Towards Stabilising Hybrid Filtering via Bounded Residual Corrections

Filtering of dynamical systems remains a central concern in science and engineering. Classical model-based algorithms such as the Extended Kalman Filter offer interpretability and stability guarantees under regularity conditions, but can perform poorly under model misspecification. To compensate, hybrid methods combine model-based approaches with neural corrections, preserving some interpretability inherent in classical filters. However, naïve embedding of neural mappings risks driving hybrid filters to instability, a severe vulnerability in safety-critical applications. Aiming to resolve this instability without severely impairing expressivity or interpretability, we propose Bounded Residual Correction (BRC), an operationally filter- and architecture-agnostic framework that augments model-based representations with norm-bounded learned residual corrections. We then prove that to preserve Reif et al. (1999)'s probability-one error boundedness when correcting local linearisation-based estimates with learned residuals, bounding them is necessary and constraining their norms below a threshold is sufficient alongside nominal regularity conditions. Empirically, across extensive evaluations, self-supervised BRC-augmented filters outperform prior works in accuracy and probabilistic calibration, confirming that despite constraining residuals' expressivity, norm-bounding can enhance rather than hinder performance.