Convex Variational Inference for Multi-Hypothesis Fractional Belief Propagation Based Data Association in Multiple Target Tracking Systems

The success of Multi-hypothesis tracking(MHT) lies in the use of multiple scans, which can often yield improved tracking performance over single scan based data association methods in radar-centric multi-target tracking(MTT) systems. However, with the increase of the number of targets associated with measurements, there is an exponentially increasing need for formulating potential hypotheses, of which the computational cost may be prohibitively expensive. In this paper, a multi-hypothesis fractional belief propagation (MHFBP) based data association algorithm is proposed by the use of a probabilistic graph model for both the previous trajectories and the current measurements. To achieve this idea, there are two main steps. First, the trajectory-related indicators associated state variables are created by making use of a convex fractional free energy (FFE)function. Second, the convex optimization algorithm is used for the objective function and the fractional belief propagation (FBP) is exploited to obtain the best marginal belief of measurement for target association. In this way, incorrect hypotheses with extremely low probability can be eliminated. Finally, the proposed method is applied to multiple scenarios for MTT by indoor radar system. From the results, we can observe that it provides higher tracking performance compared with the classical MHT, feature-aided MHT(FA-MHT) and MHT-belief propagation (MHT-BP). In addition, we see that the computational burden of the proposed method is reduced significantly to avoid the phenomenon of exponential growth with increasing the number of targets.