Design of Lunar Free-Return Trajectories Based on UKF Parameter Estimation

Abstract

A fast and convenient design-method based on UKF parameter estimation is proposed for lunar free-return trajectories. The method proposed avoids calculating the Jacobian matrix and obtains large convergence ability compared with the common differential-correction method. Given that the initial estimate of the free-return trajectory is generated under the two-body Earth-spacecraft model, the difficulty of guessing a good initial estimate is greatly reduced. Through solving the converted parameter estimation problem using the method proposed, the converged final solution can be found under a high-fidelity gravitational model by a few iterations. Despite its simplicity, the method is proves to be quite effective in finding the solution of lunar free-return trajectories with great numerical accuracy.

Keywords

lunar free-return trajectories / differential-correction method / unscented Kalman filter / parameter estimation

References

[1] Schwaniger A J. Trajectories in the earth-moon space with symmetrical free return properties, Technical Note D-1833[R]. [S. l]：National Aeronautics and Space Administration，1963.
[2] Jesick M,Ocampo. Automated generation of symmetric lunar free-return trajectories[J]. Journal of Guidance,Control,and Dynamics,2011,34(1):98-106
[3] Green B S，LewinN. A gradient method for obtaining circumlunar trajectories[C]// AIAA Astrodynamics conference. [S.l]：AIAA， 1963.
[4] Miele A,Wang T,Mancuso S. Optimal free-return trajectories for moon missions and mars missions[J]. Journal of the Astronautical Sciences,2000,48(2-3):183-206
[5] Peng Q B,Shen H X,Li H Y. Free return orbit design and characteristics analysis for manned lunar mission[J]. Science China Technological Sciences,2012,54(12):3243-3250
[6] Luo Q,Yin J,Han C. Design of earth-moon free-return trajectories[J]. Journal of Guidance,Control,and Dynamics,2012,36(1):263-271
[7] Luo Q,Meng Z,Han C. Solution algorithm to a quasi-lambert's problem with fixed flight-direction angle constraint[J]. Celestial Mechanics and Dynamical Astronomy,2011,109(4):409-427
[8] Haykin S. Kalman filtering and neural networks[M]. New York：John Wiley & Amp Sons Inc，2001.
[9] Julier S J. The spherical simplex unscented transformation [C]//Proceedings of the American Control Conference. Denver，Colorado：[s. n.]，2003.
[10] Julier S J. The scaled unscented transformation[C]//Proceedings of the American Control Conference. Anchorage：[s. n]，2002.