SOS-Based Blind Identification of Nonlinear Volterra Systems

Abstract

Discrete Volterra models appear widely in various fields of signal processing, control and communication. In this paper, blind identification of a single-input single-output (SISO) Volterra system with finite order and memory is discussed in the second-order statistical sense. The assumption of inaccessible i.i.d. stationary input signals requires that the kernel estimation is achieved based only on the output observations and the statistical properties of the input signals. The systems are composed of linear moving average (MA) models, nonlinear quadratic, cubic models as well as higher-order nonlinear models. Volterra kernels of arbitrary order are derived as functions of system output observations and are expressed in a general matrix form. Based on this formulation, it is shown that while blind identification is not possible for full-sized Volterra systems, nontrivial kernel estimates can be obtained if the system is approximated by a sparse Volterra model. Results based on simulated and experimental data are provided to confirm results.