A Novel Filtering Based Maximum Likelihood Generalized Extended Gradient Method for Multivariable Nonlinear Systems

This study proposes a filtering based maximum likelihood generalized extended gradient algorithm for multivariable nonlinear systems with autoregressive moving average noises. The parameter estimates are obtained by minimizing the half squared residual measurement which can approach the true values. An auxiliary model is also established with the measurable information of the system, and the output of the auxiliary model is used to replace the unmeasurable variables of the system, so that the output of the auxiliary model approximates these unmeasurable variables, so as to obtain the consistent estimation of the system parameters. A maximum likelihood generalized extended gradient algorithm is derived for comparison and a numerical example is provided to show the effectiveness of the proposed method and the estimates converge to the actual values quickly.