Analysis of Orthogonality Error Propagation for FRANS and HFRANS Algorithms

In this correspondence, we analyze the propagation of orthogonality error for fast Rayleigh's quotient-based adaptive noise subspace algorithm (FRANS) and FRANS with Householder transformation (HFRANS). First, we examine the propagation of orthogonality error for the numerically unstable FRANS in the mean and in the mean-square sense. Then, an upper bound on orthogonality error is derived for the HFRANS algorithm, which is much more numerically stable compared to FRANS. Numerical examples are provided to corroborate the proposed error propagation models.