Comparison of Soft and Hard Assignment ML Trackers on Multistatic Data

Abstract

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 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 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 approximated by excision of measurements that are taken by previously-discovered targets.