This paper explores evaluation of association marginals in multiple hypothesis tracking. The work builds upon recent results where loop belief propagation (LBP) has been used in single-hypothesis cases. There are two contributions in the paper. The first is a novel factor graph representation of the joint multi-hypothesis association posterior. The second contribution is two algorithms that both use LBP to evaluate association marginals. The first method uses total probability in conjunction with hypothesis-conditioned LBP, and is called PHD-LBP. The second method is an LBP algorithm running directly on the full multi-hypothesis association graph with novel, specialized message definitions that are derived in this paper and efficient to compute and store in memory, and is called MH-LBP. Results show that both algorithms perform well with high correlation with the exact marginals for the majority of the cases.

Track initiation in multi-object tracking for groups of objects traveling close to each other may require considering many unlikely tracks near each other. Limiting track numbers by not initiating within the gate, as is commonly done, does not work well in these scenarios. With many tracks, computing the exact marginal track to measurement probabilities in a joint integrated probabilistic data association (JIPDA) is computationally expensive.In addressing this problem, we consider the linear multitarget (LM) IPDA, which is a linear approximation of the data association in JIPDA. Here, we formulate it as a Poisson point process (PPP) approximation of the track measurement densities with a particular intensity function. Given our focus on track initialization, we devise how to use the LM approximation on only a subset of the tracks, while the other tracks can be treated as in JIPDA after that. This gives a novel new approximation of the track to measurement data association probabilities which we term LMS.Simulations show that using the LM technique is superior to the PHD filter in terms of posterior track existence probability. Further, it is seen that the PHD as an intensity function in LM performs worse than the original LM in terms of the data association probabilities. The LMS data association probabilities are also shown to typically have better worst-case errors than the original LM and loopy belief propagation (LBP). In terms of the GOSPA metric, initiating tracks on every measurement using LMS gives more reliable and faster track initialization for objects appearing close to already established tracks.