Paul J. Cefola

Refining Space Object Radiation Pressure Modeling with Bidirectional Reflectance Distribution Functions

High-fidelity orbit propagation requires detailed knowledge of the solar radiation pressure on a space object. The solar radiation pressure depends not only on the space object’s shape and attitude, but also on the absorption and reflectance properties of each surface on the object. These properties are typically modeled in a simplistic fashion, but are here described by a surface bidirectional reflectance distribution function. Several analytic bidirectional reflectance distribution function models exist, and are typically complicated functions of illumination angle and material properties represented by parameters within the model. In general, the resulting calculation of the solar radiation pressure would require a time-consuming numerical integration. This might be impractical if multiple solar radiation pressure calculations are required for a variety of material properties in real time; for example, in a filter where the particular surface parameters are being estimated. This paper develops a method...

Reentry Time Prediction Using Atmospheric Density Corrections

Errors in the upper atmosphere density models have a significant influence on the accuracy of orbit prediction and, specifically, on the accuracy of the prediction of the reentry time of space objects. The determination of current time corrections to the atmosphere density and their use in orbit prediction are proposed as a method for increasing the accuracy of reentry time prediction. The potential effect of increasing the accuracy of space object reentry time prediction, associated with accounting for the corrections to the Naval Research Laboratory MSIS-00 atmosphere density model, is estimated for space objects having both spherical and nonspherical shapes. The results show that the reentry time predictions obtained using this approach are significantly improved. The improvement is better for spherical objects than arbitrary shaped objects due to the time varying nature of the ballistic coefficient of arbitrary shaped objects. The use of the atmospheric density corrections provides insight into the time variations of individual space object aerodynamic characteristics and allows their use in predicting the reentry time.

Entropy-Based Space Object Data Association Using an Adaptive Gaussian Sum Filter

This paper shows an approach to improve the statistical validity of orbital estimates and uncertainties as well as a method of associating measurements with the correct resident space objects and classifying events in near realtime. The approach involves using an adaptive Gaussian mixture solution to the Fokker-Planck-Kolmogorov equation for its applicability to the resident space object tracking problem. The Fokker-Planck-Kolmogorov equation describes the time-evolution of the probability density function for nonlinear stochastic systems with Gaussian inputs, which often results in non-Gaussian outputs. The adaptive Gaussian sum lter provides a computationally ecient and accurate solution for this equation, which captures the non-Gaussian behavior associated with these nonlinear stochastic systems. This adaptive lter is designed to be scalable, relatively ecient for solutions of this type, and thus is able to handle the nonlinear eects which are common in the estimation of resident space object orbital states. The main purpose of this paper is to develop a technique for data association based on entropy theory that is compatible with the adaptive Gaussian sum lter. The adaptive lter and corresponding measurement association methods are evaluated using simulated data in realistic scenarios to determine their performance and feasibility.

Deep Resonant GPS-Dynamics Due to the Geopotential

On time scales of interest for mission planning of GNSS satellites, the qualitative motion of the semimajor axis and the node evolves primarily from resonances with the Earth’s gravitational field. The relevant dynamics of GPS orbits, which are in deep 2 to 1 resonance, is modeled with an integrable intermediary that depends only on one angle, the stroboscopic mean node, plus a two degrees of freedom perturbation that is factored by the eccentricity. Results are compared with long-term runs of the GTDS DSST showing very good agreement.

On the Computation of the Hansen Coefficients

The Hansen coefficients are one of the most important tools in the analytical or semi-analytical methods of celestial mechanics. The problem of efficient computation was investigated in detail in many papers, but this subject is still open and to date there are not standard algorithms to generate the Hansen coefficients with accuracy and good computation time. Although the analytical expressions are known through their accuracy, the formulation by recurrent relations was preferred due to their stability and applicability in the case when a large number of the Hansen coefficients are needed. In this paper we turn our attention to the polynomial approximations and we present a method to generate the polynomials associated to the Hansen coefficients and their derivatives in the particular case used in expression of disturbing function due to central-body. Using the recurrent formulas corresponding to this particular case, we define difference equations and, by their iteration, we generate the polynomials. By computational tests, we compare our polynomial approximations for the Hansen coefficients and their derivatives with the recurrent solutions in order to prove the non-regression of the accuracy and the gain in computation time.