Tensor Network Kalman Filter for Large-Scale MIMO Systems
With Application to Adaptive Optics
D. Gedon (TU Delft - Mechanical Engineering)
MHG Verhaegen – Mentor (TU Delft - Team Raf Van de Plas)
K. Batselier – Graduation committee member (TU Delft - Team Jan-Willem van Wingerden)
Carlas Smith – Graduation committee member (TU Delft - Team Raf Van de Plas)
Giulia Giordano – Graduation committee member (TU Delft - Team Tamas Keviczky)
P.J. Piscaer – Graduation committee member (TU Delft - Team Raf Van de Plas)
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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.