TOM-based blind identification of nonlinear Volterra systems

This paper extends blind single-input single-output (SISO) Volterra-system identification from the second-order statistics (SOSs) domain into the third-order statistics domain. For the full-sized Volterra system with finite order and memory, which is excited by unobservable independent identically distributed (i.i.d.) stationary random sequences, it is known that blind identifiability is not possible in the SOS domain. Although this conclusion is also true in the higher order statistics (HOSs) domain, it will be shown that under some sufficient conditions, a larger set of sparse Volterra systems can be identified blindly in third-order moment (TOM) domain than in the SOS counterpart. This is due to the fact that (n+1)(3n+2)/2 terms of different statistical quantities can be used in the third-order-statistics domain while only (n+2) terms of statistical information are nonredundant for SOS-based blind identification, where n is the memory length of the system. The validity and usefulness of the approach are demonstrated in numerical simulations as well as experiments applied to blindly identify the primary path of active-noise-control (ANC) systems in a practical scenario.