Multisensor Data Fusion Using Two-Stage Analysis on Pairs of Plots Graphs Rogério Perroti Barbosa 1,2 , Frederic Livernet 3 , Beatriz S. L. P. de Lima 1 , José Gomes de Carvalho Jr 2 1 - COPPE/ Federal University of Rio de Janeiro (UFRJ), Rio de Janeiro, Brazil 2 – Brazilian Navy Research Institute (IPQM), Rio de Janeiro, Brazil 3 – General Directorate for Armament (DGA) Toulon, France Abstract – This article provides a derivation and a description of the analysis on pair of plots graphs, useful to data fusion of multiple targets in a multiple sensors cluttered environment. The method proposes an analysis in two stages, instead of the previously proposed single-stage method, to choose the best data from possible redundant sensors. The analysis in two stages is parallelizable, which potentially brings performance gains. In this paper, the single-stage and the two- stage algorithms are evaluated in light and heavy cluttered environments. The evaluation is based in two different metrics applied over different target trajectories with hard and heavy environmental clutter conditions. Keywords- Target Monitoring; Target fusion; Graph theory. I. INTRODUCTION Command and control naval systems often obtain information from sensors such as radars, infrared sensors, sonars and radio buoys, among others. The signs provided by these sensors may suffer interference from external agents (sea state, weather conditions, etc.), or internal errors (thermal noise, sensor adjustment). These systems must be able to unify the redundant information, providing to the operator a consolidated scenario. This article concentrates in fusion of data provided by different radars. This process is known as multi-target multi- sensor data fusion. The whole task comprises a tracking estimation method preceded by a plot association process. The conventional Single-Hypothesis Tracking (SHT) [1] algorithm uses the extended Kalman filter (EKF) [2] for filtering and the Global Nearest Neighbor (GNN) [3] for data association. The SHT algorithm propagates only the best data association hypothesis over time. If the association is ambiguous, it fails in providing the hypothesis corresponding to the true association. In a different approach, the track-oriented Multiple Hypothesis Tracking (MHT) algorithm [4, 5] propagates a set of alternative association hypotheses. The least likely hypotheses are discarded, while the true hypothesis is retained. A lot of solutions are similar to MHT and many of these processes are intensive in scenarios with large amount of targets and clutter (false alarms). II. GRAPH-BASED SOLUTIONS The graph based methods are also track-oriented algorithms based on optimizing paths in a graph composed by nodes representing track’s positions provided by sensors. The optimizing function varies with model. Some authors [6], [7] proposed fusion methods based on graphs. In these articles each node of the graph represents a target position provided by a sensor in a Cartesian space or a clutter associated with this measure. The data generated by sensors (plots representing target detections or false alarms) are correlated, forming a hypothesis that represents a target path during a certain lag of time. In [8] the authors proposed a different graph-based method, where each node in the graph represents a pair of sequential position points in the Cartesian space. After that, a “pair of plots” graph is constructed using these points .The authors demonstrated that this approach optimizes the process of filtering clutter associated with sensor measures. To understand the pair of plots graph, consider two sensor providing measurements (sensor 1 and sensor 2). The plots sent by sensor 1 are represented in Fig 1 by circles and plots sent by the sensor 2 are represented by squares. Fig 2 and Fig 3 show graph of plots separated by sensor. They were built using the methodology described in [8], where each plot delivered by the sensor on a time frame is defined as a vertex or node of the graph. Any arc between two plots is built under the following condition: Dpair < Vmax ΔT + f(ε). Where Dpair is the distance between two plots, ΔT is the time elapsed between two plots, Vmax is the maximum speed for the object of interest, and f(ε) is the uncertainty on distance which depends on the measurement errors. In any case this time must obey the following condition ΔT < n*Ts where Ts is the sensor update rate and n is the number of time steps in the current window. From the graphs of Fig 2 and Fig 3, are elaborated the “pairs of plots” graphs shown in Fig 4 and Fig 5, respectively. Those graphs are constructed using the speeds and times of points that belong to each arc in the plot graph to be a new node in the “pairs of plots” graph. The previous nodes are discarded. So, a new graph is built where the nodes of the final graph are the arcs of the previous graph. 2073