<title>Multitarget tracking and multidimensional assignment problems</title>

Abstract

A fundamental problem in multi-target tracking is the data association problem of partitioning the observations into tracks and false alarms so that an accurate estimate of the true tracks can be recovered. Here, this problem is formulated as a multi-dimensional assignment problem using gating techniques to introduce sparsity into the problem, filtering techniques to generate tracks which are then used to score each assignment of a collection of observations to its corresponding filtered track. Problem complexity is further reduced by decomposing the problem into disjoint components using graph theoretic methods. A recursive Lagrangean relaxation algorithm is then developed to obtain high quality suboptimal solutions in real-time. The algorithms are, however, applicable to a large class of sparse multi-dimensional assignment problems arising in general multi-target and multi-sensor tracking. Results of extensive numerical testing are presented for a case study to demonstrate the speed, robustness, and exceptional quality of the solutions.

Multidimensional assignment formulation of data association problems arising from multitarget and multisensor tracking

“…After this review and a refinement of the definition of a partition of the data, the assignment problems are derived in three different ways. This development generalizes the various special and example cases in our earlier work [20,21,22]. A reason for this assignment formulation is that it exhibits a rich structure that can be exploited algorithmically [12,20,23,24].…”

“…The objective function is derived from a composite negative log posterior or likelihood function for each of the tracks of reports. This formulation is of sufficient generality to cover our earlier work [20][21][22][23][24] which used the scoring of Stein and Blackman [7], the popular multiple hypothesis tracking method introduced by Reid [25] and modified by Kurien [17] to include maneuvering targets and terminations, and the work of Deb, Pattipati, Somnath, Bar-Shalom [11] on centralized multisensor data fusion. Other sensor fusion problems that employ multiple hypothesis tracking methods, e.g., the work of C.-Y.…”

“…Our reason for this specific formulation is the recent development of a class of real-time and near-optimal algorithms [12,20,23,24] for solving these multidimensional assignment prob-lems to the noise level in the problem. Also, the current work differs from our earlier work [20,21,22] in the generality of the formulation, derivation of the cost coefficients, and the allowable dynamics.…”

A Survey of Motion-Based Multitarget Tracking Methods

“…The problems of non-Bayesian approaches are two: 1) The computation of heuristic optimization algorithms is time consuming; 2) Non-Bayesian algorithms make hard association decisions at the end of every frame and are characterized by poor performance in the presence of false alarms and in dense target environments [39]. So in practical application, non-Bayesian approaches are restrictedly used.…”

Simultaneous Target and Multipath Positioning

“…In our previous related work [26], Viterbi Data Association (VDA) was proposed as a multi-scan method offering improved performance in clutter over the conventional single-dwell nearest neighbor (NN), joint probabilistic data association filter (JPDAF) [30,40] and 2-D assignment methods [31][32][33], which was originally developed for tracking line-of-sight targets in high levels of backscatter clutter from the ground [28,29]. This application of VDA can be interpreted as a dynamic programing approach to the multiple hypothesis tracking (MHT) problem with a specific "Viterbi Pruning scheme".…”