Stochastic Geometric For The Modeling And Analysis Of Spatial-temporal Evolution Characteristics In Fractionated Spacecraft Network

Representing an innovative architecture of a distributed space system,contrary to traditional constellations,formations and cluster satellite formations,fractionated spacecraft does not impose strict limits on the geometry of the cluster.Fractionated spacecraft network is composed of multiple free-flight,physically-divisible small satellites called modules.The modules can be homogeneous or heterogeneous.The maintainability and flexibility of the fractionated modules are significantly improved by dispersing the quality and failure risks.The information exchange and resource sharing in the space between the modules are realized through wireless networking,which greatly improves the reliability of the system.This technical feature of "functional decomposition,structural separation,and wireless connection" makes the fractionated spacecraft network have the advantages of fast response,strong robustness,flexibility,and low cost.So,the fractionated spacecraft network is considered to be the next-generation distributed space system.Fractionated spacecraft network is an emerging research field,and its technical research is still in the initial stage.There are many technical problems that need to be solved urgently,including network topology control technology,routing technology,space interconnection protocoltechnology,and protocol cross-layer resource allocation technology.In order to achieve a new spacecraft architecture that works collaboratively among multiple modules,the topology and connection characteristics of the fractionated spacecraft network are described from the perspective of graph theory and percolation theory.Reference to provide services for increasingly complex and diverse space exploration missions.At the same time,mature Internet,mobile sensor networks,etc.serve as references for breaking through technical difficulties,with a view to providing services for increasingly complex and diverse space exploration tasks.Due to the high-speed movement of spacecraft nodes,the randomness and irregularity of the fractionated spacecraft network topology change significantly.Stochastic geometry provides a very powerful mathematical statistical tool for modeling and analysis of wireless networks with random topologies.Therefore,based on the theory of stochastic geometry,the spatial-temporal evolution characteristics of fractionated spacecraft networks is studied in this paper.And this paper enriches and develops the application and theory of stochastic geometry.In order to study the spatial-temporal evolution characteristics of the fractionated spacecraft network,based on the highly dynamic time-varying space-variation characteristics of the fractionated spacecraft network topology,the randomness of the gravitational field perturbationand transmission loss,the store-and-forward characteristics of the modules,and the intermittentness of the connection between nodes,this paper will conduct research on the node connection,power optimization and transmission capacity characteristics of the fractionated spacecraft network with cluster flight based on stochastic geometry.By introducing twin-satellites mode,a physical model of nodes movement for fractionated spacecraft network is established.This paper focuses on solving the following key scientific problems.1.Aiming at the issues of constraint to orbital elements and path formation time for the noise-limited fractionated spacecraft network percolating,the percolation characteristics of the noise-limited network are studied.The constraints of percolation in the SIR model of a fractionated spacecraft network with bounded distance between nodes are given,and the rationality of the constraints is verified by numerical simulation.Combined with the first arrival percolation of the percolation theory,the path formation time of nodes is studied.The relationship between path formation time and path length is analyzed by Dijkstra algorithm.And the percolation characteristics of the noise-limited fractionated spacecraft network are verified by simulation.The results show that the path formation time and the number of hops are almost linear with the path length and change periodically.2.Using empirical statistical methods,the characteristics of the distance distribution between nodes are studied,and the approximate probability density function of the distance distribution between nodes is determined through the comparison analysis of residuals and relative entropy.Meanwhile,the connective probability between nodes and the characteristics of spatial-temporal evolution are studied in depth.The definition of sequential path and a new matrix multiplication is given,and the probabilistic connectivity matrix of sequential path of multiple hops between nodes is derived.The numerical calculation results reveal that the connective probability between nodes and the distance distribution between nodes change periodically.3.Based on the connective characteristics between nodes in fractionated spacecraft network,from the two performance indicators of packet error rate and transmission delay,the Monte Carlo method is used to study the non-convex optimization of the transmit power of nodes with multiple QoS.The numerical results show that the transmit power allocation strategy can optimize the performance of the cluster flight spacecraft network system to the greatest extent,and can ensure the reliability of the system.4.Using the integral median theorem,the outrage probability of decode-and-forward is first derived.Then,according to the Macdonaldrandom variables form,the outrage probability of amplify-and-forward is derived.Finally,the transmission capacity of direct transmission and dual-hop are analyzed by numerical simulation.The results show that the transmission capacity exhibits strong periodicity,and the transmission capacity of dual-hop relay has better performance than direct transmission in fractionated spacecraft network.