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.