# Non-Uniform Fusion Tree Generation in a Dynamic Multi-Sensor System
## 1 Introduction
In Reference [14], the flexible fusion structure is presented, but it considers only some adjustment on the allocation of system resources to cope with the failure of nodes. In Reference [15], the dynamic assigning of fusion roles to the nodes of a sensor network is presented. However, Reference [15] requires a task graph, which defines the number of fusion and sensor nodes, as an input. In References [7; 8], the two-tier hierarchical fusion architecture is presented. However, these research works concern only fusion processes on a predefined tree structure. On the other hand, clustering sensor nodes is an effective topology control approach [16]. There are various clustering methods in the field of wireless sensor networks (WSN), but most of the clustering methods are designed to prolong the network lifetime with the residual energy of nodes. In References [17; 18], survey results on various clustering methods are presented. [PERSON] et al. [17] and [PERSON] et al. [18] report that the energy efficiency is one of the major design issues in wireless sensor networks. In References [19; 20; 21], low-energy adaptive clustering hierarchy (LEACH) and its extended versions are presented. LEACH is one of the first protocols proposed for clustering. In LEACH, each node is independent in terms of making the decision to become a cluster head, but this does not guarantee the creation of a uniform cluster head distribution across the network. In Reference [22], an efficient clustering method, which can be used for the network of a large number of nodes, is presented. In Reference [16], hybrid energy-efficient distributed (HEED) clustering is presented. The HEED guarantees the creation of a fairly uniform cluster head distribution across the network. As mentioned above, clustering is an effective topology control approach, but most of the clustering methods are designed to prolong the lifetime of a wireless sensor network. In our previous work [23], we proposed a distributed self-organized cluster-based fusion tree generation (FTG) algorithm. The FTG takes into account the fusion workload of nodes instead of the residual energy of nodes, when it selects cluster heads. In Reference [23], we showed that the performance of the FTG is better than the performance of two naive methods. However, we found that the performance of the FTG is degraded in the case of a non-uniform distribution of targets. The FTG models the fusion workload of a radar by counting the number of its neighbor nodes. This model assumes that targets are uniformly distributed. We can infer that this model induces the performance degradation of FTG in the non-uniform distribution of targets. In this paper, we present a non-uniform FTG (NU-FTG) algorithm which can generate a balanced fusion tree for the two-tier hierarchical fusion process on the DMRS. The NU-FTG is based on clustering methods. It elects a set of cluster heads whose role is the same as that of the local fusion node, and the elected cluster heads can cover the other radars via one hop. The execution of NU-FTG is fully distributed. All nodes execute NU-FTG independently with the information of their neighbors. Any prior information, such as the appropriate number of local fusion nodes, predefined tree structure, or position of radars, is not required. We evaluate the performance of the NU-FTG in the OPNET (Optimized Network Engineering Tool), network simulator. Every fusion cycle, the number of processed tracks in the SIAP is collected, and the average number of the collected tracks is calculated. The simulation results show that the NU-FTG performs better than FTG [23] and HEED [16], not only in uniform, but also in non-uniform distribution of targets. Additionally, the simulation results show that the performance of the NU-FTG is not degraded, even though the start time of the radars are not synchronized.