变步长等变自适应盲源分离算法
Variable Step？？Size Algorithm for Equivariant Adaptive Separation via Independence

针对传统盲源分离(BSS)算法采用固定步长难以同时兼顾收敛速度和稳态误差的难题,采用等变自适应盲源分离(EASI)算法,提出了一种基于分离指标的变步长等变自适应盲源分离算法(VS-SI)。该算法利用EASI收敛条件,构造表征信号分离程度的分离指标,并设计带遗忘因子的更新算法,以减小历史数据误差的影响,实现分离指标的自适应计算,并采用一个非线性单调递增函数实现步长的自适应调节。通过与固定步长的自然梯度算法(FS-NG)、固定步长的EASI算法(FS-EASI)、步长指数衰减算法(EDS)和基于权重正交约束变步长算法(AS-WO)的性能进行对比,结果表明,在无噪声和有噪声两种情况下,提出算法均有较快的收敛速度,最终性能指标分别减小了15%和20%以上,同时兼顾稳态误差和收敛速度,具有较好的数值鲁棒性。
The traditional blind source separation algorithm can not well balance the convergence rate and the steady？？state error due to the limitation of fixed step size. Based on equivariant adaptive separation via independence (EASI) algorithm, a variable step？？size algorithm with separation indicator (VS-SI) for EASI is proposed. The separation indicator (S) is constructed to reveal the separation degree by analyzing the convergence condition of EASI. Then, the adaptive updating of the S with forgetting factor is also designed to reduce the error effects of the previous data. A nonlinear monotone increasing function is proposed, which adaptively updates the step size. Compared with the fixed step？？size natural gradient algorithm (FS-NG), the fixed step？？size EASI algorithm, the exponential decay step？？size algorithm and the adaptive step？？size algorithm with weighted orthogonalization, the proposed algorithm is endowed with faster convergence rate, and the final performance indicator decreases more than 15% and 20% under noise？？free and noisy conditions respectively. The proposed method can balance the convergence rate and the steady？？state error with strong robustness