Novel Signal Processing Techniques for Ballistic Coefficient Prediction

ABSTRACT: Tracking of objects orbiting the Earth is of critical importance for continued safe development and use of space. Particularly important are low Earth orbit (LEO) objects, since these make up the majority of objects in the space catalog. To track these LEO objects, accurate models of the dominant forces are needed. Besides gravity, the dominant force on LEO objects is atmospheric drag and inaccuracies in modeling it are the leading cause of error in orbital prediction. Thus, to improve prediction of orbits for critical missions such as, for example, re-entry and collision avoidance new algorithms are needed to analyze and predict atmospheric drag. Recent advances in modeling atmospheric density have reduced orbital error, but still leave room to improve the calculation by modeling the ballistic coefficient. In this project we propose to develop novel time series analysis algorithms for the analysis and prediction of ballistic coefficient data. The algorithms will be based on recent advances in computational harmonic analysis. These advances allow some types of data to be efficiently represented as the sum of a proper rational function and a sparse trigonometric polynomial. The proper rational function captures sudden changes in the data, while the trigonometric polynomial captures oscillatory behavior. Because these new methods are nonlinear in nature, they are very efficient in representing data, with relatively few parameters. Moreover, they have superior time resolution properties, when compared with wavelet techniques. During Phase I of this project, we will further develop these novel algorithms and specialize them to the problem of analyzing and prediction ballistic coefficient data. To validate the algorithms, we will analyze historical ballistic coefficient data. During Phase II of this project, we will, working closely with Air Force personnel, further develop the algorithms and begin developing software to be integrated into orbital calculations. BENEFIT: Accurate orbital prediction is critical to cataloging artificial objects in space. Of particular interest are low-Earth-orbit (LEO) objects, since these objects comprise the bulk of artificial objects. Besides gravity, atmospheric drag, parameterized by the ballistic coefficient, is the dominate force on LEO objects. Considerable work has gone into modeling drag effects due to density variation, but relatively little work has gone into modeling and predicting surface area variations. These variations cause the ballistic coefficient to vary with time and when not accounted for lead to errors in orbit prediction. With the signal processing algorithms developed in this project, more robust and accurate prediction of ballistic coefficient data will be possible and hence the Air Force will be able to more accurately predict satellite orbit.