We present the Koopman-Inspired Learned Observations Extended Kalman Filter (KILO-EKF), which combines a standard EKF prediction step with a correction step based on a Koopman-inspired measurement model learned from data. By lifting measurements into a feature space where they are linear in the state, KILO-EKF enables flexible modeling of complex or poorly calibrated sensors while retaining the structure and efficiency of recursive filtering. The resulting linear-Gaussian measurement model is learned in closed form from groundtruth training data, without iterative optimization or reliance on an explicit parametric sensor model. At inference, KILO-EKF performs a standard EKF update using Jacobians obtained via the learned lifting. We validate the approach on a real-world quadrotor localization task using an IMU, ultra-wideband (UWB) sensors, and a downward-facing laser. We compare against multiple EKF baselines with varying levels of sensor calibration. KILO-EKF achieves better accuracy and consistency compared to data-calibrated baselines, and significantly outperforms EKFs that rely on imperfect geometric models, while maintaining real-time inference and fast training. These results demonstrate the effectiveness of Koopman-inspired measurement learning as a scalable alternative to traditional model-based calibration.

翻译：本文提出了基于库普曼启发的学习观测扩展卡尔曼滤波器（KILO-EKF），该方法将标准EKF预测步骤与基于从数据中学习的库普曼启发式测量模型的校正步骤相结合。通过将观测值提升到一个特征空间，使其在状态中呈线性，KILO-EKF能够灵活建模复杂或校准不佳的传感器，同时保留递归滤波的结构和效率。所得的线性高斯测量模型可直接从真实训练数据中以闭式形式学习，无需迭代优化或依赖显式参数化传感器模型。在推理阶段，KILO-EKF利用通过学习提升获得的雅可比矩阵执行标准EKF更新。我们在使用IMU、超宽带（UWB）传感器和下视激光的真实世界四旋翼定位任务上验证了该方法，并与多个具有不同传感器校准水平的EKF基线进行比较。KILO-EKF相比数据校准的基线实现了更高的精度和一致性，并显著优于依赖不完善几何模型的EKF，同时保持了实时推理和快速训练。这些结果证明了库普曼启发的测量学习作为传统基于模型校准的可扩展替代方案的有效性。