In this paper, we consider the design of minimum time maneuvers for multi-spacecraft interferometric imaging systems. We show that the process of image formation in a multi-spacecraft interferometric imaging system is analogous to painting a "large disk" with smaller "paintbrushes", while maintaining a minimum thickness of paint. We show that spiral maneuvers form the dominant set for the painting problem. Further, we frame the minimum time problem in the space of spiral maneuvers and obtain the Double Pantograph Problem. We show that the solution of the Double Pantograph Problem is given by the solution to two associated linear programming problems. We illustrate our results through an imaging example where the image of a fictitious exo-solar planet is formed using the maneuver prescribed by the Double Pantograph Problem.
The problem of quantifying minimum acceptable performance of multi-spacecraft interferometric imaging systems is considered. The noise corrupting the measurements is critical in the design of these systems and is dependent on the motion of the constituent spacecrafts.
Minimum acceptable performance is defined in terms of the misclassification error of an image given that the set of images has been partitioned into two distinct classes. Two measures of the noise corrupting the measurements are considered: mean squared error(MSE) and the worst case error(WCE). It is shown that these are consistent with the goal of image classification in the sense that as image estimates converge in the MSE/WCE sense, the probability
of misclassifying the image tends to zero. Error bounds are obtained on the MSE/WCE such that some minimum acceptable performance, in terms of the probability of correctly classifying an image, is acheived. An example is presented where the bandedness of the image of a planet is sought to be detected. Bounds on the noise corrupting the measurements are obtained such that a pre-specified level of performance is achieved for this case.
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