Jake Gunther, Utah State University; Todd K. Moon, Utah State University; Charles Swenson, Utah State University
Keywords: Space Situational Awareness, Orbit Estimation, Orbit Refinement, Orbit Estimation from Doppler Frequency Observation
Abstract:
This paper addresses the problem of orbit estimation. The focus here is on satellites orbiting Earth, but the proposed concepts apply in any setting where satellite motion is described by a parameterized model. We use the SGP4 orbit propagator to compute satellite trajectories and take the TLE values as the model input parameters. Therefore, in this work orbit estimation amounts to computing TLE values from data observed at multiple ground sites and incorporating data observed on multiple overpasses.
Our method is characterized by several useful features. First, the method continuously maintains parameter estimates, updating and re-estimating orbit parameters (TLEs) on each overpass. Such autonomy is useful because it reduces or eliminates dependence on organizations that maintain TLE catalogs. Furthermore, TLEs get “stale” in the sense that the orbit trajectory errors grow with time elapsed since the TLEs were last updated. Therefore, continuously updating TLEs to agree with observed data keeps TLEs “fresh” and able to accurately predict satellite motion.
Satellite motion is encoded in the Doppler frequency shift experienced by a signal transmitted from a satellite in orbit and observed at a ground station on Earth. Our method exploits that encoding to recover the TLE parameters. Following an optimization procedure, we find the TLE parameters that cause SGP4 to produce overpasses whose geometry most faithfully explains the observed Doppler shifts at multiple ground sites and at multiple times. Our figure of merit for assessing accuracy is determined by measuring residual Doppler frequency offsets in a Doppler-corrected received signal. The rationale for assessing accuracy in this way is based on the reverse implication that perfect Doppler correction over an entire overpass could only be achieved if SGP4 produced an orbit geometry that matched the actual satellite trajectory, and SGP4 could only produce the correct orbit geometry if the input TLE parameters were “correct”. Any other condition would lead to residual Doppler offset. Thus residual doppler offset accumulated over an overpass is the figure of merit for assessing the quality of TLE parameters. Ambiguities in the mapping between TLEs and orbital geometry can be eliminated by fusing measurements from multiple ground sites and from multiple overpasses. The residual doppler offset is a complicated function of the TLE parameters. Our optimization method uses the Nelder-Mead technique which locally minimizes a function using only function evaluations, i.e. no derivative calculations are needed.
Our method for orbit estimation requires the satellite to transmit a signal while passing over a ground site. In this work, we assume that the signal is a pure tone with a known frequency. In general, Doppler frequency offsets may be computed for an unknown signal provided the center frequency is known. Because estimating the center frequency of an unknown signal is possible, the proposed method may be applied to estimate orbits for uncooperative satellites. Requiring the satellite to transmit a signal may seem like a disadvantage. However, satellites often do transmit to downlink data to an Earth station. Some satellites transmit beacon signals to accomplish scientific missions such as probing the Ionosphere. This is the application in which the authors encountered the need for highly accurate and ongoing orbit estimation. Only by correctly removing so called “geometric Doppler” can scintillation parameters such as S4 and Sigma-Phi be computed accurately, and parameters like these are used to characterize the state of the Ionosphere.
The paper presented at the conference explores how the accuracy of orbit estimation is a function of the number of overpasses and the number of ground sites used in orbit estimation. In summary, we have found that increasing the number of orbits and/or the number of ground stations increases the accuracy of orbit estimation. More details will be included in the full paper.
We envision the proposed method for orbit estimation being particularly useful for missions employing small satellites such as cubesats. These spacecraft have low radar cross section and therefore they present a difficult case for traditional methods that use radar to estimate the TLEs. Many cubesats are deployed in low Earth orbit (LEO), which is a congested region of space, and radar-based methods can be prone to errors when detecting and tracking small, fast moving objects.
Date of Conference: September 27-20, 2022
Track: Astrodynamics