Many future space missions will involve fleets with a large number of satellites flying in formation. Indeed, such fleets provably offer more reliability, redundancy, scalability and repeatability. However, large fleets also represent a challenge, especially for the navigation algorithms, which must provide an accurate estimate of the state of the fleet, with minimum requirements. Furthermore, as the number of satellites in the fleet increases, the computations to be performed increase dramatically, as well as the synchronization and communication requirements, making the design of efficient algorithms a difficult challenge. Based on previous studies, Decentralized Algorithms were designed to spread the computational task. Hierarchic Algorithms were also studied in order to reduce the synchronization requirements. This thesis presents both analytical and numerical comparisons of these algorithms in terms of accuracy, computational complexity, synchronization, and communication. The Decentralized and Hierarchic Algorithms were shown to have good performance in terms of accuracy, while involving far fewer computations than the Centralized Algorithm. As a result, they can be used as scalable algorithms for large formation flying fleets.
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