压缩感知声源定位方法研究

Study on Sound Sources Localization Using Compressive Sensing

目前声源定位主要采用波束形成算法与麦克风阵列相结合的方法。常规波束形成(Conventional beamforming,CBF)方法存在以下缺陷:1空间分辨率受限于瑞利限;2动态响应范围受旁瓣的影响。高级波束形成算法则存在着计算时间过长、会出现负声源或假声源等缺陷。提出一种基于麦克风阵列与压缩感知正交匹配追踪(Orthogonal matching pursuit,OMP)算法的声源定位方法。在不同频率下通过数值仿真方法将压缩感知OMP算法与CBF算法及压缩感知基追踪(Basis pursuit,BP)算法的声源定位结果进行对比。结果表明:1与CBF算法相比,压缩感知算法显著提高定位结果的分辨率;2当声源频率为1 000 Hz时,测量矩阵的等距约束性常数(Restricted isometry constant,RIC)远高于FOUCART边界限,不满足等距约束性条件(Restricted isometry property,RIP),压缩感知OMP算法仍能定位出主要声源的位置,而压缩感知BP算法无法对主要声源进行定位。通过数值仿真方法对不同信噪比(Signal to noise ratio,SNR)及不同声源间距下压缩感知OMP算法和CBF算法声源定位的结果进行对比。结果表明:1当SNR为零时,压缩感知OMP算法能对主要的声源信号进行定位,而CBF算法无法对主要声源进行定位;2在声源频率为5 000 Hz时,OMP算法的空间分辨率为0.074 m,突破了瑞利限约束。通过试验对所提出的声源定位方法的可行性进行验证。

Beamforming algorithm combined with microphone arrays is by far the most commonly used for sound sources localization. However, conventional beamforming（CBF） suffers the following drawbacks. 1 Spatial resolution is subjected to Rayleigh＇s limit; 2 Dynamic range is affected by side lobes. While advanced beamforming methods suffer limitations as computational expensiveness or fake sources. A method which combines the microphone arrays and compressive sensing orthogonal matching pursuit（OMP） algorithm is proposed. The results of compressive sensing OMP algorithm, basis pursuit（BP） algorithm and those of CBF method are compared under different frequencies through simulations. The results show that： 1 compared with CBF method, compressive sensing reconstruction algorithm can significantly improve the resolution; 2 when the frequency of the sources is 1 000 HZ, the restricted isometry constant（RIC） of the measurement matrix is much higher than the FOUCART boundary and the restricted isometry property（RIP） does not hold. OMP algorithm can still locate the sound sources. While BP algorithm fails to locate the sound sources. The results of OMP algorithm and those of CBF method are also compared under different signal to noise ratio（SNR） and source spacing, respectively. The results show that： 1 at SNR =0 d B, OMP algorithm can locate the sound sources. While CBF method fails to locate the sound sources; 2 at 5 000 Hz, the resolution of the OMP algorithm is 0.074 m, which breaks the Rayleigh＇s limit. The feasibility of the proposed method is validated through a physical experiment.