Propagation of CubeSats in LEO using NORAD Two Line Element Sets: Accuracy and Update Frequency

Abstract

Information on the orbital characteristics of satellites and other earth-orbiting objects is made available to the public in the form of two-line element sets (TLEs), published by the North American Aerospace Defense Command (NORAD). TLEs are typically not used alone for applications that require reliable and accurate position determination because TLEs are not accompanied by any indicators of accuracy or consistency. In this paper, we analyze the characteristics of TLE updates for CubeSats in low-Earth orbit (LEO) with respect to both update frequency and accuracy. We use both catalogued TLE data from July 2011 to July 2012 alone in a Monte Carlo analysis as well as compare TLE-only propagation with “truth” on-orbit GPS data from The Aerospace Corporation’s recent satellite mission, the PicoSatellite Solar Cell Testbed 2 (PSSCT-2), which launched in 20 July 2011 and operated until 8 December 2011. In addition to calculating the error statistics between the PSSCT-2 GPS positions and TLE propagated positions using the unusually frequent TLE updates available over the 213.5 minute period of time that GPS data is available, we also calculate error statistics as a function of less frequent TLE updates as well as calculate error statistics using a Monte Carlo simulation for TLE updates. From the latter we find that a CubeSat-class mission operating in a low orbit (under 350 km) using TLE propagation may be able to resolve position determination errors to as low as: in-track with mean = 0.177 km and standard deviation = 0.619 km; cross-track with mean = 0.108 km and standard deviation 0.619 km; and radial with mean = -0.068 km and standard deviation = 0.274 km, for a total mean = 0.832 km and standard deviation = 0.444 km.