Periodicity characterization of orbital prediction error and Poisson series fitting Original Research Article

Publicly available Two-Line Element Sets (TLE) contains no associated error or accuracy information. The historical-data-based method is a feasible choice for those objects only TLE data are available. Most of current TLE error analysis methods use polynomial fitting which cannot represent the periodic characteristics. This paper has presented a methodology for periodicity characterization and Poisson series fitting for orbital prediction error based on historical orbital data. As error-fitting function, the Poisson series can describe variation of error with respect to propagation duration and on-orbit position of objects. The Poisson coefficient matrices of each error components are fitted using least squares method. Effects of polynomial terms, trigonometric terms, and mixed terms of Poisson series are discussed. Substituting time difference and mean anomaly into the Poisson series one can obtain the error information at specific time. Four satellites (Cosmos-2251, GPS-62, SLOSHSAT, TelStar-10) from four orbital type (LEO, MEO, HEO, GEO, respectively) were selected as examples to demonstrate and validate the method. The results indicated that the periodic characteristics exist in all three components of four objects, especially HEO and MEO. The periodicity characterization and Poisson series fitting could improve accuracy of the orbit covariance information. The Poisson series is a common form for describing orbital prediction error, the commonly used polynomial fitting is a special case of the Poisson series fitting. The Poisson coefficient matrices can be obtained before close approach analysis. This method does not require any knowledge about how the state vectors are generated, so it can handle not only TLE data but also other orbit models and elements.