Distributed Time-Varying Gaussian Regression via Kalman Filtering
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866910915415244800 |
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| author | Taddei, Nicola Maggioni, Riccardo Eising, Jaap De Pasquale, Giulia Dorfler, Florian |
| author_facet | Taddei, Nicola Maggioni, Riccardo Eising, Jaap De Pasquale, Giulia Dorfler, Florian |
| contents | We consider the problem of learning time-varying functions in a distributed fashion, where agents collect local information to collaboratively achieve a shared estimate. This task is particularly relevant in control applications, whenever real-time and robust estimation of dynamic cost/reward functions in safety critical settings has to be performed. In this paper, we,adopt a finite-dimensional approximation of a Gaussian Process, corresponding to a Bayesian linear regression in an appropriate feature space, and propose a new algorithm, DistKP, to track the time-varying coefficients via a distributed Kalman filter. The proposed method works for arbitrary kernels and under weaker assumptions on the time-evolution of the function to learn compared to the literature. We validate our results using a simulation example in which a fleet of Unmanned Aerial Vehicles (UAVs) learns a dynamically changing wind field. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2504_14900 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Distributed Time-Varying Gaussian Regression via Kalman Filtering Taddei, Nicola Maggioni, Riccardo Eising, Jaap De Pasquale, Giulia Dorfler, Florian Systems and Control We consider the problem of learning time-varying functions in a distributed fashion, where agents collect local information to collaboratively achieve a shared estimate. This task is particularly relevant in control applications, whenever real-time and robust estimation of dynamic cost/reward functions in safety critical settings has to be performed. In this paper, we,adopt a finite-dimensional approximation of a Gaussian Process, corresponding to a Bayesian linear regression in an appropriate feature space, and propose a new algorithm, DistKP, to track the time-varying coefficients via a distributed Kalman filter. The proposed method works for arbitrary kernels and under weaker assumptions on the time-evolution of the function to learn compared to the literature. We validate our results using a simulation example in which a fleet of Unmanned Aerial Vehicles (UAVs) learns a dynamically changing wind field. |
| title | Distributed Time-Varying Gaussian Regression via Kalman Filtering |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2504.14900 |