The combinatorial optimization problem of multidimensional assignment has been treated with renewed interest because of its extensive application in target tracking, cooperative control, robotics and image processing. In this work, we particularly concentrate on data association in multisensor-multitarget tracking algorithms, in which solving the multidimensional assignment is an essential step. Current algorithms generate good suboptimal solutions to these problems in pseudo-polynomial time. However, in dense scenarios these methods can become inefficient because of the resulting dense candidate association tree. Also, in order to generate the top m (or ranked) solutions these algorithms need to solve a number of optimization problems, which increases the computational complexity significantly.
In this paper we develop a Randomized Heuristic Approach (RHA) for multidimensional assignment problems with decomposable costs (likelihoods). Unlike many assignment algorithms the RHA does not need the complete candidate assignment tree to start with. Instead, it constructs this tree as required. Results show that the RHA requires only a small fraction of the assignment tree and these results in a considerable reduction of computational cost. Results show that the RHA, on an average, produces better solutions than those produced by Lagrange relaxation-based multidimensional assignment algorithm which has higher computational complexity. Also, using the different solutions obtained in RHA iterations, top m solutions can be constructed with no further computational requirement. These solutions can be utilized in a soft decision based algorithm which performs much better than hard decision based algorithm, as shown in this paper by a ground target tracking example.