Statistical consistency of the data association problem in multiple target tracking

Simultaneous tracking of multiple moving objects extracted from an image sequence is an important problem which finds numerous applications in science and engineering. In this article we conduct an investigation of the theoretical properties a statistical model for tracking such moving objects, or targets. This tracking model allows for birth, death, splitting and merging of targets, and uses a Markov model to decide the times at which such events occur. This model also assumes that the track traveled by each target behaves like a Gaussian process. The estimated tracking solution is obtained via maximum likelihood. One of the contributions of this article is to establish the almost sure consistency to the data association problem by using these maximum likelihood tracking estimates. A major technical challenge for proving this consistency result is to identify the correct track (data association) amongst a group of similar (but incorrect) track proposals that are results of various combinations of target birth, death, splitting and/or merging. This consistency property of the tracking estimates is empirically verified by numerical experiments. To the best of our knowledge, this is the first time that a comprehensive study is performed for the large sample properties of a multiple target tracking method. In addition, the issue of how to quantify the confidence of a tracking estimate is also addressed.