🤖 AI Summary
This work investigates the signal tracking performance of the ensemble Kalman filter (EnKF) under partial observations, focusing on optimal state subspace dimension selection when the observation operator exhibits fixed, stochastic, or adaptive variability. We propose an error-feedback-driven adaptive sequential learning mechanism that dynamically determines, online, the minimal subspace dimension ensuring bounded filtering error—thereby achieving an optimal trade-off between observational complexity and estimation accuracy. A rigorous theoretical upper bound on the tracking error is derived as a function of observation stochasticity. Experiments demonstrate that the mechanism accurately identifies critical subspaces and maintains high-precision estimation while significantly reducing observational burden. This study establishes a systematic theoretical framework and provides a practical algorithm for subspace-adaptive EnKF design under incomplete observations.
📝 Abstract
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.