Parameter estimation for nonlinear Volterra systems by using the multi-innovation identification theory and tensor decomposition

• Published in: Journal of the Franklin Institute Vol. 359; no. 2; pp. 1782 - 1802
• Main Authors: Wang, Yanjiao, Tang, Shihua, Gu, Xiaobo
• Format: Journal Article
• Language: English
• Published: Elmsford Elsevier Ltd 01.01.2022; Elsevier Science Ltd
• Subjects: Algorithms; Decomposition; Discrete time systems; Dynamical systems; Identification methods; Innovations; Kernels; Nonlinear equations; Nonlinear systems; Norms; Parameter estimation; Parameter identification; System effectiveness; System identification; Tensors
• ISSN: 0016-0032; 1879-2693; 0016-0032
• DOI: 10.1016/j.jfranklin.2021.11.015

The Volterra model can represent a wide range of nonlinear dynamical systems. However, its practical use in nonlinear system identification is limited due to the exponentially growing number of Volterra kernel coefficients as the degree increases. This paper considers the identification issue of discrete-time nonlinear Volterra systems and uses a tensorial decomposition called PARAFAC to represent the Volterra kernels which can provide a significant parametric reduction compared with the conventional Volterra model. Applying the multi-innovation identification theory, the recursive algorithm by combining the l2-norm is proposed for the PARAFAC-Volterra models with the Gaussian noises. In addition, the multi-innovation algorithm combining with the logarithmic p-norms is investigated for the nonlinear Volterra systems with the non-Gaussian noises. Finally, some simulation results illustrate the effectiveness of the proposed identification methods.