Stability and convergence analysis of the YAST subspace tracking algorithm

The YAST (Yet Another Subspace Tracker) family algorithms were known for their exceptional convergence rate, compared to other subspace tracking algorithms. A proof for the numerical stability, in respect to orthogonality, of the last version of the YAST algorithm is presented in, and it is claimed that “a sudden loss of orthogonality” has made the previous implementations of this algorithm to diverge from the desired subspace. In this paper we will show that the provided proof is not correct in all situations and under some constraints, this new implementation suffers from numerical instability. In addition, our simulation results show that this new implementation still diverges. In fact, we will prove in this paper that the divergence of the YAST algorithm is not due to the “loss of orthogonality”.