A bias-corrected estimator for nonlinear systems with output-error type model structures

Parametric identification of linear time-invariant (LTI) systems with output-error (OE) type of noise model structures has a well-established theoretical framework. Different algorithms, like instrumental-variables approaches or prediction error methods (PEMs), have been proposed in the literature to compute a consistent parameter estimate for linear OE systems. Although the prediction error method provides a consistent parameter estimate also for nonlinear output-error (NOE) systems, it requires to compute the solution of a nonconvex optimization problem. Therefore, an accurate initialization of the numerical optimization algorithms is required, otherwise they may get stuck in a local minimum and, as a consequence, the computed estimate of the system might not be accurate. In this paper, we propose an approach to obtain, in a computationally efficient fashion, a consistent parameter estimate for output-error systems with polynomial nonlinearities. The performance of the method is demonstrated through a simulation example.