Tensor network Kalman filter for LTI systems

Daniel Gedon; Pieter Piscaer; Kim Batselier; Carlas Smith; Michel Verhaegen

doi:10.23919/EUSIPCO.2019.8902976

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 volume › Conference contribution › Scientific › peer-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 language	English
Title of host publication	Proceedings of the 27th European Signal Processing Conference (EUSIPCO 2019)
Place of Publication	Piscataway, NJ, USA
Publisher	IEEE
Number of pages	5
ISBN (Electronic)	978-9-0827-9703-9
DOIs	https://doi.org/10.23919/EUSIPCO.2019.8902976
Publication status	Published - 2019
Event	27th European Signal Processing Conference, EUSIPCO 2019 - A Coruna, Spain Duration: 2 Sept 2019 → 6 Sept 2019

Conference

Conference	27th European Signal Processing Conference, EUSIPCO 2019
Country/Territory	Spain
City	A Coruna
Period	2/09/19 → 6/09/19

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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08902976Final published version, 454 KB

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title = "Tensor network Kalman filter for LTI systems",

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.",

keywords = "Curse of dimensionality, Kalman filter, Large scale systems, LTI systems, MIMO, SISO, Tensor train, Tensors",

author = "Daniel Gedon and Pieter Piscaer and Kim Batselier and Carlas Smith and Michel Verhaegen",

note = "Green Open Access added to TU Delft Institutional Repository {\textquoteleft}You share, we take care!{\textquoteright} – 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.; 27th European Signal Processing Conference, EUSIPCO 2019 ; Conference date: 02-09-2019 Through 06-09-2019",

year = "2019",

doi = "10.23919/EUSIPCO.2019.8902976",

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AU - Gedon, Daniel

AU - Piscaer, Pieter

AU - Batselier, Kim

AU - Smith, Carlas

AU - Verhaegen, Michel

N1 - 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.

PY - 2019

Y1 - 2019

N2 - 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.

AB - 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.

KW - Curse of dimensionality

KW - Kalman filter

KW - Large scale systems

KW - LTI systems

KW - MIMO

KW - SISO

KW - Tensor train

KW - Tensors

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U2 - 10.23919/EUSIPCO.2019.8902976

DO - 10.23919/EUSIPCO.2019.8902976

M3 - Conference contribution

AN - SCOPUS:85075600209

BT - Proceedings of the 27th European Signal Processing Conference (EUSIPCO 2019)

PB - IEEE

CY - Piscataway, NJ, USA

T2 - 27th European Signal Processing Conference, EUSIPCO 2019

Y2 - 2 September 2019 through 6 September 2019

ER -

Tensor network Kalman filter for LTI systems

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Keywords

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