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在无线传感器网络之中,由于在这些传感器中存在的节点是随机进行放置的,因此网络的节点数、节点的探测半径和通讯半径和探测覆盖率以及网络的连通性之间存在密切的相关,同时节点和簇首的数量能够直接的影响到整个无线传输器的成本和性能,例如其中的容错性和鲁棒性,这些都是无线传感器网络进行设计时需要重点考虑的问题。所以,需要研究无线传感器网络里面的一个固定的在区域内的探测覆盖率和连通性的问题。通过将复杂的覆盖和连通性的问题进一步的简化,之后利用数学建模、理论分析以及几何证明,使用几何理论和数学的方法进行归纳,从其中的拓扑学的角度给出了一个在传感器区域中的一种网格的划分方法。最后,从理论上分别给出了一个实现完全的无缝的覆盖和连接的传感器区域内最少需要多少个节点和最少的需求,使用解析式进行解析,即需要从理论上解决一共多少个簇才能够把整个传感器区域划分来,以及研究至少需要多少个节点才能实现完全的覆盖和连通的问题。以此为基础,给出无线传感器网络节点的通讯半径等的设计原则。
In wireless sensor networks, there are close correlations between the number of nodes in the network, the detection radius and the communication radius and the detection coverage of the nodes, and the connectivity of the network because the nodes existing in these sensors are randomly placed. At the same time, the number of nodes and cluster heads can directly affect the cost and performance of the entire wireless transmitter, such as the fault tolerance and robustness among them. These are the key issues to be considered when designing wireless sensor networks. Therefore, there is a need to study a fixed intra-area coverage and connectivity issue in wireless sensor networks. By further simplifying the problem of complex coverage and connectivity, and then using mathematical modeling, theoretical analysis and geometric proof, the use of geometric theory and mathematical methods to summarize, from which the topological point of view gives a sensor area In a grid division method. Finally, theoretically, we give the minimum number of nodes and the minimum requirements in a sensor area to achieve complete and seamless coverage and connectivity, respectively, and use analytical expressions to solve them, that is, how many clusters need to be theoretically solved The ability to partition the entire sensor area and study how many nodes are required to achieve complete coverage and connectivity. Based on this, the design principles of the communication radius of wireless sensor network nodes are given.