Tracking of the sign algorithm with a central dead zone in the noise distribution

Abstract

The paper analyzes the tracking performance of the sign algorithm when the noise distribution has a dead zone that includes the origin. The analysis is done in the context of the identification of a time-varying plant with a Gaussian input. A random-walk model of the plant variation is assumed. Upper bounds of the time-averaged mean absolute excess estimation error and the time-averaged mean norm of the weight misalignment vector are derived. The bounds hold for all values of the algorithm step size. The minima of the bounds are derived. It is found that the tracking performance of the algorithm is poor in comparison with that in the case of a Gaussian noise. The wider the dead zone in the noise distribution, the worse the performance. It is also found that the tracking performance is strongly dependent on the width of the dead zone and weakly dependent on the degree of non-stationarity of the plant. The analytical results of the paper are supported by simulations.