A N-dimensional assignment algorithm to solve multitarget tracking

This paper deals with combinatorial optimization in multitarget multisensor tracking. The cornerstone in any multitarget and/or multisensor tracking problem is the data-association problem. The approach retained in this paper deals with the combinatorial complexity; it amounts to solve a multi-dimensional assignment problem. Although this problem is known to be NP-hard, the Lagrangean relaxation provides bounds on the optimal solution by solving successive 2-dimensional assignment problems. Inherited from commonly used methods in operational research, the N-dimensional assignment problem first applied to multisensor tracking by Pattipati et al. (1992) is revisited. Particularly, issues of dummy measurements to model missed detection and false-alarms are carefully studied. General conditions required to formulate the multitarget multisensor tracking as a multi-dimensional assignment are also discussed.