Learning Meta-Dynamics for Off-Dynamics Kalman Filtering

Recursive state estimation becomes challenging when the transition model itself evolves during filtering: each recursion provides only one new noisy observation, yet the transition must be revised before state and covariance propagation. We formulate this setting as off-dynamics Kalman filtering and view the causal evolution of the transition model as meta-dynamics. We introduce the Dynamics-Adaptive Kalman Network (DyAKNet), which represents dynamics adaptation explicitly in a sparse coefficient space. DyAKNet converts the diagnostic innovation under the preceding model into coefficient-space evidence, aggregates evidence across recursions, and separately updates signed coefficient values and active support before prediction. The revised transition is then immediately reused within the same filtering recursion. Under local smoothness, boundedness, and contraction conditions, we derive a finite-horizon mean-square error bound that characterizes the contributions of vector-field mismatch and stochastic noise. Experiments span coefficient evolution, structural changes within a prescribed candidate representation, unseen noise and switching patterns, and real-world localization. Across these settings, DyAKNet consistently improves state-estimation accuracy over the evaluated adaptive and learning-based baselines, while retaining an explicit and interpretable dynamics representation. These results support same-recursion dynamics adaptation as an effective strategy for filtering under evolving model mismatch. Code is available at https://anonymous.4open.science/r/DyAKNet-191A.