Saved in:
| Main Authors: | , , , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.14106 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911159644323840 |
|---|---|
| author | Li, Yudong Cong, Yirui Wang, Shimin Guay, Martin Dong, Jiuxiang |
| author_facet | Li, Yudong Cong, Yirui Wang, Shimin Guay, Martin Dong, Jiuxiang |
| contents | Asymptotic boundedness is a crucial property of Distributed Set-Membership Filtering (DSMFing) that prevents the unbounded growth of the set estimates caused by the wrapping effect. However, this important property remains underinvestigated, compared to its noise-free and stochastic-noise counterparts, i.e., the convergence of Distributed Observers (DOs) and the bounded error covariance of Distributed Kalman Filters (DKFs). This paper studies the asymptotic boundedness of DSMFing for linear discrete-time systems. A novel concept, termed the Collective Observation-Information Tower (COIT), is introduced to characterize the fundamental relationship between the structure of graphs and the set estimates, which enables the boundedness analysis. Leveraging the COIT, an easily verifiable sufficient condition for the asymptotic boundedness of linear DSMFing is established. Surprisingly, the sufficient condition generalizes the well-known collective detectability condition for DOs and DKFs; it links DSMFs to existing distributed estimation methods and reveals the unique characteristic of DSMFs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_14106 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Asymptotic Boundedness of Distributed Set-Membership Filtering Li, Yudong Cong, Yirui Wang, Shimin Guay, Martin Dong, Jiuxiang Systems and Control Asymptotic boundedness is a crucial property of Distributed Set-Membership Filtering (DSMFing) that prevents the unbounded growth of the set estimates caused by the wrapping effect. However, this important property remains underinvestigated, compared to its noise-free and stochastic-noise counterparts, i.e., the convergence of Distributed Observers (DOs) and the bounded error covariance of Distributed Kalman Filters (DKFs). This paper studies the asymptotic boundedness of DSMFing for linear discrete-time systems. A novel concept, termed the Collective Observation-Information Tower (COIT), is introduced to characterize the fundamental relationship between the structure of graphs and the set estimates, which enables the boundedness analysis. Leveraging the COIT, an easily verifiable sufficient condition for the asymptotic boundedness of linear DSMFing is established. Surprisingly, the sufficient condition generalizes the well-known collective detectability condition for DOs and DKFs; it links DSMFs to existing distributed estimation methods and reveals the unique characteristic of DSMFs. |
| title | Asymptotic Boundedness of Distributed Set-Membership Filtering |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2509.14106 |