中文摘要：

由于球麦克风阵列本身结构的特殊性，目前它广泛的应用于声场录制、波束形成、声场重现和声场分析等等领域．利用球麦克风阵列的对称性进行三维空间的多声源定位，和传统的声源定位方法不一样，通过分析声波传播的物理特性，采用球谐函数声场分解的方法，研究和探讨了离散的球麦克风阵列求解多声源情况下球散射声场球谐系数的方法，同时采用球傅立叶变换的方法分析了多声源情况下声场的指向性因子的变化情况，并由该指向性因子的等高线图确定了三维空间中的各个声源方向． 同时还大致分析了麦克风阵列的离散化所导致的声场分解的误差，讨论了麦克风阵列的大小、麦克风位置以及声场分解模态的高低对声源定位精度的影响，最后采用了遗传算法对球麦克风阵列的麦克风位置进行设计和优化，提出了在有实际应用条件限制下设计优化球麦克风阵列的一种方法．计算机模拟表明，基于声场球谐系数求解和球傅立叶变换的方法可以同时有效的确定三维空间中任意方向的多个声源的方向．

英文摘要：

Spherical microphone arrays have been recently applied in sound recordings, beamforming, sound field reproduction and sound field analysis, as they have the advantage of spherical-symmetryfacilitating three-dimensional analysis. This paper is concerned with the problem of localization of single and multiple sources in 3D space using spherical microphone array according to the symmetry of this configuration. In contrast to existing sound localization techniques, this method takes the physics of wave propagation into account. 3D space sound fields are decomposed by using spherical harmonic as the basis functions by mounting a spherical array into a rigid sphere. Then we study the solution to the spherical harmonic coefficients of spherical scattering sound field with the existence of multiple acoustic sources. The spherical transform is used to analyze the multiple acoustic sources, which shows the diversification of the directivity of the sound field. And then the contour of the direetivity of the sound field can be used as a method of acoustic source localization. In addition, this paper discusses the factors which influence the accuracy of acoustic source localization, such as the number and the positions of microphone array, and the modal number of the sound field decomposition etc. Finally, a genetic algorithm is used to optimize the spherical microphone array. It is shown that acoustic source localization based on spherical harmonic coefficients and spherical Fourier transform has the potential to localize multiple simultaneous sources in the array＇ s full 360 degrees field-of-view.