Thermospheric Density Estimation Method Using a First-Order Gauss-Markov Process

Low-Earth-orbit (LEO) spacecraft are significantly influenced by atmospheric drag. Accurately estimating thermospheric density is pivotal for the precise calculation of drag acceleration. However, thermospheric density along a specific orbit, computed using existing thermospheric models, has certain inaccuracies. In this work, a first-order Gauss-Markov process is used to model the deviation of atmospheric drag acceleration. With the Markov parameter of the initial state iteratively computed through sequential estimation and the smoothing method, the thermospheric density is derived from high-precision GPS measurements. In simulation scenarios, the root-mean-square error and relative error of the estimated thermospheric density reduce by about 45 and 50% relative to the prior density, respectively. Using the estimated density for orbit propagation, satellite trajectories' one-day position and velocity error are, respectively, within 100 m and 0.1 m/s, and an average improvement in orbit precision is over 80%. The proposed method has been applied to the real Tsinghua Science Satellite (Q-SAT) GPS measurements for effectiveness verification. It shows strong adaptability under extreme space weather and during the occurrence of geomagnetic storms. Due to the estimated Markov parameter of the initial state obeying the Langevin dynamics properties, the proposed method also offers short-term thermospheric density forecasting potential.