Statistical characterization of GPS signal-in-space errors

For most Global Positioning System (GPS) standard positioning service (SPS) users, real-time satellite orbits and clocks are derived from predicted ephemeris and clock parameters in broadcast navigation messages. Broadcast ephemeris and clock errors, the differences between the broadcast orbits/clocks and the truth, account for a dominant portion of signal-in-space (SIS) errors. Traditionally, SIS user range errors (UREs) is assumed to follow a zero-mean normal distribution with standard deviation represented by the broadcast user range accuracy (URA). In addition, advanced receiver autonomous integrity monitoring (ARAIM) may rely on an assumption that UREs of different satellites are uncorrected. This paper is intended to examine these assumptions and give a thorough characterization of core SIS error behavior based on the statistics of recent data. The radial, alongtrack, and crosstrack ephemeris errors and clock errors are computed by comparing the broadcast ephemerides/clocks with the precise ones, followed by the generation of instantaneous SIS UREs, global-average SIS UREs, and worst-case SIS UREs. Anomalous satellite behaviors are identified and excluded by an outlier filter. Robust statistics techniques are implemented to avoid the impact of statistical outliers. An analysis of long-term stationarity is first carried out to determine the range of useful data. The SIS errors are then characterized with respect to mean and standard deviation, spatial correlation, normality, relation between rms URE and URA, and correlation among different satellites. The results show that mean of SIS errors are nonzero for several satellites; the radial errors, alongtrack errors, and clock errors are relatively strongly correlated; UREs usually have a non-Gaussian distribution; different satellites have different interpretation of URA; and the UREs of different satellites are slightly correlated.