An extension of integrated navigation algorithms to estimate elastic motions of very flexible aircrafts

This paper presents an algorithm for estimating the rigid and elastic motions of aircrafts showing significant elastic displacements, based on an EKF (Extended Kalman Filter) technique. The proposed algorithm can be applied to HALE (High Attitude Long Endurance Vehicle) unmanned vehicles, which typically show a configuration with high aspect ratios wings, fuselages with high length to diameter ratios and, above all, lightweight structures. The knowledge of their actual structure shape is fundamental essentially for three reasons: health monitoring of the structure, control purposes (Active Control Technologies) and finally for the determination of onboard sensors exact position and attitude, relative to a specified reference frame, to improve the accuracy of their measurements. Filter equations have been developed considering the coupling between rigid and elastic motions. The elastic motions are modeled in the assumptions of modal decomposition. Sensors budget of the presented algorithm, consists in two GPS Antennas/Receivers for speed/position measurements, an Inertial Measurement Unit with tri-axial accelerometers, gyros and magnetometers, and at least one auxiliary tri-axial accelerometer. The matrix formulation of the algorithm allows using the desired number of auxiliary accelerometers without changes to its implementation or its mathematical structure. Filter implementation also allows defining a numerical criterion to determine the better allocation of auxiliary accelerometers. The observability of the filter error state vector is also exhaustively analyzed, considering different scenarios concerning the elastic features of the structure. Finally simulation test results are reported, which demonstrate effectiveness of the proposed algorithm.