Stochastic convergence analysis of recursive successive over-relaxation algorithm in adaptive filtering

Leakage Analysis of the Rsor Algorithm

“…The RSOR algorithm in scalar updating form (13) can be represented in vector updating form as follows (Hatun and Koçal, 2012).…”

“…and subtracting the correct parameter vector, from the both sides of (14), the following iteration is obtained for the parameter error vector after some arrangements (Hatun and Koçal, 2012).…”

“…The RLS (Recursive Least Squares) algorithm is preferred in many applications due to its high convergence speed despite its high computational load (Haykin, 2002, Diniz, 2013. On the other hand, some alternative algorithms have been proposed: These are the RSOR (Recursive SOR) algorithm based on the single-step SOR (Successive Over-Relaxation) iteration (Hatun and Koçal, 2012), and the RI (Recursive Inverse) algorithm based on the one-step gradient iteration (Ahmad et al, 2011a). In these type algorithms, the forgetting factor, which is a positive number and taken as close to 1, is used for tracking parameter changes.…”

Decomposition‐based over‐parameterization forgetting factor stochastic gradient algorithm for Hammerstein‐Wiener nonlinear systems with non‐uniform sampling

“…8,9 The recursive identification plays an important role in the field of system identification because it can realize the online identification of the system parameters. 10,11 In recent years, some recursive estimation methods have been successfully applied to the state space systems, [12][13][14] the linear systems and the nonlinear systems. 15 The iterative and recursive estimation algorithms can be derived by means of defining and minimizing a criterion function [16][17][18] and many estimation algorithms have been reported for different systems.…”