Schur-Neural KF: Learned Schur-Consistent Corrections to the Extended Kalman Filter

Abstract:We present Schur-Neural KF (SN-KF), a learning-based correction to the extended Kalman filter (EKF) that preserves the probabilistic conditioning interpretation of the EKF. The method perturbs the predictive state-measurement cross-covariance and the Cholesky factor of the measurement noise covariance so that the resulting joint predictive covariance is always positive semidefinite. The positive semidefiniteness is ensured by a Schur complement-based parametrization. We instantiate the parametrization with a recurrent neural architecture whose matrix outputs are modulated by amplitude gates. We prove that incorporating a measurement does not increase the filter's state uncertainty, and show that no measurement can induce an arbitrarily large state correction relative to its statistical surprise. We also present a perturbative analysis suggesting SN-KF's structural strength in the data-scarce regime. We provide two numerical experiments to illustrate the practical benefits of SN-KF. In a two-radar experiment, enforcing Schur-consistency provides a much broader failure-free hyperparameter region and reduces RMSE for small training subsets, consistent with our theoretical analysis in the data-scarce regime. In the unicycle experiment, SN-KF achieves the best precision, recall, false alarm rate, and gated RMSE under innovation-based sensor-fault rejection.

8 pages. Accepted to the 65th IEEE Conference on Decision and Control (CDC 2026)

Systems and Control (eess.SY); Machine Learning (cs.LG); Signal Processing (eess.SP)

arXiv:2609.32640 [eess.SY]

(or arXiv:2609.32640v1 [eess.SY] for this version)

https://doi.org/10.48550/arXiv.2609.32640 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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