Adaptive strategies for parameter estimation of Box–Jenkins systems

This study presents a novel application of fractional adaptive algorithms for parameter identification of Box-Jenkins (BJ) systems. The idea is to adapt the unknown parameter vector of the BJ system by the fractional least mean square (FLMS) algorithm for three different values of the fractional order and then to compare the estimated results with state of the art Volterra least mean square and kernel least mean square adaptive algorithms to validate and verify the correctness of the design scheme. The reliability and effectiveness of the proposed scheme is analysed through the results of the statistical analysis based on sufficient large number of independent runs and it is found that the proposed FLMS algorithm provides consistently accurate and convergent results for BJ systems under different scenarios.