Identification of SVD-PARAFAC based third-order Volterra models using an ARLS algorithm

A broad class of nonlinear systems can be modeled by the Volterraseries representation. However, the practical use of such arepresentation is often limited due to the large number ofparameters associated with the Volterra filter structure. Thispaper is concerned with the problem of identification ofthird-order Volterra systems. The SVD technique is used torepresent the quadratic Volterra kernel and a tensorialdecomposition called PARAFAC is used to represent the cubic one.These decompositions allow to significantly reduce the parametriccomplexity of the Volterra model. Then, a new algorithm called theAlternating Recursive Least Squares (ARLS) algorithm is proposedto estimate the parameters of theVolterra kernels. Simulation results show the ability of theproposed solutions to achieve an important complexity reductionand a good identification.