Effect of Atmospheric Drag Estimation on Orbit Determination

Abstract

Determining the location of Low Earth Orbit (LEO) satellites in orbit is an important aspect when using them for navigation and performing reentry analysis. A large perturbation in LEO satellite orbits is atmospheric drag due to its orbiting altitude. This variable, unlike gravity, can be difficult to model accurately due to the variations in density and the ballistic coefficient. While in orbit, a satellite equipped with an on-board GPS receiver can malfunction and no longer receive measurements. In this case, the satellite would have to use a dynamic model to propagate its position forward in time to relay to a ground user.

Out of the two deterministic terms in the drag equation, the ballistic coefficient is the larger variable and has many terms that are difficult to determine explicitly. Due to this, it would be advantageous to estimate the ballistic coefficient while in orbit in the case that the satellite loses GPS measurements. From the estimation, the satellite could use that term when calculating atmospheric drag during propagation. This would allow the positioning solution of the satellite to increase in accuracy. With a more accurate satellite position, the ground user's navigation solution would also improve.

This thesis determines the effect the atmospheric drag has on the satellite's orbit by inducing error on the ballistic coefficient. Atmospheric drag is the second-largest perturbation affecting LEO satellites. It is important to understand how LEO satellites behave in the absence of correcting measurements to know the error when using LEO satellite signals for positioning. Throughout this research it was found that while the atmospheric drag is the second-largest perturbation, the gravitational forces are magnitudes larger causing meters of error on the propagation solution. This error in the satellite's orbit translates into meter level error at the ground receiver.

Once the error on the ballistic coefficient was studied, it was decided to attempt to estimate using the GPS measurements. Estimation of the ballistic coefficient has been performed on two-line element data, but has not been performed on GPS measurements. Through this estimation process, it was determined that noise of the GPS measurements greatly outweighed the impact of the ballistic coefficient on the overall position accuracy. With the amount of noise reduced and accurate pole placement, it was indeed found to be possible to estimate the ballistic coefficient to an accuracy of 10\% of the true coefficient.