ZA-APA with zero attractor controller selection criterion for sparse system identification

Abstract

The zero attraction affine projection algorithm (ZA-APA) is one of the sparse APAs that are based on \(l_{1}\)-norm penalty function. It provides faster convergence and lower steady-state error than the conventional APA when the system is sparse. Most of the analysis for attraction-type APA is normally based on white Gaussian assumption for the input. In this paper, a detailed performance analysis of the ZA-APA is performed using individual weight error variance (IWV) method. Using the IWV method, the condition for the convergence in mean and mean square error sense and the steady-state mean square deviation (MSD) error based on non-Gaussian input assumption is derived. Theoretical derivation reveals that the value of zero attractor controller plays a key role in the final steady-state error. Hence, a selection criterion for zero attractor controller based on the steady-state MSD error is proposed. Finally, simulations are performed to validate the analysis made in the context of unknown system identification.