This paper introduces a class of normalized natural gradient algorithms (NNG) for adaptive filtering tasks. Natural gradient techniques are useful for generating relatively simple adaptive filtering algorithms where the space of the adaptive coefficients is curved or warped with respect to Euclidean space. The advantage of normalizing gradient adaptive filters is that constant rates of convergence for signals with wide dynamic ranges may be achieved. We show that the so-called proportionate normalized least mean squares (PNLMS) algorithm, an adaptive filter that converges quickly for sparse solutions, is in fact an NNG on a certain parameter space warping. We also show that by choosing a warping that favors diverse or dense impulse responses, we may obtain a new adaptive algorithm, the inverse proportionate NLMS (INLMS) algorithm. This procedure converges quickly to and accurately tracks nonsparse impulse responses

Meeting Name

2002 IEEE International Conference on Acoustics, Speech, and Signal Processing, 2002. ICASSP '02


Electrical and Computer Engineering

Keywords and Phrases

INLMS Algorithm; PNLMS Algorithm; Adaptive Filtering; Adaptive Filters; Constant Convergence Rates; Convergence of Numerical Methods; Dense Impulse Response; Diverse Impulse Response; Filtering Theory; Gradient Methods; Inverse Proportionate NLMS; Least Mean Squares Methods; Nonsparse Systems; Normalized Natural Gradient Algorithms; Parameter Estimation; Parameter Space Warping; Proportionate Normalized Least Mean Squares; Sparse Matrices; Sparse Systems; Transient Response

Document Type

Article - Conference proceedings

Document Version

Final Version

File Type





© 2002 Institute of Electrical and Electronics Engineers (IEEE), All rights reserved.

Publication Date

01 Jan 2002