SOS for UCA output, an estimation of signal parameters via rotational invariance techniques (ESPRIT)-like and a one-dimensional MUSIC methods are performed to obtain the 2-D DOA and range spatial spectrum, respectively. The proposed SOS-based algorithm does not require high-order statistics computation and also does not require additional eigenvalue decomposition for range estimation. Simulation results demonstrate the superior performance of the proposed algorithm compared with a TSMUSIC method and a phase-based method.

Under fixed uniform circular array (UCA), 3-D parameter estimation of a source whose half-wavelength is smaller than the array aperture would suffer from a serious phase ambiguity problem, which also appears in a recently proposed phase-based algorithm. In this paper, by using the centro-symmetry of UCA with an even number of sensors, the source’s angles and range can be decoupled and a novel algorithm named subarray grouping and ambiguity searching (SGAS) is addressed to resolve angle ambiguity. In the SGAS algorithm, each subarray formed by two couples of centro-symmetry sensors can obtain a batch of results under different ambiguities, and by searching the nearest value among subarrays, which is always corresponding to correct ambiguity, rough angle estimation with no ambiguity is realized. Then, the unambiguous angles are employed to resolve phase ambiguity in a phase-based 3-D parameter estimation algorithm, and the source’s range, as well as more precise angles, can be achieved. Moreover, to improve the practical performance of SGAS, the optimal structure of subarrays and subarray selection criteria are further investigated. Simulation results demonstrate the satisfying performance of the proposed method in 3-D source localization.

A high-accuracy algorithm is presented for the localization of mixed incoherent near-field and far-field narrow-band sources under uniform circular array (UCA). Herein, considering that it is difficult to classify the mixed sources, we first decouple mixed sources’ angles and ranges by calculating centro-symmetric sensors’ phase differences. Then, as the phase differences including only sources’ angles can be transformed as indefinite equations, each source’s azimuth angle and elevation angle are obtained by performing the least squares method. After that, on the basis of the estimated angles of the mixed sources, one-dimensional (1-D) multiple signal classification (MUSIC) method and corresponding spatial spectrum are utilized to identify the mixed sources and estimate the ranges of the near-field sources. Finally, simulation and comparison results verify the superior performance of our proposed algorithm.

Localization of linear frequency modulation (LFM) source based on combination of time_ frequency analysis and spatial spectrum estimation technique has received extensive research. However, this scheme is always confined to far-field sources and suffers from high computational cost. In this letter, by performing the fractional Fourier transform (FRFT) to multiple incoherent LFM signals, a fast and closed-form algorithm based on phase difference is proposed for 3-D source localization under a uniform circular array (UCA). Firstly, the phase relationship among sensors’ maximum outputs in fractional Fourier domain is exploited to construct indefinite equations, and then the least square (LS) method is employed to estimate the source’s azimuth angle, elevation angle, and range simultaneously. Finally, comparing with current approaches, the satisfactory performance of our proposed algorithm is demonstrated, and the effectiveness for dealing with mixed far-field and near-field sources is also confirmed.

Under uniform circular array, by employing some algebraic schemes to exploit the phase information of receiving data and further estimate the source’s three-dimensional (3D) parameters (azimuth angle, elevation angle, and range), a series of novel phase-based algorithms with low computational complexity have been proposed recently. However, when the array diameter is larger than source’s half-wavelength, these algorithms would suffer from phase ambiguity problem. Even so, there always exist certain positions, where the source’s parameters can still be determined with nonambiguity. Therefore, this paper first investigates the zone of ambiguity-free source 3D localization using phase-based algorithms. For the ambiguous zone, a novel ambiguity resolution algorithm named ambiguity traversing and cosine matching (ATCM) is presented. In ATCM, the phase differences of centrosymmetric sensors under different ambiguities are utilized to match a cosine function with sensor number-varying, and the source’s unambiguous rough angles can be derived from amplitude and initial phase of the cosine function. Then, the unambiguous angles are employed to resolve the phase ambiguity of the phase-based 3D parameter estimation algorithm, and the source’s range as well as more precise angles can be achieved. Theoretical analyses and numerical examples show that, apart from array diameter and source’s frequency, the sensor number and spacing of employed sensors are two key factors determining the unambiguous zone. Moreover, simulation results demonstrate the effectiveness and satisfactory performance of our proposed ambiguity resolution algorithm.