A Numerical Study of Some Data Association Problems Arising in Multitarget Tracking

The central problem in multitarget/multisensor 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. This data association problem is formulated in this work as a multidimensional assignment problem. These NP-hard data association problems are large scale, have noisy objective functions, and must be solved in real-time. A class of Lagrangian relaxation algorithms has been developed to construct near-optimal solutions in real-time, and thus the purpose of this work is to demonstrate many of the salient features of tracking problems by using these algorithms to numerically investigate constant acceleration models observed by a radar in two dimensional space. This formulation includes gating, clustering, and optimization problems associated with filtering. Extensive numerical simulations are used to demonstrate the effectiveness and robustness of a class of Lagrangian relaxation algorithms for the solution of these problems to the noise level in the problems.