利用VLBI观测量对月球天平动参数解算及着陆器定位和测速的改进

在嫦娥三号探月工程中，月球天平动参数是影响其着陆器定位精度的重要参数，研究月球天平动参数估计方法对于中国探月工程的发展具有重要意义。目前，月球激光测距（lunar laser ranging，LLR）是解算月球天平动参数的常用方法，该方法通过数值拟合将拟合系数放在历表文件中供用户读取。首先，基于差分甚长基线干涉测量技术（very long baseline interferometry, VLBI）解算月球物理天平动参数，其仿真结果表明，与DE421星历的插值结果对比，其欧拉角$\Omega$、$i$和$\mu$的改进值分别补偿至-0.692 4″、0.009 6″和-0.009 7″；然后，基于补偿后的月球物理天平动参数求解着陆器坐标和速度，结果显示，相比于补偿前, 着陆器在X、Y、Z方向的定位精度分别提高了24.204 m、0.405 m、1.996 m，速度误差的估计精度也分别提高了0.010 6 m/s、0.013 5 m/s、0.007 2 m/s。上述研究结果可为未来月球天平动参数解算的相关研究提供参考。

Calculation of Lunar Libration Parameters Using VLBI Observations and Improvement of Lander Positioning and Velocity Measurement

  Objectives  The lunar libration parameters are important parameters that affect the positioning accuracy of the Chang'E-3 lander. Studying the lunar balance dynamic parameter estimation methods is of great significance to the development of lunar exploration projects in China. At present, the lunar libration parameters is calculated by the ephemeris method, but this method cannot guarantee the positioning accuracy of the lander.  Methods  We first establish the expressions of the very long baseline interferometry (VLBI) time delay and delay rate with the changes of the lander's position, velocity, then based on VLBI technique, the lunar physical libration parameters are calculated by using weighted least square adjustment method.  Results  Compared with the interpolation results of the DE421 ephemeris, the improvements of the Euler angles $\Omega$, $i$ and $\mu$ are compensated to -0.692 4″, 0.009 6″ and -0.009 7″ respectively.Based on the lunar physical libration parameters, the position and velocity of the lander were solved, the results show that the positioning accuracy of the lander can be improved in X, Y, Z directions by 24.204 m, 0.405 m, 1.996 m respectively.The estimation accuracy of the velocity error is also improved by 0.010 6 m/s, 0.013 5 m/sand 0.007 2 m/s in X, Y, Z directions.  Conclusions  This paper provides strong reference for the related research on the calculation of the physical libration parameters in the future.