Filtering-Based Multistage Recursive Identification Algorithm for an Input Nonlinear Output-Error Autoregressive System by Using the Key Term Separation Technique

This paper derives a data filtering-based two-stage stochastic gradient algorithm and a data filtering-based multistage recursive least-squares algorithm for input nonlinear output-error autoregressive systems (i.e., Hammerstein systems). The output of the system is expressed as a linear combination of all system parameters based on the key term separation technique. The basic idea of the proposed algorithm is to filter the input-output data and to separate the parameter vector into several vectors and to interactively identify each parameter vector. The data filtering-based two-stage stochastic gradient algorithm has higher convergence rate than the stochastic gradient algorithm. Compared with the recursive generalized least-squares algorithm, the dimensions of the involved covariance matrices in the data filtering-based multistage recursive least-squares algorithm become small, and thus the data filtering-based multistage recursive least-squares algorithm has a higher computational efficiency. The numerical simulation results indicate that the proposed algorithms are effective.