Blind identification of Volterra models using minimax optimization with higher order cumulants

In this paper, we examine the identification of a nonlinear system which is expressed as the output of a Volterra filter driven by a Gaussian input signal. Both the input signal and filter parameters are unknown, and hence, the problem can be classified as blind since we can only employ some properties of the output. The estimation of the parameters is achieved based on second and higher order cumulants properties and optimization methods. In this approach, we formulate equations that relate the unknown parameters of the model with the statistical properties of the observed output signal. The solution of these highly nonlinear equations is achieved through constrained minimax optimization techniques.