Matrix output extension of the tensor network Kalman filter with an application in MIMO Volterra system identification

TL;DR

This paper extends the tensor network Kalman filter to handle matrix outputs, enabling more efficient recursive identification of nonlinear MIMO Volterra systems with improved convergence.

Contribution

It introduces a matrix output extension to the tensor network Kalman filter and an efficient algorithm for converting output models into tensor networks.

Findings

Proposed an efficient matrix conversion algorithm.

Demonstrated improved convergence of Volterra kernel estimates.

Validated the approach with numerical experiments.

Abstract

This article extends the tensor network Kalman filter to matrix outputs with an application in recursive identification of discrete-time nonlinear multiple-input-multiple-output (MIMO) Volterra systems. This extension completely supersedes previous work, where only $l$ scalar outputs were considered. The Kalman tensor equations are modified to accommodate for matrix outputs and their implementation using tensor networks is discussed. The MIMO Volterra system identification application requires the conversion of the output model matrix with a row-wise Kronecker product structure into its corresponding tensor network, for which we propose an efficient algorithm. Numerical experiments demonstrate both the efficacy of the proposed matrix conversion algorithm and the improved convergence of the Volterra kernel estimates when using matrix outputs.