Kaczmarz Projection Algorithms with Rank Two Gain Update

Abstract

New Kaczmarz algorithms with rank two gain update, extended orthogonality property and forgetting mechanism which includes both exponential and instantaneous forgetting (implemented via a proper choice of the forgetting factor and the window size) are introduced and systematically associated in this paper with well-known Kaczmarz algorithms with rank one update. The parameter convergence was proved using Lyapunov method and convergence of the inverse of the information matrix can be used for further performance improvement. The performance of new algorithms is examined in the problem of estimation of the grid events in the presence of significant harmonic emissions.