Learned corrections improve extended kalman filter reliability and accuracy
Schur-Neural KF: Learned Schur-Consistent Corrections to the Extended Kalman Filter
Machine Learning
Summary
The extended Kalman filter (EKF) helps track changing things, but sometimes it makes mistakes with uncertain data. The authors created Schur-Neural KF, which improves the EKF by adjusting how it handles uncertainty to keep predictions stable and sensible. Their method uses a special mathematical trick to guarantee consistent results and a neural network to learn corrections from data. This makes the filter more reliable, especially when there isn’t much data available, and it works better in tests involving radar and robot movement.
What this means in practice
- •For robotics engineers: Enhance robot localization and sensor fault detection with a more stable and accurate Kalman filter correction for uncertain sensor data.
- •For radar system designers: Improve radar tracking accuracy and robustness by applying learned corrections that ensure consistent uncertainty handling in sensor fusion.
Authors
Min Kim, Lianghao Cao, Soon-Jo Chung, Andrew M. Stuart
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.