Nonlinear observer for GNSS-aided inertial navigation with quaternion-based attitude estimation

For applications with limited computational capacity, observers designed based on nonlinear stability theory offer an alternative to computationally demanding extended Kalman filters. In this paper, we present a semiglobally stable nonlinear observer for estimating position, velocity, attitude, and gyro bias by combining a GNSS receiver with an inertial measurement unit including a magnetometer. Previous work by the authors on this topic was based on local navigation equations that ignored the Earth's rotation and curvature. Moreover, the attitude was represented by an over-parameterized 9-degrees-of-freedom matrix. The current paper improves on these aspects by using navigation equations that take the Earth's rotation and curvature into account, and by representing the attitude estimate as a unit quaternion. Furthermore, the observer is tested experimentally on data from a light fixed-wing aircraft.