主奇异子空间跟踪算法与性能分析

Algorithm and its performance analysis of principal singular subspace tracking

中文关键词  主奇异子空间  收敛性分析  自稳定性分析  神经网络

英文关键词  principal singular subspace (PSS)  convergence analysis  self-stabilizing property  neural networks

中文摘要

      主奇异子空间分析是一种自适应的神经网络信号处理技术, 广泛应用于现代信号处理中. 本文提出一种新 的主奇异子空间跟踪信息准则, 并以此为基础推导出一种在线的梯度流神经网络算法. 理论分析表明, 信息准则具 有唯一的全局最小值, 且最小值对应的状态矩阵能够恰好张成输入信号的主奇异子空间. 该算法具有良好的收敛 能力, 强大的自稳定性能, 且当输入信号呈现出奇异互相关特性时, 仍呈现出良好的跟踪效果. 分别采用李雅普诺夫 函数方法和常微分方程方法分析算法的收敛性能和自稳定性. MATLAB仿真算例验证了算法的性能.

英文摘要

      Principal singular subspace analysis is an adaptive neural network signal processing technique which has been widely applied in modern signal processing. In this paper, a novel information criterion for principal singular subspace tracking is proposed and based on the information criterion an online gradient flow neural network algorithm is derived. Theoretical analysis shows that the information criterion exhibits a unique global minimum point where the state matrices corresponding to the minimum point can exactly span the principal singular subspace of the input signals. The proposed algorithm has a good performance in convergence and an excellent self-stabilizing property. What is more, even if the input signals present a singular cross-correlation characteristic, the proposed algorithm can still track the principal singular subspace of the input signals efficiently. The convergence and self-stability are analyzed via the Lyapunov function approach and ordinary differential equation approach, respectively. MATLAB simulation results verify the effectiveness of the proposed algorithm.