# Movable Platform-Based Topology Detection for a Geographic Routing Wireless Sensor Network
## 2 Background
### Location-Based Routing Protocols  
As network orienting to application scenarios, WSN uses routing protocols that differ greatly from applications. In particular, the same type of routing protocols has different details for different application scenarios. Therefore, there is not an universal routing protocol for WSN up to now. For different WSN applications, researchers brought up different routing protocols, which can be divided into four types by sensitivity of their characteristics [32]: energy aware routing, query-based routing protocol, location-based routing protocol and reliable routing protocol. We list two location-based routing protocols that are representative in terms of data receiving and sending: GEAR (Geographical and Energy Aware Routing) [33] routing protocol and GEM (Graph EMbedding for sensor networks) [34] routing protocol (illustrated in Figures 3 and 4).  
When GEAR [33] routing protocol is employed, it is assumed that all nodes know the position of sink, the position of neighbour node and the residual energy. Figure 3 describes detail. Propagation is divided into two stages: Firstly, sink node sends query command out to the node closest to sink within the event area according to geographical position of the area. Then the node will send the command to all nodes within the area. Monitoring data will be sent to sink along the reverse path of query information. GEAR routing protocols judge per-hop path according to actual cost and estimated cost. If the path is not built, nodes will estimate the routing cost from neighbour node to sink based on the known information and select the next node to hop to. After the path is built, the actual cost of each hop returns by the way it comes along with monitoring data. Next time, when the path is built, routing cost between nodes can be the actual cost. Cost estimation equation is expressed as:  
\[c(N,R)=ad(N,R)+(1-\alpha)e(N) \tag{2}\]  
Figure 2: Internals of the spatial spectrum direction finding radar.  
\(c\left(N,R\right)\) is the estimated cost from neighbour node \(N\) to event area \(R\), \(d(N,R)\) is the distance from node \(N\) to the geometric center of event area \(R\), \(e(N)\) is the residual energy of node \(N\) and \(\alpha\) is proportional parameter.  
Figure 4: The figure shows the topology diagram of the WSN corresponding to GEM routing protocol. The red node represents station. There are totally 256 nodes within the network, the maximum communication distance of nodes is 2, and 1 node is randomly distributed within each \(1\times 1\) square box.  
Figure 3: The figure shows the WSN topology corresponding to GEAR routing protocol without energy consumption factors taken into consideration. The red node represents station. There are a total of 256 nodes within the network, the maximum communication distance of nodes is 2, and 1 node is randomly distributed within each \(1\times 1\) square box.  
The basic idea of GEM [34] routing is to establish one VPCS (virtual polar coordinate system), and form a ringed tree rooted by sink to represent the actual network topology. Each node has a coordinate consisting of the hops and angle range to sink. Data transmission between nodes is completed by the ringed tree. The specific steps: sink sets its own number of hops as 0 and makes broadcast. After all nodes within one range receive it, they will set their number of hops as 1 and then make broadcast. Once receiving sub-node broadcast, sink will assign angle range for them randomly. Within 1 hop, sub-nodes seek for their sub-nodes with the same mode and assign the angle ranges they obtain. If one node receives several pieces of broadcast information at the same time, it will select the node with the strongest signal intensity as its father node, and then will form a ringed tree.