A stochastic gradient adaptive filter with gradient adaptive step size

Author

Mathews, V. John ; Xie, Zhenhua

Author_Institution

Dept. of Electr. Eng., Utah Univ., Salt Lake City, UT, USA

Volume

41

Issue

6

fYear

1993

fDate

6/1/1993 12:00:00 AM

Firstpage

2075

Lastpage

2087

Abstract

The step size of this adaptive filter is changed according to a gradient descent algorithm designed to reduce the squared estimation error during each iteration. An approximate analysis of the performance of the adaptive filter when its inputs are zero mean, white, and Gaussian noise and the set of optimal coefficients are time varying according to a random-walk model is presented. The algorithm has very good convergence speed and low steady-state misadjustment. The tracking performance of these algorithms in nonstationary environments is relatively insensitive to the choice of the parameters of the adaptive filter and is very close to the best possible performance of the least mean square (LMS) algorithm for a large range of values of the step size of the adaptation algorithm. Several simulation examples demonstrating the good properties of the adaptive filters as well as verifying the analytical results are also presented

Keywords

adaptive filters; convergence of numerical methods; filtering and prediction theory; signal processing; Gaussian noise; convergence; gradient descent algorithm; iteration; nonstationary environments; random-walk model; steady-state misadjustment; step size; stochastic gradient adaptive filter; time varying parameters; tracking performance; white noise; zero mean input; Adaptive filters; Algorithm design and analysis; Analytical models; Convergence; Estimation error; Gaussian noise; Least squares approximation; Performance analysis; Steady-state; Stochastic processes;

fLanguage

English

Journal_Title

Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1053-587X

Type

jour

DOI

10.1109/78.218137

Filename

218137