Blind identifiability of third-order Volterra nonlinear systems

A novel approach to estimate blindly the kernels of a Volterra nonlinear system up to the third order is proposed. The system is excited by an unobservable i.i.d. random sequence. Blind identifiability is achieved using second order statistics (SOS) rather than using higher order statistical (HOS) information to ensure lower complexity. Since the output of the Volterra system is linearly dependent upon its kernel parameters, conventional LMS or RLS algorithms can be used and consistent estimation of Volterra kernels can be achieved provided some conditions of persistent excitation (PE) are satisfied. Simulation demonstrated the ability of the proposed method to achieve a good estimation performance.