Calibration Method for Relativistic Navigation System Using Parallel Q-Learning Extended Kalman Filter.

For the relativistic navigation system where the position and velocity of the spacecraft are determined through the observation of the relativistic perturbations including stellar aberration and starlight gravitational deflection, a novel parallel Q-learning extended Kalman filter (PQEKF) is presented to implement the measurement bias calibration. The relativistic perturbations are extracted from the inter-star angle measurement achieved with a group of high-accuracy star sensors on the spacecraft. Inter-star angle measurement bias caused by the misalignment of the star sensors is one of the main error sources in the relativistic navigation system. In order to suppress the unfavorable effect of measurement bias on navigation performance, the PQEKF is developed to estimate the position and velocity, together with the calibration parameters, where the Q-learning approach is adopted to fine tune the process noise covariance matrix of the filter automatically. The high performance of the presented method is illustrated via numerical simulations in the scenario of medium Earth orbit (MEO) satellite navigation. The simulation results show that, for the considered MEO satellite and the presented PQEKF algorithm, in the case that the inter-star angle measurement accuracy is about 1 mas, after calibration, the positioning accuracy of the relativistic navigation system is less than 300 m.