多重解像度解析によるシステムインパルス応答の同定

抄録

In this paper, the authors propose a new identification method for the discrete-time impulse response model of a linear system from sampled input-output data using multiresolution analysis theory, especially in the case of impulse response with locally rapidly changing components. The continuous-time impulse response of the system under study which is viewed as a L²(R) function of time, is approximated by scaling and wavelet functions which are shifted and dilated based on the multiresolution analysis theory. Hence the system under study can be viewed as weighted summation of a group of subsystems in which the shifted and dilated scaling functions and wavelet functions are interpretated as their impulse responses respectively. Then the genetic algorithm and AIC are introduced to select significant subsystems such that only moderate parameters are required to be estimated in contrast to the conventional method. It is shown that the proposed method yields accurate estimate of the impulse response with locally rapidly changing components, even in the ill-posed cases of band-limited input, fast sampling rate and significant measurement noise.