An Estimation of the Performance of HRLS Algorithm
The householder RLS (HRLS) algorithm is an O(N2)
algorithm which recursively updates an arbitrary square-root of the
input data correlation matrix and naturally provides the LS weight
vector. A data dependent householder matrix is applied for such
an update. In this paper a recursive estimate of the eigenvalue
spread and misalignment of the algorithm is presented at a very low
computational cost. Misalignment is found to be highly sensitive to
the eigenvalue spread of input signals, output noise of the system and
exponential window. Simulation results show noticeable degradation
in the misalignment by increase in eigenvalue spread as well as
system-s output noise, while exponential window was kept constant.
[1] A. H. Sayed and T. Kailath, A state-space approach to adaptive RLS
filtering, IEEE Signal Processing Magazine,1994.
[2] Jr. Apolinario, QRD-RLS Adaptive filtering, Springer, 2009.
[3] S. C. Douglas, Numerically robust O(N2) RLS algorithms using Least
Squares Prewhitening, IEEE,2000.
[4] J. Benesty and T. Gansler, A recursive estimation of the condition number
in the RLS algorithm, IEEE,2005.
[5] F. Beaufays, Transform-Domain Adaptive Filters: An Analytical Approach,
IEEE transactions on signal processing, 1995.
[6] N. A. Ahmad, Comparative study of iterative search method for adaptive
filtering problems, International Conference on Applied mathematics,
2005.
[7] B. Farhang-Boroujeny, Adaptive filters: theory and applications, John
Wiley & Sons, Inc.,1998.
[8] S. Haykin, Adaptive Filter Theory, 2nd edition, Prentice Hall,1991.
[1] A. H. Sayed and T. Kailath, A state-space approach to adaptive RLS
filtering, IEEE Signal Processing Magazine,1994.
[2] Jr. Apolinario, QRD-RLS Adaptive filtering, Springer, 2009.
[3] S. C. Douglas, Numerically robust O(N2) RLS algorithms using Least
Squares Prewhitening, IEEE,2000.
[4] J. Benesty and T. Gansler, A recursive estimation of the condition number
in the RLS algorithm, IEEE,2005.
[5] F. Beaufays, Transform-Domain Adaptive Filters: An Analytical Approach,
IEEE transactions on signal processing, 1995.
[6] N. A. Ahmad, Comparative study of iterative search method for adaptive
filtering problems, International Conference on Applied mathematics,
2005.
[7] B. Farhang-Boroujeny, Adaptive filters: theory and applications, John
Wiley & Sons, Inc.,1998.
[8] S. Haykin, Adaptive Filter Theory, 2nd edition, Prentice Hall,1991.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:60888", author = "Shazia Javed and Noor Atinah Ahmad", title = "An Estimation of the Performance of HRLS Algorithm", abstract = "The householder RLS (HRLS) algorithm is an O(N2)
algorithm which recursively updates an arbitrary square-root of the
input data correlation matrix and naturally provides the LS weight
vector. A data dependent householder matrix is applied for such
an update. In this paper a recursive estimate of the eigenvalue
spread and misalignment of the algorithm is presented at a very low
computational cost. Misalignment is found to be highly sensitive to
the eigenvalue spread of input signals, output noise of the system and
exponential window. Simulation results show noticeable degradation
in the misalignment by increase in eigenvalue spread as well as
system-s output noise, while exponential window was kept constant.", keywords = "HRLS algorithm, eigenvalue spread, misalignment.", volume = "6", number = "12", pages = "1759-3", }