Observability Analysis of Flight State Estimation for UAVs and Experimental Validation

UAVs require reliable, cost-efficient onboard flight state estimation that achieves high accuracy and robustness to perturbation. We analyze a multi-sensor extended Kalman filter (EKF) based on the work by Leutenegger. The EKF uses measurements from a MEMS-based inertial system, static and dynamic pressure sensors as well as GPS. As opposed to other implementations we do not use a magnetic sensor because the weak magnetic field of the earth is subject to disturbances. Observability of the state is a necessary condition for the EKF to work. In this paper, we demonstrate that the system state is observable - which is in contrast to statements in the literature - if the random nature of the air mass is taken into account. Therefore, we carry out an in-depth observability analysis based on a singular value decomposition (SVD). The numerical SVD delivers a wealth of information regarding the observable (sub)spaces. We validated the theoretical findings based on sensor data recorded in test flights on a glider. Most importantly, we demonstrate that the EKF works. It is capable of absorbing large perturbations in the wind state variable converging to the undisturbed estimates.