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为显著提高对稀疏系统的辨识性能,提出了一种自适应算法。该算法将与稀疏性有重要关系的l1范数引入LMS算法的代价函数中,并导出新的滤波器权系数更新公式。该公式在迭代过程中向权系数不断添加一个指向零矢量的修正量,使得在稀疏系统中占主要地位的零系数加速收敛,从而显著提高自适应算法的收敛速度和跟踪速度。理论分析并推导了算法的均值收敛过程。仿真结果表明:该算法无论对一般稀疏系统还是分簇稀疏系统,都能明显改善收敛性能,并且表现出良好的稳健性和通用性。
In order to improve the recognition performance of sparse systems, an adaptive algorithm is proposed. The algorithm introduces l1 norm, which has important relationship with sparsity, into the cost function of LMS algorithm and derives a new update formula of filter weight coefficient. In the iterative process, this formula continuously adds a correction quantity pointing to the zero vector to the weight coefficient, so that the zero coefficient that predominates in the sparse system accelerates convergence, thereby significantly improving the convergence speed and the tracking speed of the adaptive algorithm. The theory analyzes and deduces the mean convergence of the algorithm. The simulation results show that the proposed algorithm can significantly improve convergence performance and show good robustness and universality both for general sparse systems and for clustered sparse systems.