An Approximate Maximum Likelihood Estimation of a Class of Nonlinear Systems Using Neural Networks and Noise Models
Shigenobu YAMAWAKI, Masashi FUJINO, Syozo IMAO
This paper proposes an identification method for a class of nonlinear systems using a neural network and a noise model. A three-layer neural network is used as a plant model of the nonlinear system, and the noise model is applied as a whitening filter. Since noise can not be observed directly, an identification method is proposed in which the neural network and the noise model are calculated with the bootstrap method. We are able to obtain the approximate maximum estimated value of the nonlinear system, where the estimated value is determined based on Akaike's information criterion.
Simulation results are shown to show the effectiveness of the proposed method. The validity of the obtained model is investigated by evaluating the covariance of an estimate error, means, and residual tests. Finally, the simulation result of the undisturbed output and the output of the obtained model are compared and it is shown that a neural network following the undisturbed output and a whitening filter are obtained.