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

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.