Noise Terms In Information Vector Research Articles

Comments on “Design of fractional adaptive strategy for input nonlinear Box–Jenkins systems”

This note points out some errors in the identification model and implementation issues of adaptive strategies presented by Chaudhary and Raja for estimation of input nonlinear Box–Jenkins (INBJ) systems (Chaudhary and Raja, 2015 [1]). This note proves that identification model presented in above mentioned paper is incorrect and in stepwise manner suggests some suitable corrections. Authors claim to propose two algorithms for INBJ systems in above mentioned paper: fractional least mean square (F-LMS) algorithm and auxiliary model fractional least mean square (AM-FLMS) algorithm. AM-FLMS algorithm is not presented in this paper, but results of this algorithm are provided. The adaptive algorithms presented by authors are not implementable due to the presence of unknown noise terms in information vector. Authors have ignored these critical issues. Finally, corrections on the basis of established techniques are also mentioned that solve the problems in the above mentioned paper.

Performance analysis of estimation algorithms of nonstationary ARMA processes

The correlation analysis based methods are not suitable for identifying parameters of nonstationary autoregressive (AR), moving average (MA), and ARMA systems. By using estimation residuals in place of unmeasurable noise terms in information vector or matrix, we develop a least squares based and gradient based algorithms and establish the consistency of the proposed algorithms without assuming noise stationarity, ergodicity, or existence of higher order moments. Furthermore, we derive the conditions for convergence of the parameter estimation. The simulation results validate the convergence theorems proposed.