We present a methodology for constrained optimal target detection in a multi sensor surveillance system that consists of mobile sensors guarding a rectangular surveillance zone crisscrossed by moving targets. Under the assumption of Poisson arrival statistics for targets a motion strategy is presented for each sensor such that it maximizes target detection for the next T time-steps under the constraint that motion strategies of sensors with higher priorities are fixed. This constrained optimization is resorted to avoid an exhaustive search in the joint space of all the sensors. 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. The coordination mechanism constrains the search by assigning priorities to the sensors and thereby arbitrating among sensory tasks. An extension of this approach to a globally optimal target detection scheme without involving the entire joint space of sensors towards the search is also presented. A comparison of this methodology with other multi target tracking schemes verifies its efficacy in maximizing detections. A tabulation of these comparisons is reported in the results section of this paper. "Sample" and "time-step" are used equivalently and interchangeably in this paper.
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