Recursive Least Squares Identification Algorithms for Multiple-Input Nonlinear Box–Jenkins Systems Using the Maximum Likelihood Principle

Multiple-input multiple-output systems can be decomposed into several multiple-input single-output systems. This paper studies identification problems of multiple-input single-output nonlinear Box–Jenkins systems. In order to improve the computational efficiency, we decompose a multiple-input nonlinear Box–Jenkins system into two subsystems, one containing the parameters of the linear block, the other containing the parameters of the nonlinear block. A decomposition based maximum likelihood generalized extended least squares algorithm is derived for identifying the parameters of the system by using the maximum likelihood principle. Furthermore, a decomposition based generalized extended least squares algorithm is presented for comparison. The numerical example indicates that the proposed algorithms can effectively estimate the parameters of the nonlinear systems and can generate more accurate parameter estimates compared with existing methods.