An Algorithm of Predictions for Chaotic Time Series Based on Volterra Filter

Abstract

Based on the Takens' delay-coordinate phase reconstruct, A third-order Volterra filter which is used to detect weak target signal in chaos is researched. A large class of Nonlinear systems have been successfully modeled using Volterra series techniques. The key to system modeling by means of a Volterra series is capturing the Volterra kernels that represent the system. Once the kernels are known, the system response to any arbitrary input can be predicted with relative ease. Therefore the success of nonlinear Volterra system modeling is dependant on the ability to accurately identify Volterra kernels. According this sense, this paper presents a new SVD- PARAFAC approach for Volterra filters with a very good performance characteristic. The method of using the singular value decomposition (SVD) and PARALLEL Factor (PARAFAC) decomposition to factor second and third order kernels is introduced. Numerical simulations illustrate the usefulness of the proposed approach. The experimental results show this method has much better prediction performance for chaotic flow than least mean square (LMS) adaptive Volterra filter and can detect out a very weak target signal in chaos when SCR gets to–70 dB. (Abstract)