Generalized YAST algorithm for signal subspace tracking

• We propose two new fast signal (or principal) subspace tracking algorithms.
• These new algorithms outperform all existing fast algorithms.
• The performance of the proposed algorithms is nearly optimal.
• These algorithms could be used for all data cases.
• The numerical stability is proved for one of the proposed algorithms.

This paper introduces two generalized versions of the Yet Another Subspace Tracker (YAST) algorithm which can estimate and track the principal subspace with low computational load and with reasonable performance. The YAST algorithm relies on an interesting idea of optimally extracting the updated subspace weighting matrix in each step. This optimal extraction, which has a high computational burden, exhibits an incredible convergence rate. However, the fast implementation of this optimal scheme has been restricted to the temporal domain data case in the existing literature. In addition, all the previous versions of the YAST algorithm suffer from numerical problems. In our new subspace trackers, computation reduction of optimal subspace extraction is achieved by an approximation, which generalizes the application of the YAST algorithm to all data cases. Performances of the YAST algorithms proposed in this paper are experimentally seen to be very close to the optimal YAST algorithm. In fact, these algorithms outperform all existing fast subspace trackers. The numerical stability, with respect to orthonormality, is proved for one of the proposed YAST algorithms.