Tensor Network alternating linear scheme for MIMO Volterra system identification

This article introduces two Tensor Train-based iterative algorithms for the identification of high order discrete-time nonlinear MIMO Volterra systems. The system identification problem is rewritten in terms of a Volterra tensor, which is never explicitly constructed, thus avoiding the curse of dimensionality. It is shown how each iteration of the two identification algorithms involves solving a linear system of low computational complexity. The presented algorithms are guaranteed to monotonically converge and numerical stability is ensured through the use of orthogonal matrix factorizations. The performance and accuracy of the two identification algorithms is illustrated by means of two experiments, where accurate degree-10 MIMO Volterra models are identified in about 1 second.