System Identifications by a Nonlinear Filter

Abstract

Most system identification problems may be reduced to the state estimation in a nonlinear system. Athans [4] synthesized a filter for nonlinear continuous systems with discrete observations through the Taylor series expansion of nonlinear functions up to the second order term about the estimated state and the minimization of the estimation error covariance under the criterion of unbiased estimate. It has been shown that the Athans’ consideration about the second order term would give the better results compared with the existing methods such as the approximate linearization method. However, in this estimation process there is tedious task to solve the parallel nonlinear differential equations about the state and the estimation error covariance. In this paper the authors have derived a forward recursive algorithm for the nonlinear filter by applying the Taylor series expansion method to the nonlinear discrete systems, in which the computation of the error covariance is simplified due to the discrete form. It has been found that this estimation method is available effectively to the identification of unknown transfer function or the learning of the unknown function in a system. Moreover, it is possible to learn nonstationary functions by expanding into the independent function series with unknown varying coefficients.