Maximal Correlation Applied to the Statistical Linearization: An Analysis and Approaches

The paper presents an approach to the statistical linearization of the input/output mapping of a non-linear discrete-time stochastic system driven by a white-noise Gaussian process. The approach is based on applying the maximal correlation function. At that, the statistical linearization criterion is the condition of coincidence of the mathematical expectations of the output processes of the system and model, and the condition of coincidence of the joint maximal correlation functions of the output and input processes of the system and the output and input processes of the model. Explicit expressions for the weight function coefficients of the linearized model are obtained; an approach to eliminate the influence of unobservable output additive disturbances under conditions when a priori information on the type of their probability distribution is available is proposed.