发表机构
California Institute of Technology (Caltech)（加州理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
SN-KF通过Schur补参数化保证半正定协方差，以学习方式修正EKF，在数据稀缺和传感器故障场景下提升性能。
AI 中文摘要
我们提出了Schur-Neural KF（SN-KF），一种基于学习的扩展卡尔曼滤波器（EKF）修正方法，该方法保留了EKF的概率条件化解释。该方法扰动预测状态-测量互协方差和测量噪声协方差的Cholesky因子，使得所得的联合预测协方差始终是半正定的。半正定性通过基于Schur补的参数化来保证。我们使用一种循环神经架构来实例化该参数化，其矩阵输出由幅度门调制。我们证明了纳入一次测量不会增加滤波器的状态不确定性，并表明没有任何测量能相对于其统计意外性引起任意大的状态修正。我们还提出了一种微扰分析，表明SN-KF在数据稀缺情况下的结构优势。我们提供了两个数值实验来说明SN-KF的实际益处。在双雷达实验中，强制Schur一致性提供了更宽的无故障超参数区域，并减少了小训练子集的RMSE，这与我们在数据稀缺情况下的理论分析一致。在独轮车实验中，在基于创新的传感器故障拒绝下，SN-KF实现了最佳的精确率、召回率、误报率和门控RMSE。
英文摘要
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.
Comments8 pages. Accepted to the 65th IEEE Conference on Decision and Control (CDC 2026)
