# Non-Uniform Fusion Tree Generation in a Dynamic Multi-Sensor System
## 4 NU-FTG Algorithm  
### Algorithm Overview  
We propose using a clustering method to generate a fusion tree for the two-tier hierarchical fusion process. Clustering sensor nodes is an effective topology control approach [16]. Research on wireless sensor networks (WSN), such as References [16; 17; 18; 19; 20; 21; 22], have applied the clustering method to prolong the network lifetime by reducing the energy consumption on sensor nodes. On the other hand, the focus of this research is to increase the number of processed tracks of the two-tier fusion process. Therefore, the existing clustering method is not suitable for generating the fusion tree of the two-tier fusion process.  
We have developed a non-uniform FTG (NU-FTG), a novel distributed fusion tree generation algorithm for the dynamic multi-radar system (DMRS). The NU-FTG elects a set of cluster heads which can cover the other radars in one hop. Some of the radars, elected as cluster heads, become local fusion nodes. The other radars become members of one of the local fusion nodes in one hop. Every radar runs the algorithm with the node information, defined in Table 1, of its neighbors. Other information, such as the position of radars, predefined tree structure, and appropriate number of cluster heads, is not required.  
The NU-FTG uses three parameters to elect local fusion nodes and balance local tracks across local fusion nodes. The three parameters, _nscore_, _fscore_, and _pdt_fltime_, are defined as follows:  
\[nscore=OT+NT+Nbr.\]In Equation (5), the _nscore_ reflects the number of own tracks, neighbors' tracks, and the number of neighbors.  
\[\textit{fscore}=OT+CT+\textit{Chd}. \tag{6}\]  
In Equation (6), the fscore reflects the number of own tracks, child radars' tracks, and the number of child radars.  
\[\textit{pdt\_ftime}=\textit{PdtModel}(OT+CT). \tag{7}\]  
In Equation (7), the _PdtModel_ predicts the time-delay of a local fusion process. A local fusion node can calculate \(T_{alg}+T_{seg}+T_{upt}\) with the _PdtModel_. The number of local tracks and fused tracks in the local SIAP are required to calculate \(T_{alg}+T_{seg}+T_{upt}\). The number of local tracks is given as \(OT+CT\). However, the number of fused tracks in the local SIAP is not available before starting the fusion process. In the _PdtModel_, it is assumed that the number of fused tracks is same to the \(OT+CT\) by considering the worst case. The _pdt_ftime_ is used to decide whether a local fusion node is available or not. A local fusion node is available only when the _pdt_ftime_ is smaller than a fusion cycle.  
The NU-FTG algorithm consists of two parts: role selection and member migration. In the first part, the _nscore_ and _pdt_ftime_ are used to select the role of radars. Some radars that have available local fusion nodes in one hop distance become a member of the local fusion node with the highest _nscore_. Others, whose _nscore_ is bigger than their neighbors', are elected as local fusion nodes. The others wait for a specified time duration and retry to select their role. As a result, radars are elected as a local fusion node only when they have no other available local fusion nodes in one hop. With this approach, the NU-FTG not only places more local fusion nodes to the area where more tracks are, but also prevents electing surplus local fusion nodes. In the second part, the _fscore_ is used to balance the fusion workload among local fusion nodes. FM nodes migrate to the one of the neighbor local fusion nodes which has the lowest _fscore_.