Comparison of soft and hard assignment ML trackers on multistatic data

About 15 years ago the maximum likelihood probabilistic data association (MLPDA) tracking architecture was proposed; it was found to be a very effective (perhaps the only) way to track very low-observable contacts. The MLPDA is based on maximizing statistical likelihood according to a precise model in which there is no process noise: the target\´s trajectory is deterministic given the parameters (usually initial position and velocity) over which maximization is done. The MLPDA, as above, maximizes the likelihood based upon an assumption - the usual one in target tracking, but perhaps one that is biased toward radar surveillance - that each target can generate at most one contact per scan of data. A dissenting view is from the PMHT (probabilistic multi-hypothesis tracker) perspective, that each contact may be taken as independent and a-priori equally-equipped to be target-generated. As opposed to the MLPDA, for whom associations between measurements and targets ought to be "hard" yes/no decisions, the PMHT have implicit associations that are actually the posterior probabilities of these associations: they are "soft". The original PMHT yields a modified Kalman smoother; here we use the PMHT likelihood function to optimize, as with the MLPDA, and call the resulting algorithm the MLPMHT ("ML" = maximum likelihood). Here we compare the MLPMHT to the MLPDA. Our results indicate that the MLPMHT is the better tracker in multistatic data. Not only is the concept of a "frame" of data less relevant for it than the MLPDA (to frame data over a long ping is suspect) since each measurement is treated independently, and not only is optimization simpler since an EM technique can replace direct optimization after the grid search; but it appears that it both works more robustly and is able to avoid contact starvation during periods of poor SNR. A further advantage of the MLPMHT is that optimal data association with multiple targets is easily incorporated, whereas in the MLPDA it is ap- - proximated by excision of measurements that are "taken" by previously-discovered targets