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

Journal article (2018)

Authors

Guido Monchen Student

B. Sinquin Team Raf Van de Plas - Mechanical, Maritime and Materials Engineering

M.H.G. Verhaegen Team Raf Van de Plas - Mechanical, Maritime and Materials Engineering

Research Group

Team Raf Van de Plas (Mechanical, Maritime and Materials Engineering) (TU Delft)

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

System identification Large-scale systems Kronecker product Recursive least-squares (RLSs) Vector autoregressive (VAR).

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Published Date

2018

Language

English

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Faculty

Mechanical, Maritime and Materials Engineering

Department

Delft Center for Systems and Control

Research Group

Team Raf Van de Plas

Abstract

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.

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