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

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

Monchen, Guido (Student TU Delft)
Sinquin, B. (TU Delft Team Raf Van de Plas)
Verhaegen, M.H.G. (TU Delft Team Raf Van de Plas)

2018

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.

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

http://resolver.tudelft.nl/uuid:bb1037f7-72b0-4ab7-be4d-d0c32bcfd2f5

https://doi.org/10.1109/TCST.2018.2834521

1063-6536

IEEE Transactions on Control Systems Technology, 27 (July 2019) (4), 1677-1684

Institutional Repository

journal article

© 2018 Guido Monchen, B. Sinquin, M.H.G. Verhaegen