Modified Volterra LMS algorithm to fractional order for identification of Hammerstein non‐linear system

Abstract

In this study, a new non-linear recursive mechanism for Volterra least mean square (VLMS) algorithm is proposed in the domain of non-linear adaptive signal processing and control. The proposed adaptive scheme is developed by applying concepts and theories of fractional calculus in weight adaptation structure of standard VLMS approach. The design scheme based on fractional VLMS (F-VLMS) algorithm is applied to parameter estimation problem of non-linear Hammerstein Box-Jenkins system for different noise and step size variations. The adaptive variables of F-VLMS are compared from actual parameters of the system as well as with the results of conventional VLMS for each case to verify its correctness. Comprehensive statistical analyses are conducted based on sufficient large number of independent runs and performance indices in terms of mean square error, variance account for and Nash-Sutcliffe efficiency establish the worth and effectiveness of the scheme.

Application of Spherical-Radial Cubature Bayesian Filtering and Smoothing in Bearings Only Passive Target Tracking

“…The rise in standard deviation of measurement noise results in exponential decay in the accuracy of both algorithms for each case of the passive tracking problem and vice versa. In future, one may investigate the fractional adaptive filtering algorithms [ 50 , 51 , 52 , 53 ] for achieving better state estimation results in an underwater noisy medium, which is still a challenging research domain and has a wide capability for progress and expansion.…”

Recursive Filter With Exponential Kernel for Nonstationary Systems

“…On the one hand, Volterra [10] developed a method that reconstructs the internal states of a non-linear system using several transformations [11]. For example, there is the Discrete Cosine Transform (DCT), which obtains coefficients whose base vectors depend on the order of the selected transformation, and not on the properties of the stochastic signal [12]; as well as Wavelets, which consider the fundamental wave and its level of decomposition to identify harmonics that contain noise, but do not estimate any characteristic parameter [13].…”

Identification scheme for fractional Hammerstein models with the delayed Haar wavelet

“…Zhao et al [2] presented a parametric identification technique of commensurate fractional-order quasi-linear kinetic battery model (KiBaM). Parameter identification methods of fractional-order chaotic system with time delay was described in [18] whereby an artificial bee colony algorithm was used to solve the multi-dimensional optimization problem. A modified Volterra least mean square (LMS) algorithm for fractional Hammerstein modeling was suggested in [19].…”