Библиографическое описание:Высокоточное восстановление орбит спутников глобальной навигационной спутниковой системы методом обучения по расширенным SP3-данным : научное издание / А. С. Пустошилов, С. П. Царев. - Текст : непосредственный // Успехи современной радиоэлектроники. - 2017. - № 12. - С. 48-52. - ISSN 2070-0784. Перевод заглавия: High-precision interpolation of the GNSS satellites orbits by machine learning on extended SP3-data
Аннотация:Предложен новый интерполяционный метод, основанный на простейшем варианте машинного обучения, который автоматически адаптируется к любому типу орбит и имеет значительно меньшую (по сравнению с рекомендованными IGS методами интерполяции) среднеквадратичную оценку отклонения между интерполированными точками и фактической спутниковой орбитой. Отмечено, что рассмотренный метод дает СКО = 0,8 см для шеститочечных шаблонов SP3-данных для орбит ГЛОНАСС и СКО = 0,3 см для такого же шеститочечного шаблона для орбит GPS.
Determination of satellite positions at any time is fundamental for GNSS positioning. The information we use in our high-precision interpolation framework are the high-precision ephemerides listed with 15-min intervals and distributed by GNSS Analytic Centers in SP3 format for all GPS and GLONASS satellites. We propose a new interpolation framework which is not limited to a specific choice of interpolating functions (polynomial, trigonometric, etc.) so it automatically adapts to any type of orbits and has a significantly smaller (compared to the interpolation methods recommended by IGS) RMS estimate of the deviation between the interpolated points and the actual satellite orbit. For example, our interpolation method gives RMS = 0,8 cm for 6-point patterns for GLONASS orbits and RMS = 0,3 cm for the same 6-point SP3 data pattern for GPS orbits. Our method is based on a simple version of machine learning and at the learning stage requires extended SP3 data (satellite positions calculated by integration of the equations of satellite motion with small time steps). On this stage, using a fixed position of the target epoch between the SP3 data epochs we find universal interpolation coefficients which fit the extended SP3 data at the target epoch. Such universal interpolation coefficients are supposed to be constant along the orbits for a long period. Then, as soon as the interpolation coefficients for a given target epoch are found, one can use them in a simple way to determine satellite positions directly from SP3 data without the knowledge of extended SP3 data. In order to use the proposed interpolation framework for any target epoch one has to precalculate the interpolation coefficients for a sufficient number of target epochs with small time step and then interpolate the results on the target epoch in question. As the numerical experiments for real IGS data show, the interpolation coefficients in our method can be set constant for at least a year (we used the IGS SP3 data for 2013). The fixed set of interpolation coefficients is valid for all satellites of GLONASS constellation for this period. The same is true for GPS satellite, although due to different orbit radius the interpolation coefficients differ from the coefficients for GLONASS satellites. In this article, we completely investigate the accuracy of our algorithm and the variation of the coefficients of universal interpolation throughout the 6-point interpolation pattern, which is of fundamental practical interest. The insufficient for our purposes precision of Earth orientation parameters distributed by the International Earth Rotation and Reference Systems Service (IERS) and recommended algorithms for their use leads to a notable «numeric jittering» of the interpolation coefficients in our method. This can be compensated by smoothing of the coefficients.
