Design of auxiliary model and hierarchical normalized fractional adaptive algorithms for parameter estimation of bilinear-in-parameter systems

This study investigates the parameter identification issues of bilinear-in-parameter systems through fractional adaptive algorithms. An auxiliary model based epsilon-normalized$$ \varepsilon \hbox{-} \mathrm{normalized} $$ modified fractional least mean square algorithm is proposed for accelerating the parameter estimation accuracy based on the auxiliary model identification idea and the introduced convergence index, a normalized modified hierarchical fractional least mean square algorithm is presented for improving the computational efficiency based on the hierarchical identification principle. The proposed normalized fractional adaptive strategies are effective and could provide more accurate parameter estimates comparing with conventional counterparts for bilinear-in-parameter identification model based on the mean square error metrics and the average predicted output error. The effectiveness and accuracy of the proposed algorithms are further verified and validated through numerical simulations for different noise variances, fractional orders and gain parameters.