Navigation constellation availability research based on multi-echelon technique for recoverable item control theory

基于多级库存管理理论的导航星座可用性研究

¹ School of Astronautics, Northwestern Polytechnical University, Xi'an 710072, China
² Innovation Academy for Microsatellites of Chinese Academy of Sciences, Shanghai 201304, China
³ School of Aeronautics, Northwestern Polytechnical University, Xi'an 710072, China
⁴ National Key Laboratory of Aircraft Configuration Design, Xi'an 710072, China
⁵ Standardization Department, COMAC Shanghai Aviation Industrial(Group)Co., Ltd., Shanghai 200232, China

Received: 13 March 2024

Abstract

In view of the problems existing in the current research on backup strategies for constellations, such as the single method and the neglect of short-term satellite failures, as well as the insufficient in-depth study of backup strategies using Markov theory, this paper proposes a constellation availability research method based on multi-level inventory management theory and considering constellation status. Firstly, a mathematical model of constellation backup strategy is established with the guarantee rate of backup satellites as the index. Then, based on Markov theory, a mathematical model of constellation service availability is further established by combining the availability of individual satellites and the probability of constellation status. Finally, a case analysis and comparison are conducted using a certain navigation constellation as an example. According to the calculation results of the model, the changes in the probability of constellation failure status are explored; the influence of the deployment position, replenishment timing, and increase in the number of backup satellites on improving constellation service availability is given; and it is verified that the impact of short-term failures on constellation availability is similar to that of long-term failures and cannot be ignored in engineering applications.

摘要

目前星座可用性的备份策略研究方法单一且忽略了卫星短期故障, 采用马尔可夫理论但对备份策略研究不够深入。针对上述问题, 提出了一种基于多级库存管理理论并考虑星座状态的星座可用性研究方法。以备份卫星的保障率为指标建立星座备份策略的数学模型; 根据马尔可夫理论, 结合单星可用性和星座状态概率进一步建立星座服务可用性数学模型; 以某导航星座为例进行案例分析对比。根据模型计算结果, 探究了星座故障状态概率变化; 给出了备份卫星部署位置、补充时机以及增加数量对提高星座服务可用性的影响; 验证了短期故障对卫星星座可用性的影响程度与长期故障相当, 在工程应用中不可忽视。