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

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