An analysis of a satellite surveillance system
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A new procedure is proposed to evaluate the effectiveness of surveillance satellites in circular orbits. It is assumed that the times of target detections by the satellite are given by a nonhomogeneous Poisson process with detection rate at time t of p(t) = f(lambda(t), Beta sub 1 (t), Beta sub 2 (t)), where lambda(t) is the angular distance between the target and subsatellite point, Beta sub 1(t) is great circle bearing from the target to the subsatellite point, and Beta sub 2(t) is great circle relative bearing from the subsatellite point to the target. In some circumstances, the dependence of p(t) on Beta sub 2(t) and Beta sub 2(t) can be ignored, making p(t) only a function of lambda(t). Then the probability of target detection on a single satellite pass becomes a function of only the minimum angular distance, or lateral range, between the target and subsatellite point. A numerical method using Newton's method is developed for computing the local minimum of lambda(t). Probabilities of detection using this procedure are compared to those computed with existing methods of Wertz and Washburn.
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