Extended Kalman Filtering with Low-Rank Tensor Networks for MIMO Volterra System Identification

Abstract

This article reformulates the multiple-input-multiple-output Volterra system identification problem as an extended Kalman filtering problem. This reformulation has two advantages. First, it results in a simplification of the solution compared to the Tensor Network Kalman filter as no tensor filtering equations are required anymore. The second advantage is that the reformulation allows to model correlations between the parameters of different multiple-input-single-output Volterra systems, which can lead to better accuracy. The curse of dimensionality in the exponentially large parameter vector and covariance matrix is lifted through the use of low-rank tensor networks. The computational complexity of our tensor network implementation is compared to the conventional implementation and numerical experiments demonstrate the effectiveness of the proposed method.