Nonparametric identification of two-channel nonlinear systems

In this paper, a discrete-time two-channel non-linear system is identified. Each branch of the system has the form of the Hammerstein model, i.e., a nonlinear gain function followed by a dynamic linear system. The dynamic subsystems are recovered using the standard correlation method. The main results are concerned with the estimation of the nonlinear memoryless subsystems. The class of nonlinearities considered in the paper, consists of those Borel functions that do not increase faster than linear functions. The identification algorithm is a nonparametric kernel estimate of the regression function. The statistically dependent, as well as independent random signal inputs are assumed. For the first case, the algorithm achieves a rate of convergence of the order O(n-1/4) while the latter one, O(n-1/3) is achieved in probability, where n is the sample size.