Polynomial time algorithm for data association problem in multitarget tracking

The aim of this work is to propose a semigreedy algorithm for solving the data association problem (DAP) arising in multitarget tracking. The DAP is characterized as a maximum weighted set partitioning problem (MWSPP). A semigreedy algorithm that first generates a number of different solutions using a polynomial number of operations and then selects the best among the solutions generated is presented. Theoretically we prove that the value of the solution returned by the algorithm approximates the value of the optimal solution within a guaranteed factor. This factor only depends on the dimension of the sliding window used. Computational experiments indicate that the quality of the solutions returned is quite satisfactory.