Abstract This paper proposes a solution for multiple-impulse orbital maneuvers near circular orbits for special cases where orbital observations are not globally available and the spacecraft is being observed through a limited window from a ground or a space-based station. The current study is particularly useful for small private launching companies with limited access to global observations around the Earth and/or for orbital maneuvers around other planets for which the orbital observations are limited to the in situ equipment. An appropriate cost function is introduced for the sake of minimizing the total control/impulse effort as well as the orbital uncertainty. It is subsequently proved that for a circle-to-circle maneuver, the optimization problem is quasi-convex with respect to the design variables. For near circular trajectories the same cost function is minimized via a gradient based optimization algorithm in order to provide a sub-optimal solution that is efficient both with respect to energy effort and orbital uncertainty. As a relevant case study, a four-impulse orbital maneuver between circular orbits under Mars gravitation is simulated and analyzed to demonstrate the effectiveness of the proposed algorithm.

中文翻译：

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具有有限观察窗的多脉冲轨道机动

摘要 本文针对圆形轨道附近的多脉冲轨道机动提出了一种解决方案，用于在轨道观测不是全球可用的特殊情况下，从地面或天基站通过有限的窗口对航天器进行观测。当前的研究对于小型私人发射公司特别有用，他们无法获得围绕地球的全球观测和/或围绕其他行星的轨道机动，其轨道观测仅限于现场设备。为了最小化总控制/脉冲努力以及轨道不确定性，引入了适当的成本函数。随后证明，对于圆到圆的机动，优化问题相对于设计变量是准凸的。对于近圆形轨迹，通过基于梯度的优化算法最小化相同的成本函数，以提供在能量努力和轨道不确定性方面均有效的次优解决方案。作为相关案例研究，对火星引力下圆轨道之间的四脉冲轨道机动进行了模拟和分析，以证明所提出算法的有效性。