Analysis of Orthogonality Error Propagation for FRANS and HFRANS Algorithms

Author

Yang, Lu ; Attallah, Samir ; Mathew, George ; Abed-Meraim, Karim

Author_Institution

Dept. of Electr. & Comput. Eng., Nat. Univ. of Singapore, Singapore

Volume

56

Issue

9

fYear

2008

Firstpage

4515

Lastpage

4521

Abstract

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.

Keywords

adaptive signal processing; error analysis; FRANS algorithm; HFRANS algorithm; Householder transformation; fast Rayleigh quotient-based adaptive noise subspace algorithm; orthogonality error propagation; Adaptive estimation; Algorithm design and analysis; Computational complexity; Covariance matrix; Eigenvalues and eigenfunctions; Error analysis; Numerical stability; Signal processing algorithms; Upper bound; Very large scale integration; Error analysis; numerical stability; propagation; subspace estimation;

fLanguage

English

Journal_Title

Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1053-587X

Type

jour

DOI

10.1109/TSP.2008.923199

Filename

4599182