Data-Driven Filtering Based on Model Mismatch Error Compensation

In traditional state estimation methods for linear systems, model mismatch between the assumed state-space model and the actual system often leads to divergence in the estimation process. To address this issue, this paper proposes a learning-based approach utilizing Temporal Kolmogorov–Arnold Networks (TKAN) to directly learn the mismatched component from data generated by a standard Kalman filter data flow. This approach, termed MMNet (Model Mismatch Network), is designed to compensate for state-space model errors under model mismatch conditions. A key innovation of MMNet lies in its loss function, which is constructed based on the orthogonality of the innovation sequence. This design eliminates the need for ground-truth state information and enables optimization using only measurable observations. Additionally, prior knowledge or structural assumptions regarding the model mismatch component are incorporated to accelerate convergence and reduce the learning complexity. By integrating both data-driven and model-driven paradigms, the proposed method maintains strong flexibility while enhancing robustness. Numerical experiments demonstrate that MMNet effectively compensates for modeling errors and significantly improves the accuracy of state estimation.