# Non-Uniform Fusion Tree Generation in a Dynamic Multi-Sensor System
## 1 Introduction  
A fusion process is required to obtain a single integrated air picture (SIAP) with air tracks from a dynamic multi-radar system (DMRS). The DMRS consists of numerous mobile radars that are connected via a wireless ad hoc network. Air tracks from multi-radar should be fused to create a SIAP. The SIAP is the product of fused, near-real-time and real-time data from multiple radars to allow the development of common, continuous, and unambiguous tracks of all airborne objects in the surveillance area [1]. A fusion process, which factors out duplicate information [2] and improves on the state estimation of tracks with duplicate information [3], is required to obtain a SIAP for the DMRS. The centralized fusion architecture is theoretically optimal [3], but this architecture requires high network bandwidth and high computing resources at the central server. In this architecture, radars send all observed measurements to the central server for every observation cycle. The central server executes the tracking process to create tracks and the fusion process to create the SIAP by combining tracks that originate from the same target. On the other hand, in the hierarchical fusion architecture, presented in References [4; 5; 6], radars execute the tracking process and the central server executes the fusion process. Every fusion cycle, radars send the created tracks to the central server to be fused. In this approach, the required network bandwidth can be dramatically reduced. The fusion cycle ismuch longer than the observation cycle; however, the fusion process is still concentrated at the central server. Both centralized and hierarchical fusion architectures are not suitable for the DMRS, which consists of numerous nodes. Therefore, a two-tier hierarchical fusion architecture, presented in References [7; 8], is applied for the fusion process of the DMRS. In this architecture, the fusion process is divided into local and global to reduce the number of tracks processed at the central server. This architecture consists of radars, local fusion nodes, and a central server. Radars form clusters, and one of the radars in each cluster becomes the local fusion node. This structure can be modeled as a tree which is called a fusion tree. Each radar, local fusion node, and the central server is a leaf node, internode, and the root node of the fusion tree, respectively. Local fusion nodes execute the local fusion process to create the local SIAP, and the central server executes the global fusion process to create the global SIAP with the tracks from local fusion nodes. As a result, duplicate tracks in each cluster are combined at local fusion nodes, and the number of tracks to be processed at the central server can be reduced. The two-tier hierarchical fusion architecture requires a balanced fusion tree, which balances tracks across local fusion nodes, to prevent some of the local fusion nodes from becoming bottleneck nodes. However, it is hard to generate a balanced fusion tree on the DMRS, since the possible number of fusion trees exponentially increases as the number of radars increases. Therefore, topology control, which selects the role of the nodes and the flow of the fusion process, is required to generate a balanced fusion tree. There are numerous research works in the field of multi-sensor data fusion. However, most of the research works in this field do not consider topology control to create a balanced fusion tree. In Reference [9], various problems about multi-sensor data fusion, such as data imperfection, outliers and spurious data, conflicting data, data modality, data correlation/association, etc., is presented. However, topology control is not included. In References [10; 11; 12], various techniques are presented on assigning and scheduling fusion tasks to sensors. However, their application is not the correct fusion process to obtain a SIAP. In Reference [13], a multi-target tracking problem is presented, but this research work deals with the sensor deployment problems.