Coarse Initial Orbit Determination for a Geostationary Satellite Using Single-Epoch GPS Measurements

Abstract

A practical algorithm is proposed for determining the orbit of a geostationary orbit (GEO) satellite using single-epoch measurements from a Global Positioning System (GPS) receiver under the sparse visibility of the GPS satellites. The algorithm uses three components of a state vector to determine the satellite’s state, even when it is impossible to apply the classical single-point solutions (SPS). Through consideration of the characteristics of the GEO orbital elements and GPS measurements, the components of the state vector are reduced to three. However, the algorithm remains sufficiently accurate for a GEO satellite. The developed algorithm was tested on simulated measurements from two or three GPS satellites, and the calculated maximum position error was found to be less than approximately 40 km or even several kilometers within the geometric range, even when the classical SPS solution was unattainable. In addition, extended Kalman filter (EKF) tests of a GEO satellite with the estimated initial state were performed to validate the algorithm. In the EKF, a reliable dynamic model was adapted to reduce the probability of divergence that can be caused by large errors in the initial state.

Proposals for Surmounting Sensor Noises

“…Xiong et al addressed systematic centroid errors and poor attitude accuracy by augmenting star trackers with an image intensifier [ 6 ]. Kim et al proposed an algorithm for determining the orbit of a geostationary satellite using single-epoch measurements from a global positioning system receiver with sparse visibility of the global positioning system satellites [ 7 ]. Takayama illustrated weaknesses with global navigation system signals and proposed novel sensor noise models used to enhance sensor sensitivity [ 8 ].…”

Proposals for Surmounting Sensor Noises

“…Xiong, et al addressed systematic centroid errors and poor attitude accuracy by augmenting star trackers with an image intensifier [5]. Kim, et al proposed an algorithm for determining the orbit of a geostationary satellite using single-epoch measurements from a global positioning system receiver with sparse visibility of the global positioning system satellites [6]. Takayama illustrated weaknesses with global navigation system signals and proposed novel sensor noise models used to enhance sensor sensitivity [7].…”