Nearspace hypersonic flight vehicles have become a new threat to national defense due to their characteristics of high speed

large maneuverability

and global arrival. The vehicle has non-inertial trajectory and complex strategic maneuvers

which brings new challenges to its trajectory estimation. In order to deal with vehicle maneuvers and improve the trajectory estimation performance

a trajectory estimating method was proposed based on the learnable extended Kalman filter (L-EKF) by combining the recurrent neural networks (RNNs) and the extended Kalman filter (EKF). First

a parametric characteristic model was established to describe the vehicle maneuvers. Then

the L-EKF was proposed

in which two RNNs were designed and embedded into EKF. By training with available trajectory data of the vehicle

the two embedded RNNs could find the hidden laws of the vehicle maneuvers and dynamically compensate for the parametric and model uncertainties online. Finally

the proposed L-EKF method was compared with EKF and adaptive EKF methods in several typical estimation scenarios of a hypersonic vehicle. Simulation results show that the proposed L-EKF had a higher estimation accuracy and better dynamic performance than EKF and adaptive EKF

especially when the flight vehicle performs unknown complex maneuvers.