Tensor Network Kalman Filter for Large-Scale MIMO Systems

With Application to Adaptive Optics

Master thesis (2019)

Authors

D. Gedon Mechanical Engineering

Contributors

M.H.G. Verhaegen Team Raf Van de Plas - Mechanical, Maritime and Materials Engineering (supervisor 1)
K. Batselier Team Jan-Willem van Wingerden - Mechanical, Maritime and Materials Engineering (supervisor 2)
C.S. Smith Team Raf Van de Plas - Mechanical, Maritime and Materials Engineering (supervisor 2)
G. Giordano Team Tamas Keviczky - Mechanical, Maritime and Materials Engineering (supervisor 2)
P.J. Piscaer Team Raf Van de Plas - Mechanical, Maritime and Materials Engineering (supervisor 2)
Faculty
Mechanical Engineering
Copyright: © 2019 Daniel Gedon
Kalman Filter Tensor decomposition Adaptive Optics Curse of dimensionality Large Scale Tensors
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Published Date

05-07-2019

Language

English

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Faculty

Mechanical Engineering

Abstract

For large-scale system with tens of thousands of states and outputs the computation in the conventional Kalman filter becomes time-consuming such that Kalman filtering in large-scale real-time application is practically infeasible. A possible mathematical framework to lift the curse of dimensionality is to lift the problem in higher dimensions with the use of tensors and then decompose it. The tensor-train decomposition is chosen due to its computational advantages for systems with low tensor-train rank. Within this thesis two main limitations of the existing tensor Kalman filter are solved. First, a method is developed based on tensor-train rank truncation of the covariances to increase the computational speed for more general systems. Second, a MIMO tensor Kalman filter is developed for a specific class of systems. The power of the developed methods is shown on the example of adaptive optics which fits into the framework. A comparison with state-of-the-art large-scale estimation algorithms shows the computational advantage of the tensor Kalman filter at the cost of approximation errors.