This paper elaborates on a new class of orthonormal power-based algorithms for fast estimation and tracking of the principal or minor subspace of a vector sequence. The proposed algorithms are closely related to the natural power method that has the fastest convergence rate among many power-based methods such as the Oja method, the projection approximation subspace tracking (PAST) method, and the novel information criterion (NIC) method. A common feature of the proposed algorithms is the exact orthonormality of the weight matrix at each iteration. The orthonormality is implemented in a most efficient way. Besides the property of orthonormality, the new algorithms offer, as compared to other power based algorithms, a better numerical stability and a linear computational complexity.

中文翻译：

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一类主次空间跟踪的正交算法

本文阐述了一种新的基于正交功率的正交算法，用于快速估计和跟踪矢量序列的主子空间或次子空间。所提出的算法与自然功率方法密切相关，自然功率方法在许多基于功率的方法（例如Oja方法，投影近似子空间跟踪（PAST）方法和新颖的信息准则（NIC）方法）中具有最快的收敛速度。所提出算法的共同特征是每次迭代时权重矩阵的精确正交性。正交性以最有效的方式实现。除了正交性的特性外，与其他基于幂的算法相比，新算法还提供了更好的数值稳定性和线性计算复杂性。