Advancing Convergence Speed of Distributed Consensus Time Synchronization Algorithms in Unmanned Aerial Vehicle Ad Hoc Networks

Time synchronization is a critical prerequisite for unmanned aerial vehicle ad hoc networks (UANETs) to facilitate navigation and positioning, formation control, and data fusion. However, given the dynamic changes in UANETs, improving the convergence speeds of distributed consensus time synchronization algorithms with only local information poses a major challenge. To address this challenge, this study first establishes a convex model on the basis of graph theory and relevant theories of random matrices to approximate the original problem. Subsequently, three acceleration schemes for consensus algorithms are derived by minimizing the Frobenius norm of the iteration matrix. Additionally, this study provides a new upper bound for constant communication weights and discusses the limitations of existing metrics used to measure the convergence speeds of consensus algorithms. Finally, the proposed schemes are compared with existing ones through simulation. Our results indicate that the three proposed schemes can achieve faster convergence while maintaining high-precision synchronization in scenarios with static or known topological structures of networks. In scenarios where the topological structure of a UANET is time-varying and unknown, the scheme proposed in this paper achieves the fastest convergence speed.