Improved Varient for FOC-based Adaptive Filter for Chaotic Time Series Prediction

An improved normalized fractional least mean square (iNFLMS) has been proposed in this study. Least mean square (LMS) and fractional LMS (FLMS) are both prone to the problem of sensitivity to the input. In the proposed algorithm, the sensitivity of the FLMS to the input is reduced by normalization. The summation of the fractional and conventional gradients is made convex to obtain better convergence rate and keeping minimum error in steady state. To make the algorithm less computationally expensive, the gamma function is now absorbed into the fractional learning rate. Through the experiment it is quite clear that the efficacy of the proposed method is promising considering the parameters of steady-state error and convergence rate when compared to that of LMS, FLMS, MFLMS and NFLMS algorithm.