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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.04867 |
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| _version_ | 1866918136139218944 |
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| author | Abedini, Nazanin de Wiljes, Jana Dubinkina, Svetlana |
| author_facet | Abedini, Nazanin de Wiljes, Jana Dubinkina, Svetlana |
| contents | State estimation that combines observational data with mathematical models is central to many applications and is commonly addressed through filtering methods, such as ensemble Kalman filters. In this article, we examine the signal-tracking performance of a continuous ensemble Kalman filtering under fixed, randomised, and adaptively varying partial observations. Rigorous bounds are established for the expected signal-tracking error relative to the randomness of the observation operator. In addition, we propose a sequential learning scheme that adaptively determines the dimension of a state subspace sufficient to ensure bounded filtering error, by balancing observation complexity with estimation accuracy. Beyond error control, the adaptive scheme provides a systematic approach to identifying the appropriate size of the filter-relevant subspace of the underlying dynamics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_04867 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Filtering with Randomised Observations: Sequential Learning of Relevant Subspace Properties and Accuracy Analysis Abedini, Nazanin de Wiljes, Jana Dubinkina, Svetlana Numerical Analysis Machine Learning Statistics Theory 93E11, 60G35, 65C35, 62L05, 60H10, 86A10 G.1.7; I.2.6; J.2; G.3 State estimation that combines observational data with mathematical models is central to many applications and is commonly addressed through filtering methods, such as ensemble Kalman filters. In this article, we examine the signal-tracking performance of a continuous ensemble Kalman filtering under fixed, randomised, and adaptively varying partial observations. Rigorous bounds are established for the expected signal-tracking error relative to the randomness of the observation operator. In addition, we propose a sequential learning scheme that adaptively determines the dimension of a state subspace sufficient to ensure bounded filtering error, by balancing observation complexity with estimation accuracy. Beyond error control, the adaptive scheme provides a systematic approach to identifying the appropriate size of the filter-relevant subspace of the underlying dynamics. |
| title | Filtering with Randomised Observations: Sequential Learning of Relevant Subspace Properties and Accuracy Analysis |
| topic | Numerical Analysis Machine Learning Statistics Theory 93E11, 60G35, 65C35, 62L05, 60H10, 86A10 G.1.7; I.2.6; J.2; G.3 |
| url | https://arxiv.org/abs/2509.04867 |