Data-Driven Koopman Operator-Based Error-State Kalman Filter for Enhanced State Estimation of Quadrotors in Agile Flight

Highly dynamic maneuvers pose a challenge to conventional state estimators of quadrotors in rapidly tracking the pose. This paper proposes a data-driven Koopman operator-based error-state Kalman filter (K-ESKF) to enhance pose estimation in agile flight. Our method uses the Koopman operator theory to transform the full-state nonlinear quadrotor dynamics into a lifted bilinear control system driven by accelerations and angular rates. A deep neural network (DNN) is used to represent the Koopman observable functions. Our proposed K-ESKF extends the propagation step of a standard error-state Kalman filter (ESKF) using the lifted bilinear control system. An open-source quadrotor dataset, NeuroBEM, is used for training and evaluating the DNN and for testing the K-ESKF. The learned Koopman bilinear system demonstrates a 60% less attitude errors compared to the first-order Euler method in terms of model accuracy. Using real trajectories from the dataset, our proposed K-ESKF can estimate the pose as accurately as the ESKF during normal flight. More importantly, our proposed approach outperforms the ESKF by achieving about 50% less attitude and velocity estimation errors in a highly agile flight. During drastic attitude and velocity changes, the K-ESKF can still estimate the pose while the ESKF loses tracking.