Identification of Linear System by Neural Networks Under Unknown Noise Density

The paper considers a problem of the modelling and the parameter estimation for a linear dynamical system, where the density of an observation noise is not available. The system parameters are estimated by a least squares method for candidate models, for the probability density and statistical values are not available here. The system structure is estimated by using a neural networks. The learning rules are used batchwise for candidate models with typical types of distributions. The connection coefficients of the neural network are optimized by the groups consisted of known structures. In the real case, since the system structure is unknown, the cases that the true system structure is not contained in the group for learning data are considerd.