基于加权核范数最小化的非同步测量声源定位

Non-synchronous Measurements of Sound Source Localization Based on Weighted Nuclear Norm Minimization

非同步测量声源定位中基于核范数最小化模型的补全算法求解互谱矩阵时,奇异值赋予相同权重,忽略对互谱矩阵奇异值具有的先验知识。针对核范数最小化模型的不足,提出了基于加权核范数最小化的交替方向乘子法和加速近端梯度算法,对缺省互谱矩阵进行补全,以完成声源定位。基于加权核范数最小化的补全算法在不同的奇异值上自适应地分配权重,能够更好地解决非凸非光滑低秩极小化问题。在不同频率和不同信噪比条件下进行了数值仿真和实验,对加权核范数最小化和核范数最小化两种模型的算法进行了对比。结果表明,基于加权核范数最小化的矩阵补全算法精度更高,且非同步测量声源定位结果在较低信噪比下能够有效缩小主瓣,抑制旁瓣,提高阵列的空间分辨率。

When solving the cross-spectral matrix by the matrix completion algorithm based on nuclear norm minimization(NNM)model in the non-synchronous measurements of sound source localization,the singular values are given the same weights,and the prior knowledge of the singular values is ignored.For the deficiency of NNM model,the alternating direction method of multipliers(ADMM) and the accelerated proximal gradient(APG) algorithms based on weighted nuclear norm minimization(WNNM) are proposed to complete the cross-spectral matrix with missing data in non-synchronous measurement of sound source localization,and finally complete the sound source localization.The matrix completion algorithms based on WNNM can better solve the non-convex and non-smooth low rank minimization problem,which assigns weights adaptively on different singular values.The algorithms based on WNNM and NNM are compared under the numerical simulation and experiment of different frequencies and SNRs.The results show that the matrix completion algorithms based on WNNM have higher matrix completion accuracy,and the results of non-synchronous measurement based on WNNM can effectively reduce the main lobe,suppress the sidelobes and improve the spatial resolution of the array under low SNRs.