Geometrical Variations of Gain Patterns

This paper studies the effect of the altitude and the elliptical nature of the Earth on projected antenna pattern functions (APFs). These variations can play a significant role in spatial filter algorithms, such as the Backus-Gilbert method. In this paper, a solution for projecting an APF from an arbitrary sensor and platform onto an elliptical Earth is presented. A general time integration of this projection is presented, which is important for dynamically generating the effective antenna pattern functions (EAPFs) in cases where the variations are nonnegligible. It is shown that the elliptical nature of the Earth provides a variation of order 1% in the area of the EAPF. These results suggest that approximating the Earth as a sphere is valid. It is also shown that elliptical orbits should consider the implication of the altitude variation before precomputing EAPFs