Abstract:

：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 atdB, 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.

Key words: BP algorithm, CBF method, compressive sensing, OMP algorithm, RIP condition, microphone array