Common estimation of time scales and orbits of navigation satellites

As is known, the highest accuracy of coordinate determinations based on radio observations of navigation spacecraft  (NSC) is achieved by using, in addition to code measurements, also phase measurements of navigation radio signals. The main disadvantage of phase measurements is the integer ambiguity of the phase of the navigation signal, as well as its abrupt changes or disruptions. Earlier, the authors developed a method of normalization of onboard time scales (TS) based on the model of the rubidium frequency standard and the application of the Stratonovich filter to onboard TS. As a result of applying the filter, a continuous and smooth series of corrections to the onboard time scale of the NSC is obtained, the use of which in processing navigation satellite measurements reduces the number of pseudo-phase disruptions of the carrier navigation radio signal [1].

Earlier, the authors showed [2, 3] that the standard means of maintaining the onboard time scale of the NSC can lead to erroneous definitions of integer phase ambiguity and, as a consequence, to a decrease in positioning accuracy. The proposed algorithm for normalization of onboard scales avoids such errors. As it was shown by the authors, the existing jumps at the biginning of the day and many intraday jumps do not reflect the real course of the onboard clock, but are the result of incorrect processing. To improve the corrections of the NSC clock, various researchers have proposed various methods of improvement [4, 5], however, they all propose to eliminate jumps in manual mode, which is an obstacle to their practical use when processing large arrays of observations. The authors proposed an algorithm for eliminating these errors in automatic mode. In addition to determining the global quadratic trend and using the Stratonovich filter, which is assumed in one form or another by all the proposed methods for improving the clock, we have made an assumption about the presence of unaccounted local linear trends. As a result of applying the algorithm, a continuous series of corrections is obtained for the onboard time scale of the navigation spacecraft. As a result of the analysis, the effectiveness of the proposed algorithm for normalization of on-board time scales of the NSC based on structural analysis is shown. The application of the algorithm makes it possible to eliminate errors in determining the integer ambiguity of the phase of the navigation signal and, consequently, positioning errors when using the absolute method of determining the coordinates of points from GNSS observations [3].

However, the normalization of only the TS of the NSC without taking into account its orbit is incomplete, since the TS and the orbits of the NCA are determined jointly, and correlate with each other. As experience shows, it is difficult to separate the errors of the position of the NSC and its TS. Thus, the independently estimated NSC TS may contain errors in the positions of the NSC in orbit. Thus, in order to obtain consistent corrections of the TS of the TSC and its ephemerides, it is necessary to perform a joint estimation of the TS and the orbit of the apparatus. The paper proposes a new joint algorithm for estimating the SW and the orbit of a navigation spacecraft based on the Stratonovich filter for the TS, as well as an analytical model of the orbital motion of the spacecraft proposed in [6]. As is known, numerical methods for determining the orbits of the NCA are widely used at present. The analytical model of the orbital motion of the navigation device has one important advantage. Unlike the numerical model, it provides smoothness of the NSC ephemeris over a long, several-day time interval, which further increases the reliability of determining the pseudophase of the carrier signal.