Structural flexibility of advanced, large-wingspan aircrafts is a crucial factor which has huge influence on the dynamics and stability of these vehicles. In case of a highly flexible wing structure, there is a need for an efficient observer to measure and predict the structural changes and dynamics of the wing. However, the modal coordinates of the wing cannot be measured directly so designing a state observer is necessary. Since the flexible aircraft model is nonlinear, the classical Kalman filter approach can have limited performance. Instead, two state observer approaches are investigated in the paper. First, we present a model-based method for designing an extended Kalman filter (EKF) when only a linear parameter-varying model (LPV) is available to describe the behaviour of the real aircraft. Second, we present a datadriven approach for this problem which is based on the new KalmanNet architecture. Finally, the results of the two methods are evaluated on the T-Flex model of the FLiPASED H2020 project