Generating Periodic Orbits for Explorations of Elongated Asteroids

A practical method is proposed to search for periodic orbits of elongated asteroids. The method obtains required initial variables of periodic orbits by using the rotating mass dipole with appropriate parameters, and then implement local iterations to obtain the real orbits over an asteroid in the polyhedral model. In this paper the dipole and polyhedral models, and list detailed procedures of the searching method are introduced. A planar single lobe orbit is presented to evaluate the effectiveness of the method, with the asteroid 216 Kleopatra of the triple asteroid system as a representative elongated body. By applying the above method, ten families of periodic orbits around Kleopatra are identified and discussed with respect to their orbital stabilities and periods. One sample of the sombrero orbit is checked by calculating 1.000 hours to examine its orbital behavior. Besides the above orbits, the intriguing head-surrounding orbit is also analyzed.     

近地小行星仅测角相对导航可观性判据

针对近地小行星仅测角相对导航系统的非线性可观测性分析问题,本文基于非线性系统局部弱可观性理论给出了新的可观测性判据.首先,通过分析非线性系统李导数的共有属性,给出了李导数梯度空间的共有子空间.进一步,利用该共有子空间和非线性系统局部弱可观性定义给出了新的可观性判据.经理论证明,该判据适用于非线性系统任意阶李导数,并且给出的可观性结论可与高阶可观性矩阵秩判据的结论等价.与传统的秩判据相比,该判据具有无需进行高阶李导数运算,无需进行高维矩阵运算的优点.因此该判据适合在轨计算,具有一定的工程价值.最后仿真结果验证了可观性判据的有效性.     

Autonomous determination of orbit for probe around asteroids using unscented Kalman filter

The observed images of the asteroid and the asteroid reference images are used to obtain the probe-to-asteroid direction and the location of the limb features of the asteroid in the inertial coordinate. These information in combination with the shape model of the asteroid and, attitude information of the probe are utilized to obtain the position of the probe. The position information is then input to the UKF which determines the real-time orbit of the probe. Finally, the autonomous orbit determination algorithm is validated using digital simulation. The determination of orbit Using UKF is compared with that using extended Kalman filter (EKF), and the result shows that UKF is superior to EKF.