Fast and Stable YAST Algorithm for Principal and Minor Subspace Tracking
Fast and Stable YAST Algorithm for Principal and Minor Subspace Tracking
复制标题
DOI：
10.1109/tsp.2008.925924
复制
发表时间：
2008-08
影响因子：
5.4
通讯作者：
R. Badeau;G. Richard;B. David
中科院分区：
文献类型：
--
作者：
R. Badeau;G. Richard;B. David
提出了一种新的主、次子空间跟踪算法YAST的实现方法。YAST最初是由Davila的子空间投影(SP)算法发展而来的，与其他经典的主子空间跟踪器相比，该算法以其优异的收敛速度而闻名。YAST算法的新奇之处在于较低的计算成本(如果数据相关矩阵满足所谓的平移不变性质，则为线性)，并扩展到次子空间跟踪。然而，YAST算法的原始实现遇到了数值稳定性问题(子空间加权矩阵慢慢失去其正交性)。因此，本文提出了一种新的YAST实现方法，从理论上证明了其稳定性，并通过数值模拟对其进行了验证。该算法结合了子空间跟踪器所需的所有特性：极高的收敛速度、最低的稳态误差、线性复杂度和对子空间加权矩阵的正交性的数值稳定性。
This paper presents a new implementation of the YAST algorithm for principal and minor subspace tracking. YAST was initially derived from the subspace projection (SP) algorithm by Davila, which was known for its exceptional convergence rate, compared with other classical principal subspace trackers. The novelty in the YAST algorithm was the lower computational cost (linear if the data correlation matrix satisfies a so-called shift-invariance property), and the extension to minor subspace tracking. However, the original implementation of the YAST algorithm suffered from a numerical stability problem (the subspace weighting matrix slowly loses its orthonormality). We thus propose in this paper a new implementation of YAST, whose stability is established theoretically and tested via numerical simulations. This algorithm combines all the desired properties for a subspace tracker: remarkably high convergence rate, lowest steady-state error, linear complexity, and numerical stability regarding the orthonormality of the subspace weighting matrix.