基于非线性主成分分析的自适应变步长盲源分离算法

算法的迭代步长对于算法的收敛性能有着重要影响。针对固定步长的非线性主成分分析(NPCA)算法不能兼顾收敛速度和估计精度的情形，提出基于梯度的自适应变步长NPCA算法和最优变步长NPCA算法两种自适应变步长算法来改善其收敛性能。特别地,最优变步长NPCA算法通过对代价函数进行一阶线性近似表示,从而计算出当前的最优迭代步长。该算法的迭代步长随估计误差的变化而变化,估计误差大,迭代步长相应大,反之亦然;且不需要人工设置任何参数。仿真结果表明,当算法的估计精度相同时,与固定步长NPCA算法相比,两种自适应变步长NPCA算法相对固定步长NPCA算法都具有更好的收敛速度或跟踪性能,且最优变步长NPCA算法的性能优于基于梯度的自适应变步长NPCA算法。

Adaptive variable step-size blind source separation algorithm based on nonlinear principal component analysis

The design of the step-size is crucial to the convergence rate of the Nonlinear Principle Component Analysis (NPCA) algorithm. However, the commonly used fixed step-size algorithm can hardly satisfy the convergence speed and estimation precision requirements simultaneously. To address this issue, the gradient-based adaptive step-size NPCA algorithm and optimal step-size NPCA algorithm were proposed to speed up the convergence rate and improve tracking ability. In particular, the optimal step-size NPCA algorithm linearly approximated the contrast function and figured out the optimal step-size currently. The optimal step-size NPCA algorithm utilized an adaptive step-size whose value was adjusted in sympathy with the value of the contrast function and free from any manual parameters. The simulation results show that the proposed adaptive step-size NPCA algorithms have faster convergence rate or better tracking ability in comparison with the fixed step-size NPCA algorithm when the estimation precisions are same. The convergence performance of the optimal step-size NPCA algorithm is superior to that of the gradient-based adaptive NPCA algorithm.