KILO-EKF: Koopman-Inspired Learned Observations Extended Kalman Filter

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.