Generalized principal component analysis (GPCA) has been an active area of research in statistical signal processing for decades. It is used, e.g., for denoising in subspace tracking as the noise of different nature is incorporated into the procedure of maximizing signal-to-noise ratio (SNR). This paper presents a fixed-point approach concerning the principal generalized eigenvector extraction. It is based on the basis iteration for maximizing the generalized Rayleigh quotient (GRQ) with a given matrix pencil. The proposed approach extracts multiple generalized eigenvectors of a matrix pencil by exploiting the orthogonal complement structure of its estimation. It has no requirement to choose the commonly used step size. This enhances its practical applicability, as selecting an appropriate step size is a bottleneck for most gradient flow based algorithms. Our approach is more suitable for online processing because of its easy implementation and low computational complexity. To show the efficacy, efficiency and practical applicability of the proposed algorithm, we conduct several experiments, two of which concern smart antenna and blind source separation applications. Our simulation results show that the proposed algorithm outperforms several existing algorithms in terms of convergence speed as well as computational time.

中文翻译：

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通过定点方法在线提取广义特征向量

几十年来，广义主成分分析（GPCA）一直是统计信号处理研究的活跃领域。它被用于子空间跟踪中的降噪，因为不同性质的噪声已合并到最大化信噪比（SNR）的过程中。本文提出了一种关于主要广义特征向量提取的定点方法。它基于基本迭代，用于使用给定的矩阵笔最大化广义瑞利商（GRQ）。所提出的方法通过利用其估计的正交互补结构来提取矩阵笔的多个广义特征向量。不需要选择常用的步长。这增强了它的实际适用性，因为选择合适的步长是大多数基于梯度流的算法的瓶颈。我们的方法更容易实现且计算复杂度低，因此更适合在线处理。为了显示该算法的有效性，效率和实用性，我们进行了几次实验，其中两个涉及智能天线和盲源分离应用。仿真结果表明，该算法在收敛速度和计算时间上均优于现有的几种算法。其中两个涉及智能天线和盲源分离应用。仿真结果表明，该算法在收敛速度和计算时间上均优于现有的几种算法。其中两个涉及智能天线和盲源分离应用。仿真结果表明，该算法在收敛速度和计算时间上均优于现有的几种算法。