Tensor Network Kalman Filter for Large-Scale MIMO Systems

Tensor Network Kalman Filter for Large-Scale MIMO Systems: With Application to Adaptive Optics

Gedon, Daniel (TU Delft Mechanical, Maritime and Materials Engineering)

Verhaegen, Michel (mentor)
Batselier, Kim (graduation committee)
Smith, Carlas (graduation committee)
Giordano, Giulia (graduation committee)
Piscaer, Pieter (graduation committee)

Delft University of Technology

Mechanical Engineering | Systems and Control

2019-07-05

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.

Kalman Filter
tensors
Large Scale
tensor decomposition
curse of dimensionality
Adaptive Optics

http://resolver.tudelft.nl/uuid:2188c114-05ed-4fe6-9603-85de71e9bffd

2020-02-21

Student theses

master thesis

© 2019 Daniel Gedon