Global and asymptotically efficient identification of nonlinear rational systems via a two-step method

Abstract

Identification of nonlinear rational systems defined as the ratio of two nonlinear functions of past inputs and outputs is considered in this paper. Although this problem has a long history, there is still lack of a globally consistent identification algorithm for such identification problem. This paper develops a globally consistent algorithm by the following steps: model transformation, bias analysis, noise variance estimation, and compensation. First, the paper studies the prediction error type estimator (nonlinear least square estimators) and the corresponding solving algorithm (Gauss-Newton algorithms). It is shown that the Gauss-Newton algorithm is locally convergent but actually asymptotically efficient by calculating the Cramer-Rao lower bound under Gaussian observation noises. This motivates that a global and asymptotically efficient estimator can be constructed by combining the proposed globally consistent estimator with the Gauss-Newton algorithm. So, a two-step method is proposed, which consists of first executing the globally consistent algorithm and then applying the Gauss-Newton algorithm with the consistent estimate serving as the initial value. A simulation example is provided to verify the good performance of the proposed two-step method.