🤖 AI Summary
This work proposes a data-driven state estimation algorithm that integrates the extended Kalman filter (EKF) with Koopman operator theory to address the challenge of modeling complex or poorly calibrated sensors. By lifting nonlinear observations into a linearly observable Koopman space, the method enables closed-form learning of a linear Gaussian observation model directly from ground-truth data—without requiring an explicit sensor model or iterative optimization. Crucially, Jacobian matrices are computed online to preserve the recursive structure and real-time performance of the EKF. Evaluated on a real-world quadrotor localization task, the approach substantially outperforms conventional EKF implementations reliant on imperfect geometric models and data-driven calibration baselines, achieving significant improvements in estimation accuracy, consistency, and computational efficiency.
📝 Abstract
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.