A novel mixing matrix estimation algorithm in instantaneous underdetermined blind source separation

Due to the lack of sufficient prior information, how to estimate the mixing matrix in multiple underdetermined blind source separation (UBSS) models is a difficult problem. This study proposes an algorithm, which is used for the estimation of mixing matrix in instantaneous UBSS. Firstly, we propose an efficient single-source-points detection criterion with the transformation for the mixed signal vector, which is used as the basis for the clustering process. There are some shortcomings in the classical clustering algorithms, including the dependence on input parameters, restrictions on the data dimension, the requirement of the prior knowledge of the source signals and high complexity. To overcome these drawbacks, the modified density peaks clustering algorithm is used for the estimation of the initial clustering centers to adapt to different circumstances. Based on the idea of mean clustering, the single source points near each initial cluster center are processed, respectively, and the final estimation results of the mixing matrix are obtained. A variety of simulation experiments demonstrate the universality and validity of the proposed algorithm. The proposed method also has excellent performance even under the circumstance of low signal-to-noise ratio.