Recursive Kronecker-based Vector AutoRegressive identification for large-scale adaptive optics

Guido Monchen, Baptiste Sinquin, Michel Verhaegen

Research output: Contribution to journalArticleScientificpeer-review

2 Citations (Scopus)
70 Downloads (Pure)


This brief presents an algorithm for the recursive identification of Vector AutoRegressive (VAR) models of large dimensions. We consider a VAR model where the coefficient matrices can be written as a sum of Kronecker products. The algorithm proposed consists of recursively updating the Kronecker factor matrices at each new time step using alternating least squares. When the number of terms in the Kronecker sum is small, a significant reduction in computational complexity is achieved with respect to the recursive least squares algorithm on an unstructured VAR model. Numerical validation of nonstationary atmospheric turbulence data, both synthetic and experimental, is shown for an adaptive optics application. Significant improvements in accuracy over batch identification methods that assume stationarity are observed while both the computational complexity and the required storage are reduced.

Original languageEnglish
Pages (from-to)1677-1684
JournalIEEE Transactions on Control Systems Technology
Volume27 (July 2019)
Issue number4
Publication statusPublished - 2018


  • Kronecker product
  • large-scale systems
  • recursive least-squares (RLSs)
  • system identification
  • vector autoregressive (VAR).


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