An improved method to localize simultaneously close and coherent sources based on symmetric-Toeplitz covariance matrix

Abstract

There is a need to develop better algorithms for resolving multiple sound sources which are close or coherent. The Multiple Signal Classification method works satisfactorily in such situations when used along with spatial smoothing only when the SNR is high and array size is large. The MUSIC-Group Delay (MGD) method when used in conjunction with spatial smoothing works even for low SNR signals coming from close and coherent sources. However, it is computationally expensive and needs large arrays. To address these limitations, we propose the Improved MGD (IMGD) method which uses a symmetric-Toeplitz matrix derived from covariance matrices of regular sensor data and their conjugates for calculating the direction of arrival of sound sources. Such a method will work for close sources as we have shown that noise subspaces of conventional and symmetric-Toeplitz covariance matrices as well as phase characteristics of MUSIC spectra derived from these matrices are equivalent. Such a method will also work for coherent sources as we have shown that the spatially smoothened symmetric-Toeplitz covariance matrix, very much like the ordinary covariance matrix used for non-coherent sources, is positive semi-definite. In this way we have established the mathematical validity of the IMGD method. Next, we conducted several simulations to compare the efficacy of the proposed method relative to the MGD method. Our results show that the proposed method markedly performs better in terms of accuracy, and resolution capability. Finally, we also conducted experiments to validate the proposed method. Our experimental data show that the IMGD method is better than MGD in all aspects significantly.