Identification of Svd-parafac Based Third-order Volterra Models Using an Arls Algorithm

A broad class of nonlinear systems can be modeled by the Volterra series representation. However, the practical use of such a representation is often limited due to the large number of parameters associated with the Volterra filter structure. This paper is concerned with the problem of identification of third-order Volterra systems. The SVD technique is used to represent the quadratic Volterra kernel and a tensorial decomposition called PARAFAC is used to represent the cubic one. These decompositions allow to significantly reduce the parametric complexity of the Volterra model. Then, a new algorithm called the Alternating Recursive Least Squares (ARLS) algorithm is proposed to estimate the parameters of the linear, quadratic and cubic Volterra kernels. Simulation results show the ability of the proposed solutions to achieve an important complexity reduction and a good identification. Copyright c 2005 IFAC