For critical navigation applications such as aircraft approach and landing, there is a general desire to use multi-constellation global navigation satellite systems (GNSS) to enhance availability and reliability. The Russian Global Navigation Satellite System (GLONASS) is so far the only other constellation nearly as developed as the Global Positioning System (GPS). A thorough characterization of GLONASS signal-in-space errors is beneficial to not only the GLONASS users but also the development of next-generation multi-constellation GNSS integrity monitoring systems such as advanced receiver autonomous integrity monitoring. In this paper, we characterize the nominal GLONASS ephemeris errors (without counting in clock errors) based on the data in the past three years. The ephemeris errors are computed by comparing broadcast ephemerides with precise ones, both of which were obtained from International GNSS Service. The formula for GLONASS global-average rms user range error (URE) has been derived. Anomalous satellite behaviors and bad receiver data are excluded by an outlier filter. Ephemeris errors are characterized with respect to long-term stationarity, resultant user range errors (UREs), mean, spatial correlation, and distribution. The results show that GLONASS broadcast ephemerides have achieved stable sub-meter orbital accuracy, and the traditional assumption of spatial-independent zero-mean Gaussian distribution is not generally valid for ephemeris errors.