The linear multitarget IPDA and its application on only a subset of the tracks

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.