基于符号算子的变步长不完整自然梯度算法

摘要

通过引入不完整约束使不完整自然梯度算法有效克服传统自然梯度算法的缺点和不足，即当源信号幅度随时间快速变化或在某段时间为零时，不完整算法仍能较好地工作。同时，从一般动态分离模型中推导出的符号算子可改善算法的收敛性。结合上述两种思想提出一种基于符号算子的不完整自然梯度算法，增加基于代价函数梯度的变步长运算以平衡算法中收敛速度和稳态误差之间的矛盾。仿真结果表明，改进算法的性能明显优于传统算法，在保持良好稳态误差的基础上大大加快收敛速度。%By introducing the nonholonomic constraints, the nonholonomic natural gradient algorithm effectively overcomes the shortcoming and the insufficiency of the traditional natural gradient algorithm, namely,it can still work well when the amplitude of source signal changes rapidly over time or is equal to zero in a certain period of time. Meanwhile, the sign operator derived from a general dynamic separation model can improve the convergence of the algorithm. Thus, a nonholonomic natural gradient algorithm based on the sign operation is obtained by combining the above two ideas. Furthermore, a variable step-size based on the gradient of cost function is also applied to the proposed algorithm to balance the contradiction between the convergence speed and the steady-state error. The simulation results show that the performance of the proposed algorithm is superior to that of traditional algorithm, and it improves convergence speed without worsening the steady-state error seriously.