Code pseudorange measurements of the Chinese GNSS BeiDou reveal variations which result in code–phase divergences of more than 1 m. We have analyzed these delay variations based on observation data of the International GNSS Service and its Multi-GNSS Experiment campaign. Our results confirm that these code variations are elevation-dependent when observed by receiving antennas on the earth’s surface. In addition, we found significant differences between two groups of satellites and among carrier frequencies. These delay variations have only little effects on absolute BeiDou positioning using broadcast ephemerides due to the limited accuracy of the obtainable positions. But, all precise applications which use code measurements are severely affected. These applications include, e.g., certain algorithms used in Precise Point Positioning (PPP), especially PPP ambiguity fixing and single-frequency PPP based on the ionosphere-free code–carrier combination. We developed a correction model and determined correction parameters in order to accommodate these symptoms. Application examples demonstrate the successful mitigation of these code pseudorange variations.

GPS code pseudorange measurements exhibit group delay variations at the transmitting and the receiving antenna. We calibrated C1 and P2 delay variations with respect to dual-frequency carrier phase observations and obtained nadir-dependent corrections for 32 satellites of the GPS constellation in early 2015 as well as elevation-dependent corrections for 13 receiving antenna models. The combined delay variations reach up to 1.0 m (3.3 ns) in the ionosphere-free linear combination for specific pairs of satellite and receiving antennas. Applying these corrections to the code measurements improves code/carrier single-frequency precise point positioning, ambiguity fixing based on the Melbourne–Wübbena linear combination, and determination of ionospheric total electron content. It also affects fractional cycle biases and differential code biases.

GNSS satellite and receiving antennas exhibit group delay variations (GDV), which affect code pseudorange measurements. Like antenna phase center variations, which affect phase measurements, they are frequency-dependent and vary with the direction of the transmitted and received signal. GNSS code observations contain the combined contributions of satellite and receiver antennas. If absolute GDV are available for the receiver antennas, absolute satellite GDV can be determined. In 2019, an extensive set of absolute receiver antenna GDV was published and, thus, it became feasible to estimate absolute satellite antenna GDV based on terrestrial observations. We used the absolute GDV of four selected receiver antenna types and observation data of globally distributed reference stations that employ these antenna types to determine absolute GDV for the GPS, GLONASS, Galileo, BeiDou, and QZSS satellite antennas. Besides BeiDou-2 satellites whose GDV are known to reach up to 1.5 m peak-to-peak, the GPS satellites show the largest GDV at frequencies L1 and L5 with up to 0.3 and 0.4 m peak-to-peak, respectively. They also show the largest satellite-to-satellite variations within a constellation. The GDV of GLONASS-M satellites reach up to 25 cm at frequency G1; Galileo satellites exhibit the largest GDV at frequency E6 with up to 20 cm; BeiDou-3 satellites show the largest GDV of around 15 cm at frequencies B1-2 and B3. Frequencies L2 of GPS IIIA, E1 of Galileo FOC, and B2a/B2b of BeiDou-3 satellites are the least affected. Their variations are below 10 cm.

The code observable of global navigation satellite systems (GNSS) is influenced by group delay variations (GDV) of transmitter and receiver antennas. For the Global Positioning System (GPS), the variations can sum up to 1 m in the ionosphere-free linear combination and thus can significantly affect precise code applications. The contribution of the GPS transmitters can amount to 0.8 m peak-to-peak over the entire nadir angle range. To verify the assumption of their time-invariance, we determined daily individual satellite GDV for GPS transmitter antennas over a period of more than two years. Dual-frequency observations of globally distributed reference stations and their multipath combination form the basis for our analysis. The resulting GPS GDV are stable on the level of a few centimeters for C1, P2, and for the ionosphere-free linear combination. Our study reveals that the inconsistencies of the GDV of space vehicle number (SVN) 55 with respect to earlier studies are not caused by temporal instabilities, but are rather related to receiver properties.

Group delay variations (GDV) of GNSS satellite and receiver antennas affect GNSS code pseudoranges. GDV are frequency-dependent and vary with signal transmission and receiving direction due to direction-dependent properties of the satellite and receiver antennas. Since GNSS code measurements contain both the GDV of the satellite and that of the receiver antenna, the exact separation of both parts is a special challenge. It only becomes possible if absolute GDV are available for one of the antennas. Based on absolute GDV of four receiver antenna types (Wübbena et al. 2019), observations of terrestrial reference stations, and the code-minus-carrier linear combination, we estimated GDV for a large part of the satellite antennas of GPS, GLONASS, Galileo, BeiDou, and QZSS (Beer et al. 2021). Aside from the BeiDou‑2 satellites, whose GDV are known to amount to 1.5 m, GPS satellites show the largest variations of several decimeters on frequencies L1 und L5, and also the largest satellite-to-satellite variations within a constellation. The GDV at frequency bands L2, E1, and B2a/B2b of GPS IIIA, Galileo, and BeiDou-3 satellite antennas, respectively, stay below 10 cm and are the least affected. It is shown that terrestrial observations of one orbit period are sufficient to estimate the GDV of each satellite antenna for its entire nadir angle range, and that orbit periods of several sidereal days significantly facilitate data acquisition. Wübbena G, Schmitz M, Warneke A (2019) Geo++ absolute multifrequency GNSS antenna calibration. EUREF AC workshop, Warsaw, Poland. http://www.geopp.com/pdf/gpp_cal125_euref19_p.pdf Beer S, Wanninger L, Heßelbarth A (2021) Estimation of absolute GNSS satellite antenna group delay variations based on those of absolute receiver antenna group delays. GPS Solut 25, 110 (2021). https://doi.org/10.1007/s10291-021-01137-8