A Sparse-Reconstruction-Based Fast Localization Algorithm for Mixed Far-Field and Near-Field Sources

FU Shijian; QIU Longhao; LIANG Guolong

doi:10.11999/JEIT250165

Article Contents

Article Navigation > Journal of Electronics & Information Technology > 2025 >

FU Shijian, QIU Longhao, LIANG Guolong. A Sparse-Reconstruction-Based Fast Localization Algorithm for Mixed Far-Field and Near-Field Sources[J]. Journal of Electronics & Information Technology. doi: 10.11999/JEIT250165

Citation:

FU Shijian, QIU Longhao, LIANG Guolong. A Sparse-Reconstruction-Based Fast Localization Algorithm for Mixed Far-Field and Near-Field Sources[J]. Journal of Electronics & Information Technology. doi: 10.11999/JEIT250165

Citation:

PDF( 3153 KB)

A Sparse-Reconstruction-Based Fast Localization Algorithm for Mixed Far-Field and Near-Field Sources

doi: 10.11999/JEIT250165 cstr: 32379.14.JEIT250165

FU Shijian^{1, 2, 3},
QIU Longhao^{1, 2, 3
,
,},
LIANG Guolong^{1, 2, 3}

1.
National Key Laboratory of Underwater Acoustic Technology, Harbin Engineering University, Harbin 150001, China
2.
Key Laboratory of Marine Information Acquisition and Security (Harbin Engineering University), Ministry of Industry and Information Technology Harbin 150001, China
3.
College of Underwater Acoustic Engineering, Harbin Engineering University, Harbin 150001, China

Funds: National Natural Science Foundation of China(62301183)

Received Date: 2025-03-17
Accepted Date: 2025-11-03
Rev Recd Date: 2025-11-03

Available Online: 2025-11-13

Abstract

Abstract

Objective Source localization is a critical research area in array signal processing, with applications in radar, sonar, and wireless communications. Traditional localization methods, which are based on either far-field or near-field models individually, face significant challenges in effectively separating and localizing mixed far-field and near-field sources. Existing algorithms, such as subspace-based methods, suffer from high computational complexity, limited localization accuracy, and degraded performance in low Signal-to-Noise Ratio (SNR) scenarios. In addition, these methods assume that near-field sources are located within the Fresnel Region, leading to localization errors and a reduction in effective array aperture. Improved algorithms, such as Multiple Sparse Bayesian Learning for Far and Near-field sources (FN-MSBL), successfully overcame these limitations and achieved higher localization accuracy. However, the high computational cost of matrix inversion during each iteration restricts its real-time applicability. Therefore, this paper aims to address these limitations and issues by proposing a novel algorithm that not only develops a sparse representation model for mixed near-field and far-field sources based on the covariance domain but also integrates sparse reconstruction with the Generalized Approximate Message Passing (GAMP) and Variational Bayesian Inference (VBI) frameworks. The primary goal is to achieve high-precision localization of mixed sources while significantly reducing computational costs, thereby enabling real-time applicability. Methods The proposed algorithms, termed Covariance-based VBI for Far and Near-field sources (FN-CVBI) and Covariance-based GAMP-VBI for Far and Near-field sources (FN-GAMP-CVBI), are developed through several key methods. First, a unified sparse representation model for mixed far-field and near-field sources is constructed based on the covariance vector. This model leverages the improved SNR of the covariance vector compared to the original array output, enabling more accurate far-field Direction Of Arrival (DOA) estimation. Second, to mitigate the estimation errors in the sample covariance matrix, a pre-whitening operation is applied to the covariance vector. This step effectively minimizes the correlation between the elements of the covariance vector, thereby enhancing the robustness of the sparse reconstruction algorithm. Third, a hierarchical Bayesian model is established to enforce sparsity, and VBI is employed to estimate the parameters. The VBI framework iteratively updates the posterior distributions of the hidden variables, ensuring convergence to a near-optimal solution. Fourth, to address the significant computational complexity associated with traditional VBI methods, the GAMP algorithm is embedded into the VBI framework. GAMP replaces the computationally expensive matrix inversion operations in VBI, significantly reducing the computational burden. The detailed implementation steps of GAMP are provided in Table 1. In conclusion, by combining the advantages of sparse reconstruction, VBI, and GAMP, the proposed algorithm not only improves localization accuracy but also significantly reduces computational complexity, making it suitable for real-time applications. Results and Discussions The proposed algorithm FN-GAMP-CVBI demonstrates significant improvements in both localization accuracy and computational efficiency. Computational complexity analysis demonstrates that the algorithm significantly reduces computational costs (Table 2). In terms of localization accuracy, the proposed algorithms, FN-CVBI and FN-GAMP-CVBI, both outperform compared methods such as LOFNS and FN-MSBL (Fig.3, Fig.4), particularly in low SNR and sufficient snapshots scenarios (Fig.5, Fig.6), and demonstrate superior performance in resolving closely spaced far-field sources (Fig.7). Experimental validation using lake trial data further confirms the effectiveness of the proposed algorithms, as evidenced by sharper spectral peaks and minimal false peaks in the background noise of Bearing Time Recording (BTR) (Fig.9). In addition, FN-CVBI achieves the highest accuracy in far-field DOA estimation and near-field localization. The computational time of FN-GAMP-CVBI is reduced by up to 95% compared to FN-MSBL, making the algorithm highly efficient for real-time applications (Table 4). Overall, the proposed FN-GAMP-CVBI algorithm strikes an effective balance between localization accuracy and computational efficiency. Conclusions This paper presents a novel approach to mixed far-field and near-field source localization by integrating sparse reconstruction with the GAMP-VBI framework. The proposed FN-GAMP-CVBI algorithm addresses the limitations of traditional methods, offering a balanced trade-off between computational efficiency and localization accuracy. The simulation results demonstrate superior performance, particularly in scenarios with sufficient snapshots and low SNR. Experimental validation further confirms the effectiveness and efficiency of the proposed algorithms. Overall, the proposed FN-GAMP-CVBI algorithm strikes an effective balance between localization accuracy and computational efficiency. Its ability to simultaneously handle both far-field and near-field sources, combined with its low computational complexity, positions it as a promising solution for real-time mixed source localization in complex environments.

FullText(HTML)

References(19)

References

[1]	LIANG Guolong, CHEN Yu, WANG Jinjin, et al. Enhanced noise resilience in passive tone detection via broad-receptive field complex-valued convolutional neural networks[J]. The Journal of the Acoustical Society of America, 2024, 155(6): 3968–3982. doi: 10.1121/10.0026438.
[2]	DU Zhiyao, HAO Yu, QIU Longhao, et al. Sparsity-based direction-of-arrival estimation in the presence of near-field and far-field interferences for small-scale platform sonar arrays[J]. The Journal of the Acoustical Society of America, 2024, 156(5): 2989–3005. doi: 10.1121/10.0034240.
[3]	LEE J H, CHEN Y M, and YEH C C. A covariance approximation method for near-field direction-finding using a uniform linear array[J]. IEEE Transactions on Signal Processing, 1995, 43(5): 1293–1298. doi: 10.1109/78.382421.
[4]	LIANG Junli and LIU Ding. Passive localization of mixed near-field and far-field sources using two-stage MUSIC algorithm[J]. IEEE Transactions on Signal Processing, 2010, 58(1): 108–120. doi: 10.1109/TSP.2009.2029723.
[5]	HE Jin, SWAMY M N S, and AHMAD M O. Efficient application of MUSIC algorithm under the coexistence of far-field and near-field sources[J]. IEEE Transactions on Signal Processing, 2012, 60(4): 2066–2070. doi: 10.1109/TSP.2011.2180902.
[6]	ZUO Weiliang, XIN Jingmin, ZHENG Nanning, et al. Subspace-based localization of far-field and near-field signals without eigendecomposition[J]. IEEE Transactions on Signal Processing, 2018, 66(17): 4461–4476. doi: 10.1109/tsp.2018.2853124.
[7]	LI Chenmu, LIANG Guolong, QIU Longhao, et al. An efficient sparse method for direction-of-arrival estimation in the presence of strong interference[J]. The Journal of the Acoustical Society of America, 2023, 153(2): 1257–1271. doi: 10.1121/10.0017256.
[8]	WANG Bo, LIU Juanjuan, and SUN Xiaoying. Mixed sources localization based on sparse signal reconstruction[J]. IEEE Signal Processing Letters, 2012, 19(8): 487–490. doi: 10.1109/lsp.2012.2204248.
[9]	CHEN Mengya, LIN Wei, ZHAO Yongwei, et al. Gridless mixed-field sources localisation algorithm based on covariance matrix reconstruction[J]. Journal of Physics: Conference Series, 2024, 2849: 012117. doi: 10.1088/1742-6596/2849/1/012117.
[10]	QI Meibin, REN Weijie, and XIANG Houhong. Separation of mixed near-field and far-field sources and DOA estimation based on deep learning[C]. ICAIT 2023 - 2023 IEEE 15th International Conference on Advanced Infocomm Technology, Hefei, China, 2023: 226–233. doi: 10.1109/ICAIT59485.2023.10367306.
[11]	LIANG Guolong, ZHAO Benbin, and FAN Zhan. Direction of arrival estimation under near-field interference using matrix filter[J]. Journal of Computational Acoustics, 2015, 23(4): 1540007. doi: 10.1142/S0218396X1540007X.
[12]	HAWKES M and NEHORAI A. Acoustic vector-sensor correlations in ambient noise[J]. IEEE Journal of Oceanic Engineering, 2001, 26(3): 337–347. doi: 10.1109/48.946508.
[13]	邱龙皓, 梁国龙, 王燕, 等. 稀疏贝叶斯学习远近场混合源定位方法[J]. 声学学报, 2018, 43(1): 1–11. doi: 10.15949/j.cnki.0371-0025.2018.01.001. QIU Longhao, LIANG Guolong, WANG Yan, et al. Mixed near-field and far-field sources localization method using sparse Bayesian learning[J]. Acta Acustica, 2018, 43(1): 1–11. doi: 10.15949/j.cnki.0371-0025.2018.01.001.
[14]	刘章孟. 基于信号空域稀疏性的阵列处理理论与方法[D]. [博士论文], 国防科学技术大学, 2012. LIU Zhangmeng. Spatial sparsity-based theory and methodsof array signal processing[D]. [Ph. D. dissertation], National University of Defense Technology, 2012.
[15]	AL-SHOUKAIRI M, SCHNITER P, and RAO B D. A GAMP-based low complexity sparse bayesian learning algorithm[J]. IEEE Transactions on Signal Processing, 2018, 66(2): 294–308. doi: 10.1109/TSP.2017.2764855.
[16]	LI Ninghui, ZHANG Xiaokuan, ZONG Binfeng, et al. An off-grid direction-of-arrival estimator based on sparse Bayesian learning with three-stage hierarchical Laplace priors[J]. Signal Processing, 2024, 218: 109371. doi: 10.1016/j.sigpro.2023.109371.
[17]	TIPPING M E. Sparse Bayesian learning and the relevance vector machine[J]. The Journal of Machine Learning Research, 2001, 1: 211–244. doi: 10.1162/15324430152748236.
[18]	TZIKAS D G, LIKAS A C, and GALATSANOS N P. The variational approximation for Bayesian inference[J]. IEEE Signal Processing Magazine, 2008, 25(6): 131–146. doi: 10.1109/msp.2008.929620.
[19]	RANGAN S. Generalized approximate message passing for estimation with random linear mixing[C]. IEEE International Symposium on Information Theory, St. Petersburg, Russia, 2011: 2168–2172. doi: 10.1109/ISIT.2011.6033942.