In multitarget tracking, we start with time evolving sets of noisy measurements of detected targets and false alarms, and we sequentially associate the detections over time to form multiple target tracks. With one class of track estimators, termed Multiple Hypothesis Trackers (MHT's) [1,2], this is accomplished by considering all hypothesized track sets. A Maximum A Posterior (MAP) criterion, which is commonly used to compare hypotheses, can account for missed detections and false alarms. MAP costs are computed using Kalman filter generated innovations and a priori track set probabilities. The principal disadvantage of MHT is that the number of hypothesized track sets to be evaluated increases exponentially with time. An effective alternative approach is based on conditional mean estimation of the target states. The class of resulting tracking algorithms is referred to as Bayesian. Single [3] and multiple [4] target Bayesian algorithms have been developed. Since the conditional mean is computed as a weighted sum of the means conditioned on each hypothesized track set, Bayesian algorithms incur the same computational burden as MHT. MHT and Bayesian tracking algorithms are sometimes referred to as measurement and track based, respectively, since the former algorithms associate measurements while the latter tend to extend existing tracks.
Numerous approaches to hypothesis pruning and merging have been developed to reduce the computational burden of MHT and Bayesian trackers. Two basic approaches are measurement and likelihood gating, which have been proposed in both MHT [1,2], and Bayesian [3,4], algorithms. A shortcoming of both gating and likelihood based pruning is that the optimum track can be dropped, for example, during a target maneuver or after a few missed detections. Track merging is implemented in practical, suboptimal Bayesian single track estimators. For a single track, Singer et al. [3] suggest merging all tracks that share measurements for the past N times. The Probabilistic Data Association Filter (PDAF) [5], an approximate Bayesian tracker, has been interpreted as the N=0 case. Joint PDAF (JPDAF) [6], which extends PDAF to multitarget tracking, time-recursively extends multiple existing tracks which share measurements in their pruning gates. JPDAF, like other suboptimum trackers, can generate diverged tracks during target maneuvers or after a few missed detections. The Viterbi MHT algorithm [7] uses a trellis diagram formulation and a generalized Viterbi algorithm to manage pruning and merging, in the context of multitrack MAP based MHT, so as to keep a certain number of less likely tracks which could later become optimum. This approach can reduce the occurrence of dropped and diverged tracks. Allowance for an unknown and possibly time-varying number of tracks can be made within the context of either MHT or Bayesian multitarget tracking. For a fixed number of tracks, within an optimum MHT framework, this has been accomplished [2] by employing a MAP cost for hypothesized track-sets which represent different numbers of tracks. Although in that reference the number of tracks was assumed constant over the processing interval, this approach can be generalized to allow for a changing number of tracks. Generally, the number-of-tracks estimation problem can be viewed as a model order selection problem [8], and methods from the statistical and signal processing literature can be considered for adaptation for multitarget tracking. In this paper we consider what is termed a "Bayesian" model selection approach, which leads to algorithms that extend the MAP MHT approach [2]. Furthermore, we employ the Viterbi MHT algorithm to control computational requirements through managed pruning and merging.