Geospatial Representation, Analysis and Computing Using Bandlimited Functions.

摘要

Space surveillance, navigation of aircraft and missiles require detailed representations of gravity and efficient methods for determining orbits and trajectories. However, many of the current mathematical representations and associated numerical algorithms were developed at the beginning of the computer era and are not efficient on today's computers. Under this grant new, computationally efficient, localized representations of gravity have been developed and tested. As a step in developing a new approach to estimating gravitational potentials, a multiresolution representation for gravity estimation has been proposed. New near optimal quadratures for integration on the sphere have been developed. These quadratures (with many additional applications) also yield a new method of interpolation on the sphere and will play a role in solving multiresolution estimation problem. New ODE integrators for orbit and trajectory calculations were developed and have been transferred to the Air Force. New integrators reduce the number of evaluations of the gravity forces and have improved stability while retaining accuracy and speed of the traditional integrators.