# Tensor Network alternating linear scheme for MIMO Volterra system identification

arXiv: https://arxiv.org/abs/1607.00127 · HTML: https://mlsanity.com/paper/1607.00127/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Jul 2016.

## Built on by (most cited first, 13 of 13)

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## Abstract (arXiv)

This article introduces two Tensor Network-based iterative algorithms for the identification of high-order discrete-time nonlinear multiple-input multiple-output (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 proposed 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 are illustrated by numerical experiments, where accurate degree-10 MIMO Volterra models are identified in about 1 second in Matlab on a standard desktop pc.