Using Informational Measures of Dependence in Statistical Linearization

Abstract

Some problems arising in identification of stochastic systems due to using nonlinear measures of dependence of random variables (processes) were analyzed. Recent publications describing approaches based on a consistent measure of dependence such as the mutual information were discussed. A constructive procedure of creating the linear input-output model that is statistically equivalent to the nonlinear dynamic stochastic system with white-noise Gaussian input process was proposed. The condition for coincidence of the mutual information of the input and output processes of the system and the mutual information of the input and output processes of the model which is used as a criterion for statistical linearization is pivotal to this procedure. This approach enables one to establish explicit relations defining the weight coefficients of the linearized model without using the unrealistic—in the context of identification—a priori condition for knowledge of the joint distribution of the output processes of system and model.