改进低秩矩阵逼近算法的非同步测量声源定位

doi:10.3901/JME.2023.16.137

机械工程学报 ›› 2023, Vol. 59 ›› Issue (16): 137-146.doi: 10.3901/JME.2023.16.137

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改进低秩矩阵逼近算法的非同步测量声源定位

宁方立¹, 姚克强¹, 韦娟²

1. 西北工业大学机电学院西安 710072;
2. 西安电子科技大学通信工程学院西安 710071

收稿日期:2022-08-25 修回日期:2022-11-15 出版日期:2023-08-20 发布日期:2023-11-15
通讯作者: 宁方立(通信作者),男,1974年出生,博士研究生导师。主要研究方向为声信号处理。E-mail:ningfl@nwpu.edu.cn
基金资助:
国家自然科学基金(52075441);陕西省重点研发计划(2023-YBGY-219);2023重点产业链攻关(2023JH-RGZNGG-0033);航空科学基金(20200015053001)资助项目。

Improved Low Rank Matrix Approximation Algorithm for Non-synchronous Measurement of Sound Source Localization

NING Fangli¹, YAO Keqiang¹, WEI Juan²

1. School of Mechanical Engineering, Northwestern Polytechnical University, Xi'an 710072;
2. School of Telecommunications Engineering, Xidian University, Xi'an 710071

Received:2022-08-25 Revised:2022-11-15 Online:2023-08-20 Published:2023-11-15

摘要/Abstract

摘要： 非同步测量声源定位可以提高定位的频率范围和空间分辨率。然而,在低信噪比的环境下现有矩阵补全算法的非同步测量声源定位结果精度较差。提出改进低秩矩阵逼近矩阵补全算法:首先,对不完整的互谱矩阵进行矩阵补全;其次,应用参数化非凸惩罚函数的去噪方法对互谱矩阵进行去噪处理。最终通过常规波束形成算法实现非同步测量声源定位。将改进低秩矩阵逼近算法与核范数最小化补全算法、主成分分析算法在不同频率与低信噪比下进行非同步测量声源定位数值仿真与试验对比。仿真与试验结果表明:①不同低信噪比下,改进低秩矩阵逼近算法较核范数最小化补全算法、主成分分析算法的补全误差均要小。②相比于核范数最小化补全算法、主成分分析算法的声源定位结果,改进的低秩矩阵逼近算法可以有效缩小主瓣宽度、抑制旁瓣,提高声源定位的分辨率,能够适用于信噪比较低的复杂工业环境。

关键词: 非同步测量, 矩阵补全, 声源定位, 低秩矩阵逼近

Abstract: Non-synchronous measurement sound source localization can improve the frequency range and spatial resolution of localization. However, in the environment of low signal to noise ratio（SNR）, the accuracy of the non-synchronous measurement sound source localization result of the existing matrix completion algorithm is poor. An improved low rank matrix approximation algorithm（LRMA） is proposed to perform matrix completion: First, incomplete cross-spectral matrix is completed; Second, the cross-spectral matrix is denoised by using the method of parameterized non-convex penalty function; In the end, the non-synchronous measurement sound source localization is realized through the conventional beamforming algorithm（CBF）. The improved LRMA and the nuclear norm minimization completion algorithm and principal component analysis algorithm（PCA） are compared with the numerical simulation and experiment of non-synchronous measurement sound source localization at different frequencies and low SNRs. The simulation and experiment results show that:① Under different low SNRs, the improved LRMA has smaller matrix completion error（MCE） than the nuclear norm minimization completion algorithm and PCA algorithm.② Compared with the sound source localization results of the nuclear norm minimization completion algorithm and PCA algorithm,the sound source localization result of the improved LRMA can effectively reduce the main lobe width, suppress the side lobes, improve the resolution of sound source localization, which can be applied to the complex industrial environments with low SNR.

Key words: non-synchronous measurement, matrix completion, sound source localization, low rank matrix approximation

中图分类号:

TB51
TP391

宁方立, 姚克强, 韦娟. 改进低秩矩阵逼近算法的非同步测量声源定位[J]. 机械工程学报, 2023, 59(16): 137-146.

NING Fangli, YAO Keqiang, WEI Juan. Improved Low Rank Matrix Approximation Algorithm for Non-synchronous Measurement of Sound Source Localization[J]. Journal of Mechanical Engineering, 2023, 59(16): 137-146.

参考文献

[1] XIONG W,HE Q,PENG Z. Fibonacci array-based focused acoustic camera for estimating multiple moving sound sources[J]. Journal of Sound and Vibration,2020,478:115351.
[2] 褚志刚,陈涛,赵书艺,等.基于声压贡献的球面阵波束形成声源识别滤波求和算法[J].机械工程学报,2018(4):238-244.CHU Zhigang, CHEN Tao, ZHAO Shuyi, et al.Filter-and-sum beamforming sound source identification algorithm for spherical microphone arrays based on pressure contrition[J]. Journal of Mechanical Engineering,2018(4):238-244.
[3] 宁方立,张超,潘峰,等.飞机起落架噪声源定位的压缩感知算法[J].航空学报,2018,39(5):121810.NING Fangli, ZHANG Chao, PAN Feng, et al.Compressive sensing algorithm for sound source location of aircraft landing gear[J]. Acta Aeronauticaet Astronautica Sinica,2018,39(5):121810.
[4] SCHMIDT R. Multiple emitter location and signal parameter estimation[J]. IEEE Transactions on Antennas and Propagation,1986,34(3):276-280.
[5] SIGTSMA P. CLEAN based on spatial source coherence[J]. International Journal of Aeroacoustics,2007,6(4):357-374.
[6] BROOKS T F,HUMPHREYS W M. A deconvolution approach for the mapping of acoustic sources(DAMAS)determined from phased microphone arrays[J]. Journal of Sound and Vibration,2006,294(4-5):856-879.
[7] SIMARD P,ANTONI J. Acoustic source identification:Experimenting the?1 minimization approach[J]. Applied Acoustics,2013,74(7):974-986.
[8] 宁方立,卫金刚,刘勇,等.压缩感知声源定位方法研究[J].机械工程学报,2016,52(19):42-52.NING Fangli,WEI Jingang,LIU Yong,et al. Study on Sound Sources Localization Using Compressive Sensing[J]. Journal of Mechanical Engineering,2016,52(19):42-52.
[9] BARRE S, PUHLE C. Acoustic sources distribution reconstruction from non-synchronous sound pressure measurements[C]//INTER-NOISE and NOISE-CON Congress and Conference Proceedings. Institute of Noise Control Engineering,2017,255(5):2929-2935.
[10] OPPENHEIM A V,LIM J S. The importance of phase in signals[J]. Proceedings of the IEEE,1981,69(5):529-541.
[11] KWON H S,KIM Y J,BOLTON J S. Compensation for source non stationarity in multireference, scan-based near-field acoustical holography[J]. The Journal of the Acoustical Society of America,2003,113(1):360-368.
[12] SIGTSMA P,DINSENMEYER A,ANTONI J,et al.Beamforming and other methods for denoising microphone array data[C]//25th AIAA/CEAS Aeroacoustics Conference. 2019:2653.
[13] GAO J,YU L,JIANG W. Extraction of target sources from incoherent and partially coherent background noise using low-rank and sparse decomposition of the cross-spectral matrix[C]//INTER-NOISE and NOISECON Congress and Conference Proceedings. Institute of Noise Control Engineering,2019,259(8):1547-1555.
[14] WANG J,WANG Y,XU Z,et al. Accelerated low rank matrix approximate algorithms for matrix completion[J].Computers&Mathematics with Applications,2019,77(2):334-341.
[15] 张丽,孔旭,孙忠贵.基于非局部自相似性和低秩矩阵逼近的补全算法[J].计算机应用,2020,40(11):3327-3331.ZHANG Li, KONG Xu, SUN Zhonggui. Matrix completion algorithm based on nonlocal self-similarity and low-rank matrix approximation[J]. Journal of Computer Applications,2020,40(11):3327-3331.
[16] SIGTSMA P. Phased array beamforming applied to wind tunnel and fly-over tests[R]. NLR-TP-2010-549,2010.
[17] 项亚南,潘丰.一种基于信噪比确定主元个数的方法[J].计算机系统应用,2015(2):200-205.XIANG Yanan,PAN Feng. Method based on the fault signal noise ratio to determine the number of principal component[J]. Computer Systems&Applications,2015(2):200-205.
[18] DINSENMEYER A,ANTONI J,LECLERE Q,et al. A probabilistic approach for cross-spectral matrix denoising:Benchmarking with some recent methods[J]. The Journal of the Acoustical Society of America,2020,147(5):3108-3123.
[19] 岳佳,王士同.高斯混合模型聚类中EM算法及初始化的研究[J].微计算机信息,2006(11X):244-246.YUE Jia, WANG Shitong. Algorithm EM and its initialization in gaussian-mixture-model based clustering[J]. Microcomputer Information,2006(11X):244-246.
[20] YU L, ANTONI J, LECLERE Q. Spectral matrix completion by Cyclic Projection and application to sound source reconstruction from non-synchronous measurements[J]. Journal of Sound and Vibration,2016,372:31-49.
[21] PAREKH A, SELESNICK I W. Enhanced low-rank matrix approximation[J]. IEEE Signal Processing Letters,2016,23(4):493-497.
[22] MA R, MIAO J, NIU L, et al. Transformed?1regularization for learning sparse deep neural networks[J].Neural Networks,2019,119:286-298.
[23] YU L,ANTONI J,WU H,et al. Fast iteration algorithms for implementing the acoustic beamforming of non-synchronous measurements[J]. Mechanical Systems and Signal Processing,2019,134:106309.

改进低秩矩阵逼近算法的非同步测量声源定位

Improved Low Rank Matrix Approximation Algorithm for Non-synchronous Measurement of Sound Source Localization

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