Autonomous Predictions Realized in Navigation Receivers for the Motion of GLONASS and GPS Spacecraft
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nomous Predictions Realized in Navigation Receivers for the Motion of GLONASS and GPS Spacecraft S. M. Kudryavtseva, * a
Sternberg Astronomical Institute, Moscow State University, Universitetskii pr. 13, Moscow, 119899 Russia *e-mail: [email protected] Received June 5, 2020; revised July 30, 2020; accepted July 30, 2020
Abstract—A new algorithm for autonomous long-term predictions realized in ground navigation receivers for ephemerides of GLONASS and GPS spacecraft is developed and analyzed. The algorithm can be applied to determinations of user’s coordinates, when it is impossible or difficult to receive the spacecraft ephemerides (for example, in conditions of a bad radio-visibility of the satellites). It is shown that the accuracy of the method exceeds similar characteristics of other known solutions. It is also shown that the coefficients, which take account of the solar pressure and are specific for each satellite, differ for different generations of spacecraft. Simultaneously with parameters of the satellite motion, the Earth’s polar coordinates can be determined with the accuracy of several arc milliseconds. Using the autonomous algorithm for predictions of spacecraft ephemerides significantly advances both the search for visible GLONASS and GPS satellites and the first determination of user’s coordinates after “cold” starts of receivers. This article is based on the report presented at the conference Astrometry Yesterday, Today, and Tomorrow, conducted at Sternberg Astronomical Institute, October 14–16, 2019. DOI: 10.1134/S1063772920120057
1. INTRODUCTION Every GLONASS and GPS spacecraft periodically transmits radio signals, which are received by ground navigation receivers. These signals, in particular, announce the time of signal sending and the satellite ephemerides. Receivers compare the time of signal sending (by the spacecraft clock) with the time of signal receiving (by the receiver clock) and calculate the corresponding pseudodistance between the receiver and the spacecraft. (The term pseudo indicates that the clocks used to determine the time of signal propagating are different.) Using pseudodistances calculated by up to four navigation spacecraft, the receiver determines its current location in space and a possible correction to its clock. Satellite ephemerides are sets of orbit elements of GPS spacecraft or rectangular coordinates of GLONASS spacecraft for a certain initial epoch. Using the standard built-in algorithm predicting the spacecraft’s motion, initial ephemerides of each satellite can be used (or reproduced) during a time interval, which does not exceed 4 h for GPS or 30 min for GLONASS spacecraft. Beyond these intervals, the accuracy of the standard algorithm predicting the spacecraft motion sharply descreases. Because of low throughputs of the communication channels (50 b/s), the time spent for one pseudodistance measurement reaches 2 s for GLONASS and 6 s for GPS spacecraft. However, the time used for receiving the complete ephemerides of one satellite reaches
18–36 s. At insufficient
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