Tracking Multiple Objects with Particle Filtering

Multitarget tracking (MTT) deals with the state estimation of an unknown number of moving targets. Available measurements may both arise from the targets if they are detected, and from clutter. Clutter is generally considered as a model describing false alarms. Its (spatio-temporal) statistical properties are quite different from those of the target, which makes the extraction of target tracks from clutter possible. To perform MTT the observer can rely on a huge amount of data, possibly collected on multiple receivers. Elementary measurements are receiver outputs, e.g., bearings, ranges, time-delays, Dopplers, etc. The main difficulty, however, comes from the assignment of a given measurement to a target model. These assignments are generally unknown, as are the true target models. This is a neat departure from classical estimation problems. Thus, two distinct problems have to be solved jointly: the data association and the estimation. The simplest approach is probably the nearest neighbor approach. Using only the observation the closest to the predicted state, this algorithm is not robust enough in many situations. As long as the association is considered in a deterministic way, the possible associations must be exhaustively enumerated. This leads to an NP-hard problem because the number of possible associations increases exponentially with time, as in the multiple hypotheses tracker (MHT) [1]. To cope with this problem, pruning and gating eliminate the less likely hypotheses but can unfortunately eliminate good ones as well. In the joint probabilistic data association filter (JPDAF) [2], the association variables are considered as stochastic variables and one needs only to evaluate the validated association probabilities at each time step. However, the dependence assumption on the associations implies the exhaustive enumeration of all possible associations at the current time step. When the association variables are instead supposed statistically independent like in the probabilistic MHT (PMHT [3, 4]), the complexity is reduced. For instance in [3, 4], the algorithm is presented as an incomplete data problem solved by an EM algorithm. There is no measurement gating as in the JPDAF and all the associations are considered. The results are then satisfactory when the measurement equation is linear and when the trajectories are deterministic. In [5] the algorithm is extended to the tracking of maneuvering targets with an hidden “model-switch” process controlled by a Markov probability structure. A comparison of the PMHT with the JPDAF is described in a practical two-target scenario in [6], focusing on the mean-square estimation errors and the percentage of lost tracks. Unfortunately, the above algorithms do not cope with nonlinear models and non-Gaussian noises.