А.S. Pustoshilov – Post-graduate Student,

Siberian Federal University (Krasnoyarsk)

E-mail: alphasoft@inbox.ru

In various problem of the post-processing of navigation information, the final (refined) orbits of navigation satellites are used, which are calculated by various analytical centers. The final orbits of the satellites of the global navigation systems are available in daily  intervals and contain information about the satellite ephemeris (X, Y, Z coordinates and the time point to which these coordinates belong) with a time step of 15 minutes. When combining such daily intervals, anomalies in the orbits of navigation satellites can be observed. The purpose of this work: to provide statistics on such anomalies for GLONASS navigation satellites. A method is proposed for detecting small (with an amplitude of the order of 10-11 relative to typical values of the initial data) anomalies in sparse data series by approximation by high degree polynomials. The main problem in the practical application of the method was to over-come the effect of numerical instability in the construction of the corresponding discrete orthogonal polynomials of high degrees. The effectiveness of this method is demonstrated by the example of the final orbits of the GLONASS navigation satellites. The article demonstrates anomalies («jumps», «outliers») at the day boundary. The values of the observed anomalies in most cases fluctuate within a few centimeters, and, in rare cases, reach several meters. Statistics of detected anomalies from January 1, 2010 to December 31, 2018 for the final orbits of the GLONASS satellites calculated by the analytical centers of the IAC PNT, CODE, IGS, ESA are presented. The proposed method can be used for an independent assessment of the quality of the final orbits, as well as in other areas, for finding anomalies in sparse rapidly changing data series describing sufficiently smooth functions.

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