Exact Algorithm for Sparse Multitarget Multisensor Tracking

Abstract

A generalization of single target single sensor tracking is the Multitarget Multisensor Tracking (MTMST) problem in which noisy measurements are made by an arbitrary number of spatially diverse sensors. The objective is to nd the most likely true positions of several targets by associating the measurements from di®erent sensors. The data association problem arising from MTMST is often modeled as a Multidimensional Assignment Problem (MAP). This is an extension of the two-dimensional assignment problem (2AP) in which we wish to nd an optimal matching of elements between two mutually exclusive sets. Although the 2AP has been shown to be solvable in polynomial time, MAP's with dimensions higher than two are NP-complete. This work presents a branch and bound approach for solving MAP's with cost arrays generated from MTMST simulations. Depending on the number and locations of the sensors, we can often ignore measurement to target associations that are feasible but highly unlikely. The result is an MAP with a sparse cost array. Our branch and bound algorithm takes advantage of this cost structure to e±ciently nd an optimal without having to explore unlikely solutions. We show that this approach signi cantly improves upon previous exact algorithms for sparse MAP's.