Kalman Filtering of Stationary Graph Signals
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866916951087906816 |
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| author | Chen, Yang Lee, Yeonju Shi, Yao Sun, Qiyu |
| author_facet | Chen, Yang Lee, Yeonju Shi, Yao Sun, Qiyu |
| contents | In this paper, we propose a novel definition of stationary graph signals, formulated with respect to a symmetric graph shift, such as the graph Laplacian. We show that stationary graph signals can be generated by transmitting white noise through polynomial graph channels, and that their stationarity is preserved under polynomial channel transmission.
In this paper, we also investigate Kalman filtering to dynamical systems characterized by polynomial state and observation matrices. We demonstrate that Kalman filtering maintains the stationarity of graph signals, while effectively incorporating both system dynamics and noise structure. In comparison to the static inverse filtering method and naive zero-signal strategy, the Kalman filtering procedure yields more accurate and adaptive signal estimates, highlighting its robustness and versatility in graph signal processing. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_12605 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Kalman Filtering of Stationary Graph Signals Chen, Yang Lee, Yeonju Shi, Yao Sun, Qiyu Signal Processing In this paper, we propose a novel definition of stationary graph signals, formulated with respect to a symmetric graph shift, such as the graph Laplacian. We show that stationary graph signals can be generated by transmitting white noise through polynomial graph channels, and that their stationarity is preserved under polynomial channel transmission. In this paper, we also investigate Kalman filtering to dynamical systems characterized by polynomial state and observation matrices. We demonstrate that Kalman filtering maintains the stationarity of graph signals, while effectively incorporating both system dynamics and noise structure. In comparison to the static inverse filtering method and naive zero-signal strategy, the Kalman filtering procedure yields more accurate and adaptive signal estimates, highlighting its robustness and versatility in graph signal processing. |
| title | Kalman Filtering of Stationary Graph Signals |
| topic | Signal Processing |
| url | https://arxiv.org/abs/2509.12605 |