Matrix output extension of the tensor network Kalman filter with an application in MIMO Volterra system identification
For researchers working on recursive identification of nonlinear MIMO systems, this provides an incremental extension of an existing method to a more general output format.
This work extends the tensor network Kalman filter to handle matrix outputs, enabling recursive identification of MIMO Volterra systems. Numerical experiments show improved convergence of Volterra kernel estimates compared to prior scalar-output methods.
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.