Dynamical Low-Rank Approximations for Kalman Filtering
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912585794715648 |
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| author | Nobile, Fabio Trindade, Thomas Trigo |
| author_facet | Nobile, Fabio Trindade, Thomas Trigo |
| contents | We propose a dynamical low rank approximation of the Kalman-Bucy process (DLR-KBP), which evolves the filtering distribution of a partially continuously observed linear SDE on a small time-varying subspace at reduced computational cost. This reduction is valid in presence of small noise and when the filtering distribution concentrates around a low dimensional subspace. We further extend this approach to a DLR-ENKF process, where particles are evolved in a low dimensional time-varying subspace at reduced cost. This allows for a significantly larger ensemble size compared to standard EnKF at equivalent cost, thereby lowering the Monte Carlo error and improving filter accuracy. Theoretical properties of the DLR-KBP and DLR-ENKF are investigated, including a propagation of chaos property. Numerical experiments demonstrate the effectiveness of the technique. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_11210 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Dynamical Low-Rank Approximations for Kalman Filtering Nobile, Fabio Trindade, Thomas Trigo Numerical Analysis 60G35, 60H35, 65C30, 65C35 We propose a dynamical low rank approximation of the Kalman-Bucy process (DLR-KBP), which evolves the filtering distribution of a partially continuously observed linear SDE on a small time-varying subspace at reduced computational cost. This reduction is valid in presence of small noise and when the filtering distribution concentrates around a low dimensional subspace. We further extend this approach to a DLR-ENKF process, where particles are evolved in a low dimensional time-varying subspace at reduced cost. This allows for a significantly larger ensemble size compared to standard EnKF at equivalent cost, thereby lowering the Monte Carlo error and improving filter accuracy. Theoretical properties of the DLR-KBP and DLR-ENKF are investigated, including a propagation of chaos property. Numerical experiments demonstrate the effectiveness of the technique. |
| title | Dynamical Low-Rank Approximations for Kalman Filtering |
| topic | Numerical Analysis 60G35, 60H35, 65C30, 65C35 |
| url | https://arxiv.org/abs/2509.11210 |