Mildly formalized system identification based on consistent measures of dependence

The paper presents a nonparametric approach to input/output system identification under the condition that no analytical model of the system is assumed to be known. Within the approach, the key issue of the problem is a proper handling of inherent dependence between the input and output variables of the system. Using a consistent measure of stochastic dependence of random processes has been proposed within the identification scheme. The measure of dependence is the maximal correlation function. It properly reflects actual nonlinear dependence between random processes, while those based on the dispersion and, moreover, ordinary product correlation functions do not. In addition, the measure directly leads to determining the input/output relationship of the investigated system. Within the approach, a degree of system nonlinearity based on the maximal correlation is proposed