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In this paper, we study the problem of optimal trajectory generation for a team of mobile sensors tracking a moving target using distance-only measurements. This problem is shown to be NP-hard, in general, when constraints are imposed on the speed of the sensors. We propose two algorithms, modified Gauss-Seidel relaxation and linear programming (LP) relaxation, for determining the set of feasible locations that each sensor should move to in order to collect the most informative measurements; i.e., distance measurements that minimize the uncertainty about the position of the target. These algorithms are applicable regardless of the process model that is employed for describing the motion of the target, while their computational complexity is linear in the number of sensors. Extensive simulation results are presented demonstrating that the performance attained with the proposed methods is comparable to that obtained with grid-based exhaustive search, whose computational cost is exponential in the number of sensors, and significantly better than that of a random, toward the target, motion strategy.
Date of Publication: Oct. 2008