Vishal Ray, University of Colorado Boulder; Daniel J. Scheeres, University of Colorado Boulder; Suood Alnaqbi, University of Colorado Boulder
Keywords: Atmospheric drag, density, drag-coefficient, orbit determination
Abstract:
Uncertainties in atmospheric density and satellite drag-coefficient are the primary contributors to orbit determination and prediction errors in low altitude low Earth orbit (LEO) satellites. In most orbit determination scenarios, the atmospheric density is modeled using semi-empirical models such as NRLMSISE-00 and JB2008 while the drag-coefficient is estimated as a constant. More sophisticated physics-based models of drag-coefficient exist in literature, but their use have been limited due to the lack of knowledge of input parameters across orbital regimes and space weather conditions. Time-variations in the drag-coefficient, governed by the physics of gas-surface interactions, are usually averaged out by assuming the drag-coefficient to be a constant in the estimation process. This introduces errors in the drag-coefficient obtained through the estimation method. Additionally, errors in the semi-empirical atmospheric density models, especially during active space weather conditions, are absorbed by the drag-coefficient estimate which can lead to a non-physical value. These errors in the drag-coefficient will severely degrade the orbit prediction accuracy. Ideally, the best solution would be to simultaneously estimate time-varying corrections to both the density and drag-coefficient but due to their product form in the drag equation, they are unobservable in the estimation process. A potential method to simultaneously estimate both the parameters was developed by Wright et al. [1] based on Gauss-Markov processes. In this method, both the density and drag-coefficient are modeled as first order Gauss-Markov processes with very different decay time constants. The density is assumed to vary much more rapidly than the drag-coefficient, which allowed the two to be decorrelated in the filter. The method was used by McLaughlin et al. [2] to estimate densities for CHAMP and GRACE. But as pointed out by Mehta [3], the estimation of drag-coefficient did not make a significant impact on the obtained densities and the biases in the two cannot be separated using this method. Moreover, the method ignores high frequency variations in the drag-coefficient due to changes in attitude.
We have developed a framework to simultaneously estimate density and drag-coefficient based on Wrights method of modeling density corrections using Gauss-Markov processes and our Fourier drag-coefficient models [4]. The density corrections are modeled using second-order Gauss-Markov processes since they are more suitable for approximately periodic processes such as the gravitational harmonics. The drag-coefficient is modeled as a Fourier series expansion in the body frame with the Fourier coefficients being estimated in the filter. This allows the time-variations in the drag-coefficient due to changes in attitude to be estimated using tracking data. The estimated Fourier coefficients and gas-surface interaction models are leveraged to calculate the bias term in the filter. Preliminary results show the potential to obtain unbiased densities using our method [5] for inertially stabilized satellites. The method requires the satellite to have attitude variations in order to obtain unbiased densities.
In this work, the developed method will be studied for common satellite shapes, orbital regimes and space weather conditions. The errors in the obtained densities will be quantified as a function of attitude variations for each satellite shape. This can serve as a guideline for future missions as to the magnitude of attitude variations that can be temporarily introduced in the satellite to calibrate the drag model. The method will be validated with real tracking data from the SPIRE satellite. High-fidelity force models will be used to understand what level of accuracy is required to reduce uncertainties on the estimated densities.
[1] J. R. Wright and J. Woodburn, Simultaneous Real-Time Estimation of Atmospheric Density and Ballistic Coefficient, tech. rep., Analytical Graphics, Inc., 2004.
[2] C. A. McLaughlin, A. Hiatt, and T. Lechtenberg, Precision Orbit Derived Total Density,
Journal of Spacecraft and Rockets, vol. 48, no. 1, 2011, pp. 166-174.
[3] P.K. Mehta, Thermospheric density and satellite drag modeling, PhD Dissertation, University of Kansas, 2013.
[4] V. Ray, D. J. Scheeres, S. G. Hesar, and M. Duncan, A drag coefficient modeling approach using spatial and temporal Fourier expansions for orbit determination, Journal of the Astronautical Sciences, 2019. doi: 10.1007/s40295-019-00200-4.
[5] V. Ray, D.J. Scheeres, E.K. Sutton, and M. Pilinski, Density estimation using second-order Gauss Markov processes, AAS/AIAA Astrodynamics Specialist Conference, AAS 21-340, 2021.
Date of Conference: September 14-17, 2021
Track: Atmospherics/Space Weather