Statistical characterization of GLONASS broadcast clock errors and signal-in-space errors

With more than 70 navigation satellites orbiting the Earth, global navigation satellite systems (GNSS) users are fascinated to use multiple constellations to enhance positioning availability, accuracy, integrity, continuity, and robustness. As the Russian Global'naya Navigatsionnaya Sputnikovaya Sistema (GLONASS) has fully restored its constellation, not only does a combination of GLONASS and the Global Positioning System (GPS) attract ever-increasing multi-constellation-based navigation applications, but it also serves as a ready-made proving ground for various next-generation multi-constellation GNSS integrity monitoring systems. Although both GLONASS and GPS employ the same concept of time-of-arrival positioning, GLONASS is different from GPS in terms of constellation design, signal modulation, ephemeris format, atomic frequency standards, ground monitor facilities, etc. These differences may make GLONASS show a different signal-in-space (SIS) behavior from GPS. A thorough characterization of GLONASS SIS errors helps the development of multi-constellation GNSS integrity monitoring systems such as advanced receiver autonomous integrity monitoring. Broadcast ephemeris and clock errors are two dominant factors in SIS user range errors (UREs). As an extension of our previous paper on broadcast GLONASS ephemeris errors, this paper introduces broadcast GLONASS clock errors and focuses on resultant SIS UREs. Broadcast GLONASS clocks are propagated from validated GLONASS navigation messages, which are generated from all the GLONASS navigation data logged by the International GNSS Service (IGS) volunteer stations. Raw GLONASS clock errors are derived from a comparison between broadcast clocks with the precise clock solutions from three IGS Analysis Centers. Although the three solutions do not agree with each other due to unknown time-variant common biases, we overcome this difficulty via a clock alignment algorithm. The ephemeris errors computed in our previous paper and the aligned clock errors are combined into four metrics of SIS user range errors (UREs). An outlier filter and a few robust statistics techniques are used to cope with anomalous satellite behaviors and data-logging errors. We first analyze long-term stationarity of SIS URE performance to determine the time span for the statistics. The clock errors and SIS UREs in the last three years are then characterized with respect to mean and standard deviation, distribution, correlation among satellites, and geographic dependency. The results show that 1) clock error behavior dominate SIS URE behavior; 2) clock errors and SIS UREs are usually biased and super Gaussian distributed; 3) SIS UREs of different satellites are usually slightly correlated, but the heavy tail of chi-square statistics may imply large UREs occasionally occurring on several satellites simultaneously. These results indicate that the traditional independent, zero-mean Gaussian assumptions for SIS UREs are too ideal. In addition, due to limited geographic distribution of GLONASS ground monitor stations, we observe that SIS URE performance of a satellite is partially dependent on whether the satellite is monitored.