Tensor network Kalman filter for LTI systems

Daniel Gedon*, Pieter Piscaer, Kim Batselier, Carlas Smith, Michel Verhaegen

*Corresponding author for this work

Research output: Chapter in Book/Conference proceedings/Edited volumeConference contributionScientificpeer-review

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Abstract

An extension of the Tensor Network (TN) Kalman filter [2], [3] for large scale LTI systems is presented in this paper. The TN Kalman filter can handle exponentially large state vectors without constructing them explicitly. In order to have efficient algebraic operations, a low TN rank is required. We exploit the possibility to approximate the covariance matrix as a TN with a low TN rank. This reduces the computational complexity for general SISO and MIMO LTI systems with TN rank greater than one significantly while obtaining an accurate estimation. Improvements of this method in terms of computational complexity compared to the conventional Kalman filter are demonstrated in numerical simulations for large scale systems.

Original languageEnglish
Title of host publicationProceedings of the 27th European Signal Processing Conference (EUSIPCO 2019)
Place of PublicationPiscataway, NJ, USA
PublisherIEEE
Number of pages5
ISBN (Electronic)978-9-0827-9703-9
DOIs
Publication statusPublished - 2019
Event27th European Signal Processing Conference, EUSIPCO 2019 - A Coruna, Spain
Duration: 2 Sep 20196 Sep 2019

Conference

Conference27th European Signal Processing Conference, EUSIPCO 2019
CountrySpain
CityA Coruna
Period2/09/196/09/19

Bibliographical note

Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care

Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.

Keywords

  • Curse of dimensionality
  • Kalman filter
  • Large scale systems
  • LTI systems
  • MIMO
  • SISO
  • Tensor train
  • Tensors

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