Nobile, FabioTrigo Trindade, Thomas Simon Spencer2025-10-212025-10-212025-10-202025-09-25https://doi.org/10.48550/arXiv.2509.11210https://infoscience.epfl.ch/handle/20.500.14299/255149https://arxiv.org/abs/2509.11210v1We 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.enDynamical Low-Rank Approximations for Kalman FilteringKalman-Bucy processesEnsemble Kalman Filterstext::preprint