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We present a methodology for optimal target detection in a multi sensor surveillance system. The system consists of mobile sensors that guard a rectangular surveillance zone crisscrossed by moving targets. Targets penetrate the surveillance zone with poisson rates at uniform velocities. Under these conditions we present a motion strategy computation for each sensor such that it maximizes target detection for the next T time-steps. A coordination mechanism among sensors ensures that overlapping and overlooked regions of observation among sensors are minimized. This coordination mechanism is interleaved with the motion strategy computation to reduce detections of the same target by more than one sensor for the same time-step. To avoid an exhaustive search in the joint space of all the sensors the coordination mechanism constrains the search by assigning priorities to the sensors and thereby arbitrating among sensory tasks. A comparison of this methodology with other multi target tracking schemes verifies its efficacy in maximizing detections. "Sample" and "time-step" are used equivalently and interchangeably in this paper.