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

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。

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:①Under different low SNRs,the improved LRMA has smaller matrix completion error(MCE)than the nuclear norm minimization completion algorithm and PCA algorithm.②Compared 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.