大气阻力摄动下平均轨道根数在轨实时确定方法

Onboard Real-time Estimation of Mean Orbital Elements with Atmospheric Drag

为了满足卫星长期自主运行的任务需求,本文同时考虑了大气阻力摄动和非球形摄动带谐项两种摄动对卫星平均轨道根数的影响,提出了采用滤波算法在轨实时估计平均轨道根数的方法.基于指数大气密度模型推导了大气阻力摄动下平均轨道根数的变化率,分析了非球形带谐项摄动势函数对平均轨道根数的影响并推导了该影响下平均轨道根数变化率的通用计算方法,由此建立了滤波状态方程以及以瞬时轨道根数为观测量的量测方程并分析了测量噪声特性;为减小计算量以便于在轨实现,提出采用基于球形单边Sigma采样的平方根UKF(Unscented Kalman filter)滤波来估计平均轨道根数.数值仿真结果表明,该算法有效、精度较高且鲁棒性好,能够满足卫星长期自主在轨实时计算平均轨道根数的要求.

To solve the problem of mean orbital elements calculation for long-term autonomous missions, a filter estimation method is used to estimate the mean orbital elements with the effects of atmospheric drag and the gravitational potential of zonal harmonics. The effects of atmospheric drag are analyzed by virtue of analytical orbital mechanics with the spherical exponential model of atmospheric density. The general formulas are derived for the rates of change of mean orbital elements perturbed by gravitational potential zonal harmonics. The state equations and measurement equations are established to treat the mean orbital elements as state variables and the osculating orbital elements as measurements. The distribution of the measurement noise is analyzed. In this estimator, the spherical simplex sigma-point selection and the square root form of unscented Kalman filter （UKF） are fused for less computational cost and better numerical stability on-board. Numerical simulations are performed to demonstrate the viability of the proposed method. Comparison with another approach shows that the proposed one can estimate mean orbital elements on-board for a real-time and long-term mission and can offer a higher accuracy.