Modified Frequency-Sliding Generalized Cross Correlation for Time Delay Difference Estimation of Microphone Array

Estimating the time delay difference between two microphones is important in many systems, including sonar, radar, wireless, and acoustics imaging systems. The generalized cross correlation (GCC) approach is the most widely used for time delay estimation, and many researchers are trying to improve its performance. Frequency-sliding GCC (FS-GCC), which utilizes frequency-sliding and principal eigenvector extraction, has developed in recent work. This study proposes a new approach based on deconvolving the subband GCCs of the designed windows group. The proposed algorithm has three essential core ideas, one of which is to design a windows group where each member slides the phase of the cross-power spectrum of GCC into overlapping subbands to generate subband GCCs. The pruning approach is then employed to reduce the dimensions of the subband GCCs matrix. Then, the matrix low-rank approximation is carried out on the pruned subband GCCs. The principal eigenvector corresponding to each member window of the windows group is then extracted. The second aspect is to deconvolute the principal eigenvector corresponding to each member window mentioned previously, which aids in reducing the sidelobe leakage and narrowing the main lobe. The deconvolved principal eigenvectors are then multiplied, merging with each other to obtain the time delay estimation in the third aspect. An extensive set of experiments is performed to validate the better performance of the proposed algorithm in comparison with other counterparts, such as a lower probability of anomalous, less estimation error, and a higher first-to-second peak ratio (FSPR). Concretely, an ablation experiment shows that the windows group can help to reduce the probability of anomalous. Pruning, deconvolution, and merging are beneficial to reducing the estimation error, and in addition, deconvolution and merging operation can improve the FSPR.