Mean Performance Optimization of an Orbiting Distributed Aperture by Warped Aperture Image Plane Comparisons

摘要

This work models the aggregate performance of satellite receiver formations functioning as orbiting interferometers as compared to filled apertures of similar geometries. These models facilitate selecting initial conditions for formations such that their control-free dynamics yield interferometry performance with minimal errors as compared to the filled apertures. The solution method draws on the dynamic models of an orbiting planar satellite formation to define the size and shape of a reference aperture and to define the degrees of freedom for the formation members. The paths of formation elements yield geometries for which the aggregate performance of the array of discrete receivers may be calculated. The objective of the optimization process is therefore minimizing the time-average square of the difference between the filled aperture's intensity map and that generated by the discrete receiver array. This yields a formation whose configuration offers minimum errors for imaging processes beginning at any arbitrary start time. The problem as posed is non-convex, and requires implementation of a global search method. Genetic algorithms are used. The solution method includes a new analytic solution for the intensity map of an elliptical aperture and a technique for generalizing this solution to include the effect of non-ideal viewing geometries.