An extension of the Tensor Network (TN) Kalman filter ,  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.
|Title of host publication||Proceedings of the 27th European Signal Processing Conference (EUSIPCO 2019)|
|Place of Publication||Piscataway, NJ, USA|
|Number of pages||5|
|Publication status||Published - 2019|
|Event||27th European Signal Processing Conference, EUSIPCO 2019 - A Coruna, Spain|
Duration: 2 Sep 2019 → 6 Sep 2019
|Conference||27th European Signal Processing Conference, EUSIPCO 2019|
|Period||2/09/19 → 6/09/19|
Bibliographical noteGreen 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
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- Curse of dimensionality
- Kalman filter
- Large scale systems
- LTI systems
- Tensor train