TOM-based blind identification of nonlinear Volterra systems

TitleTOM-based blind identification of nonlinear Volterra systems
Publication TypeJournal Article
Year of Publication2006
AuthorsTan, H. - Z., and T. Aboulnasr
JournalInstrumentation and Measurement, IEEE Transactions on
Pagination300 - 310
Date Publishedfeb.
Keywordsactive-noise-control systems, blind identifiability, finite order, higher order statistics domain, identification, memory length, method of moments, nonlinear modeling, nonlinear systems, nonlinear Volterra systems, numerical simulations, second-order statistics domain, signal processing, single-input single-output, SOS-based blind identification, stationary random sequences, statistical analysis, statistical information, third-order moments, third-order statistics domain, tom-based blind identification, Volterra series, Volterra-system identification

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.


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