Identification of Volterra-PARAFAC models using partial update LMS algorithms

Volterra models can be used to represent a nonlinear systems with vanishing memory. The main drawback of these models is their huge number of parameters to be estimated. To reduce this parametric complexity, we can consider Volterra kernels of order (p > 2) as symmetric tensors and we use a parallel factor (PARAFAC) decomposition of the kernels to derive Volterra-PARAFAC models. In this paper, we present partial update LMS algorithms for identifying nonlinear third-order Volterra-PARAFAC models. Two partial update adaptive LMS algorithms are proposed when input-output signals are real-valued: periodic and sequential partial update version of the LMS. Some simulation results illustrate the proposed identification methods.