抄録
In this paper, a method is presented for the system modelling from noisy data, where the unknown system model is specified by an n-th order linear stochastic differential equation with time-varying coefficients. The goal of the system modelling is to estimate the system order n and to identify the unknown, time-varying coefficients.
A decision rule is first established on the notion of the multi-hypothesis testing. Secondly, a procedure to estimate simultaneously the unknown system order and the unknown coefficients is given within the framework of estimation theory. An algorithm is described for determining the system model from noisy data where the likelihood-ratio function plays a key role. Salient features of the proposed method are emphasized by two examples. One is a simulation experiment which illustrates the extent of the theoretical results obtained. The other is an application of the present method to geophysical data by which a dynamical model is established. This simulation experiment has shown a possibility of an extensive use of this method to identify earthquake waves.
