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Two-point free nonlinear interpolation of coordinates and velocities of navigation satellites from SP3 data

DOI 10.18127/j20700784-201812-30


A.S. Pustoshilov – Post-graduate Student, Siberian Federal University (Krasnoyarsk)
Yu.Yu. Ushakov – Ph.D. (Phys.-Math.), Associate Professor, Siberian Federal University (Krasnoyarsk)
S.P. Tsarev – Dr.Sc. (Phys.-Math.), Professor, Siberian Federal University (Krasnoyarsk)

We extend the previously proposed new free interpolation framework introducing nonlinear terms and astronomical data on lunar and solar tidal forces. The input information of our 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. The proposed free interpolation framework is not limited to polynomial or trigonometric interpolating functions and uses a simple machine learning approach for definition of the interpolation coefficients. It requires extended SP3 data (satellite positions calculated by integration of the equations of satellite motion with small time steps) at the learning stage. 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 use the standard polynomial interpolation to find the positions and velocities on the target epoch in question.
The new nonlinear interpolation framework finds intermediate positions and velocities using only two standard SP3 points with high precision: deviations of the interpolated values and the known satellite orbits and velocities have RMS= 3 mm for positions and RMS = 0,0016 mm/s for velocities. In order to achieve this precision one has to introduce additional terms with luno-solar tidal forces into the framework. This additional required information can be found with sufficient for our purpose precision using the standard GPS (GLONASS) ICD routines. Comparing our interpolation results with the data of other IGS centers for other years we
conclude that the interpolation coefficients in our method can be set constant for several years. This allows one to use the proposed interpolation framework for solution of navigation problems with high precision. The fixed set of interpolation coefficients is valid for all satellites of GLONASS constellation. The same is true for GPS satellite, although due to different orbit radius the interpolation coefficients differ from the coefficients for GLONASS satellites.
The proposed interpolation procedure is numerically stable and shows very little degradation of precision if the input SP3 ephemerides have lower precision (with RMS deviations of the order of few centimeters or decimeters).

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