Mean performance optimization of an orbiting distributed aperture by warped aperture image plane comparisons

This work investigates the aggregate performance of satellite receiver formations functioning as orbiting interferometers as compared to filled apertures of similar geometries. The resulting models facilitate selecting initial conditions for formations such that their control-free dynamics yield interferometry performance with near-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 modelled paths of formation elements yield predictable geometries at any time for which the aggregate performance of the array of discrete receivers may be calculated. The objective of the optimization process is to minimize the time-averaged 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 near-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 genetic algorithms construct populations of generic coefficients, adaptable to the number of degrees of freedom for each proposed formation. The fitness assigned to members of each population is the average aggregate error its formation generates over the simulation duration. 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 effects of non-ideal viewing geometries.