An Efficient & Stable Algorithm for Minor Subspace Tracking and Stability Analysis

In this paper, we present a theoretical stability analysis of the YAST algorithm used for tracking the noise subspace of the covariance matrix associated with time series. This analysis demonstrates the instability of the YAST and a more stable alternative solution is proposed. In addition to its stability, the resulting algorithm is less expensive than the YAST and has a computational complexity of order O(nr) flops per iteration where n is the size of the observation vector and r <; n is the minor subspace dimension. Finally, we pay a special attention to the case r = 1 due to its importance in many quadratic optimization problems. In that particular case, we propose a simplified version of the algorithm to estimate either the first principal eigenvector or the last minor eigenvector of the covariance matrix. Simulation results are provided at the end to validate the theoretical stability analysis and to illustrate the tracking capacity of the proposed algorithm.