Design of auxiliary model based normalized fractional gradient algorithm for nonlinear output-error systems

A new avenue of fractional calculus applications has emerged that investigates the design of fractional gradient based novel iterative methods for analyzing fractals and nonlinear dynamics in solving engineering and applied sciences problems. The most discussed algorithm in this regard is fractional least mean square (FLMS) algorithm. This study presents an auxiliary model based normalized variable initial value FLMS (AM-NVIV-FLMS) algorithm for input nonlinear output error (INOE) system identification. First, NVIV-FLMS is presented to automatically tune the learning rate parameter of VIV-FLMS and then the AM-NVIV-FLMS is introduced by incorporating the auxiliary model idea that replaces the unknown values of the information vector with the output of auxiliary model. The proposed AM-NVIV-FLMS scheme is accurate, convergent, robust and reliable for INOE system identification. Simulation results validate the significance and efficacy of the proposed scheme.