First of all, the author reviewed the environmental torque considered in LEO. For LEO spacecrafts, the aerodynamic torque and gravity gradient torque were mainly considered. The gravity gradient torque was often utilized to stabilize the Earth pointing with several degrees of error. The aerodynamic torque played a dominant role in the LEO and interfered the control system, causing the spacecraft to reverse at the end of the mission. Afterwards, the author demonstrated the kinematics and dynamics framework of attitude prediction. The attitude of satellite was usually defined by the rotation between the Earth Centered Inertial system (ECI) and the body fixed frame. The Euler angle rotation sequence used in this work was yaw-pitch-roll. The attitude kinematics equation was usually described by the Euler angle or quaternions. The author chose quaternions considering the main advantage of the quaternion representation was that the attitude kinematic equation was free of singularities, and the kinematics equation matrix was linear.
Next, the author introduced the filtering and determination method of attitude. In the open-loop prediction, the accurate measurement of satellite attitude was very important. A tiny initial deviation could cause the prediction results to gradually deviate from the actual condition. The most straightforward method to estimate the satellite attitude for a long time was to combine the dynamic model with the observation data, and then calculated the optimal estimation according to the principle of minimum variance. After obtaining the attitude estimation, the high-order unmodeled information could be extracted from the original data through the extended state identification, which was instrumental to refine the dynamic model. Thus, in detail, the estimation results of the satellite state were obtained by the extended Kalman filter (EKF), and then the unmodeled torque of satellite was estimated by series of the extended state observer (ESO). It was worth noting that in the process of EKF, the process noise and measurement noise must meet the conditions of the linear uncorrelation, the zero mean and Gaussian distribution, otherwise the filtering result may be inaccurate. On the other hand, the uncertainty estimation, including the internal coupling, the external unknown disturbances and the unmodeled dynamics could be determined with rarely observation information by building an extended state observer. After obtaining the optimal attitude estimation with the EKF, a series of extended state observer was introduced to extract the high-order unmodeled information hiding in the attitude.
Then, a double hidden layer back propagation (BP) network was constructed to learn the unmodeled environment torque in the satellite. The BP Neural network had high generalization and self-learning ability and could reconstruct the mapping relationship between the state and the environmental torque, which played a critical role in attitude prediction system. In the three-layer neural network, the input layer of the network was the measured attitude information, and the tutor signal of supervised learning was the unmodeled torque. The activation function of the first hidden layer was the “Relu” function. While the activation function of the second hidden layer was a “Sigmoid” function. Mover, the normalization of the network was essential. Since the magnitude of the identified environmental torque was too small, the training set should be mapped to the range of [0,1] by normalization for a better raining efficiency. The corresponding linear transformation was also required raining efficiency.
Finally, the author presented the whole process and simulation results of the prediction system. The target spacecraft was selected as Tiangong-1 Space Station descending into the atmosphere. Due to the coupling effect of the spacecraft orbit and attitude, it was difficult to consider the independent influence of the environmental torque independently. Therefore, 13 state parameters including a three-axis position, a three-axis velocity (both expressed in J2000 coordinate system), a quaternion and an angular velocity were used in the simulation. A disturbance was artificially added to the simulation as the unmodeled environmental torque. The simulation results showed that this method had high prediction accuracy and high reliability with discontinuous measurement, which proved the superiority and feasibility of the new method. In addition, this method had high expansibility and could be applied to various high-precision prediction fields with unmodeled disturbances. Excellent prediction results could be obtained easily by optimizing the identification algorithm and designing appropriate activation function.
