Bayesian learning-based Kalman smoothing for linear dynamical systems with unknown sparse inputs

Rupam Kalyan Chakraborty; Geethu Joseph; Chandra R. Murthy

doi:10.1109/ICASSP48485.2024.10446534

Bayesian learning-based Kalman smoothing for linear dynamical systems with unknown sparse inputs

Rupam Kalyan Chakraborty^*, Geethu Joseph, Chandra R. Murthy^*

^*Corresponding author for this work

Signal Processing Systems

Research output: Chapter in Book/Conference proceedings/Edited volume › Conference contribution › Scientific › peer-review

1 Citation (SciVal)

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Abstract

We consider the problem of jointly estimating the states and sparse inputs of a linear dynamical system using noisy low-dimensional observations. We exploit the underlying sparsity in the inputs using fictitious sparsity-promoting Gaussian priors with unknown variances (as hyperparameters). We develop two Bayesian learning-based techniques to estimate states and inputs: sparse Bayesian learning and variational Bayesian inference. Through numerical simulations, we illustrate that our algorithms outperform the conventional Kalman filtering based algorithm and other state-of-the-art sparsity-driven algorithms, especially in the low-dimensional measurement regime.

Original language	English
Title of host publication	2024 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2024 - Proceedings
Publisher	IEEE
Pages	13431-13435
Number of pages	5
ISBN (Electronic)	9798350344851
DOIs	https://doi.org/10.1109/ICASSP48485.2024.10446534
Publication status	Published - 2024
Event	49th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2024 - Seoul, Korea, Republic of Duration: 14 Apr 2024 → 19 Apr 2024

Publication series

Name	ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
ISSN (Print)	1520-6149

Conference

Conference	49th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2024
Country/Territory	Korea, Republic of
City	Seoul
Period	14/04/24 → 19/04/24

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

Gaussian prior
Kalman smoothing
robust filtering
sparse Bayesian learning
variational Bayesian inference

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Bayesian_Learning-Based_Kalman_Smoothing_For_Linear_Dynamical_Systems_With_Unknown_Sparse_InputsFinal published version, 1.01 MB

Cite this

Chakraborty, R. K., Joseph, G., & Murthy, C. R. (2024). Bayesian learning-based Kalman smoothing for linear dynamical systems with unknown sparse inputs. In 2024 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2024 - Proceedings (pp. 13431-13435). (ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings). IEEE. https://doi.org/10.1109/ICASSP48485.2024.10446534

Chakraborty, Rupam Kalyan ; Joseph, Geethu ; Murthy, Chandra R. / Bayesian learning-based Kalman smoothing for linear dynamical systems with unknown sparse inputs. 2024 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2024 - Proceedings. IEEE, 2024. pp. 13431-13435 (ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings).

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abstract = "We consider the problem of jointly estimating the states and sparse inputs of a linear dynamical system using noisy low-dimensional observations. We exploit the underlying sparsity in the inputs using fictitious sparsity-promoting Gaussian priors with unknown variances (as hyperparameters). We develop two Bayesian learning-based techniques to estimate states and inputs: sparse Bayesian learning and variational Bayesian inference. Through numerical simulations, we illustrate that our algorithms outperform the conventional Kalman filtering based algorithm and other state-of-the-art sparsity-driven algorithms, especially in the low-dimensional measurement regime.",

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Chakraborty, RK , Joseph, G & Murthy, CR 2024, Bayesian learning-based Kalman smoothing for linear dynamical systems with unknown sparse inputs. in 2024 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2024 - Proceedings. ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings, IEEE, pp. 13431-13435, 49th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2024, Seoul, Korea, Republic of, 14/04/24. https://doi.org/10.1109/ICASSP48485.2024.10446534

Bayesian learning-based Kalman smoothing for linear dynamical systems with unknown sparse inputs. / Chakraborty, Rupam Kalyan ; Joseph, Geethu; Murthy, Chandra R.
2024 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2024 - Proceedings. IEEE, 2024. p. 13431-13435 (ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings).

Research output: Chapter in Book/Conference proceedings/Edited volume › Conference contribution › Scientific › peer-review

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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.

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N2 - We consider the problem of jointly estimating the states and sparse inputs of a linear dynamical system using noisy low-dimensional observations. We exploit the underlying sparsity in the inputs using fictitious sparsity-promoting Gaussian priors with unknown variances (as hyperparameters). We develop two Bayesian learning-based techniques to estimate states and inputs: sparse Bayesian learning and variational Bayesian inference. Through numerical simulations, we illustrate that our algorithms outperform the conventional Kalman filtering based algorithm and other state-of-the-art sparsity-driven algorithms, especially in the low-dimensional measurement regime.

AB - We consider the problem of jointly estimating the states and sparse inputs of a linear dynamical system using noisy low-dimensional observations. We exploit the underlying sparsity in the inputs using fictitious sparsity-promoting Gaussian priors with unknown variances (as hyperparameters). We develop two Bayesian learning-based techniques to estimate states and inputs: sparse Bayesian learning and variational Bayesian inference. Through numerical simulations, we illustrate that our algorithms outperform the conventional Kalman filtering based algorithm and other state-of-the-art sparsity-driven algorithms, especially in the low-dimensional measurement regime.

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Chakraborty RK , Joseph G, Murthy CR. Bayesian learning-based Kalman smoothing for linear dynamical systems with unknown sparse inputs. In 2024 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2024 - Proceedings. IEEE. 2024. p. 13431-13435. (ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings). doi: 10.1109/ICASSP48485.2024.10446534

Bayesian learning-based Kalman smoothing for linear dynamical systems with unknown sparse inputs

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