**Satellite antenna phase centre corrections**

Global Navigation Satellite System (GNSS) measurements always refer to the *electrical* phase centre of the particular satellite transmitting antenna. The point of reference for describing the motion of a satellite, however, is the centre of mass (CM) of the spacecraft. The vector between those two points needs to be precisely known so that the GNSS measurements can be tied consistently to the satellite’s CM. The electrical antenna phase centre is, however, neither a physical nor a stable point in space. The variation of the phase centre location as a function of the direction of the outgoing signal for a specific frequency is what we call the phase centre variation (PCV). The PCVs are usually given with respect to the *mean* phase centre which is defined as the point for which the phase of the signal shows the smallest (in the sense of least-squares) PCV for a given nadir range. The difference between the position of the mean phase centre and the CM is what we call the phase centre offset (PCO).

**Satellite antenna PCV estimation with NAPEOS**

Satellite antenna PCVs are usually described by piece-wise linear functions of the nadir angle. Besides this rather simple one-dimensional approach, ESOC’s GNSS analysis software, the Navigation Package for Earth Observation Satellites (NAPEOS), provides the option of using a fully normalized spherical harmonic expansion instead. Unlike piece-wise linear functions the representation based on spherical harmonics is physically more meaningful because spherical harmonics are smooth basic functions without any edges. Moreover, they are well-suited to take possible azimuth-dependent PCVs into account. Experiences with the GPS satellite antennas have actually shown that azimuth-dependent PCVs in the order of a few Millimetres have to be expected, presumably due to the certain arrangement of the 12 single antenna elements (Fig. 1).

Fig. 1: Estimated antenna patterns for SVN-62 (left) and SVN-63 (right), the first two satellites of the GPS Block II “follow-on” (Block IIF) series (Dilssner 2011).

**Contributions to the “igs08.atx” antenna phase centre model**

The Navigation Support Office (NSO) has gathered wide-ranging experience in the field of satellite antenna phase centre modelling for GPS, GLONASS and GIOVE (Galileo). As one of our contributions to the International GNSS Service (IGS) antenna model “igs08.atx”, we provided almost 16 years of weekly SINEX files containing satellite-specific PCO estimates for all GPS spacecraft launched between January 1995 and September 2010. The solutions were generated within the frame of the first IGS reprocessing campaign (“repro1”).

Since the repro1 campaign was restricted to GPS-only, we additionally reprocessed more than three years (January 2008 – February 2011) of GLONASS tracking data in order to provide an up-to-date set of consistent satellite antenna PCOs and PCVs for the GLONASS space segment as well. The solution was generated according to a rigorously combined multi-GNSS processing scheme ensuring full consistency between the GPS and the GLONASS system. The station coordinates were aligned to the IGS realisation of the International Terrestrial Reference Frame (ITRF) 2008. The PCOs and PCVs for all receiving antennas as well as for the transmitting antennas of all GPS Block II/IIA/IIR satellites were fixed to their igs08.atx values.

An independent comparison with the results obtained at the Centre for Orbit Determination in Europe (CODE; Switzerland) has shown that there is an excellent agreement between the GLONASS PCV curves of the two analysis centre (AC) clearly below 1 mm (Fig. 2). The PCOs’ vertical components (“z-offsets”) differ by a common bias of around 7 ± 4 cm (Fig. 3). The agreement between the two AC solutions is quite remarkable bearing in mind that the parameters have been estimated with independent software packages using different analysis strategies (Dilssner et al. 2011a).

Fig. 2: Group-specific PCVs from CODE (red) and ESOC (blue) for the GLONASS/GLONASS-M satellite antennas.

Fig. 3: Satellite-specific z-offset estimates from CODE (red) and ESOC (blue).

**Combined ground/space-based data processing**

We analysed more than four years of GPS tracking data acquired by the advanced-codeless BlackJack receivers on-board the low-Earth orbiting (LEO) Jason-1 and Jason-2 spacecraft. The measurements are processed simultaneously along with ground-based GPS data from a globally well-distributed set of IGS tracking stations. Rather than introducing the GPS ephemeris and clocks as fixed quantities into the least-squares analysis and post-fitting the observation residuals for recovering the phase centre characteristics, as proposed by other groups, the orbit and clock parameters of all spacecraft involved are jointly estimated along with the GPS and LEO satellite antenna parameters (Dilssner et al. 2011b).

The inclusion of GPS observables from a LEO receiver at 1336-km altitude into the processing scheme allows determination of the GPS satellite antenna PCVs up to 17° boresight angle without the need of setting up additional troposphere parameters (Fig. 4). Another great benefit is that the orbital scale (mean altitude) of the Jason-1/2 spacecraft is well-determined from the dynamical POD constraint (GM) implying that we do not have to adopt the scale of an external terrestrial reference frame (TRF) solution in order to solve for the PCOs’ vertical components (z-offsets). This makes us independent from other space geodetic techniques like Satellite Laser Ranging (SLR) and Very Long Baseline Interferometry (VLBI) which usually determine the scale of the TRF solution. We are therefore able to derive the GPS satellite antenna z-offsets exclusively from GPS without having to rely upon the SLR and/or VLBI scale (Fig. 5).

Fig. 4: Estimated GPS satellite antenna PCVs from combined ground/space-based data processing vs. IGS standards.

Fig. 5: Estimated GPS satellite antenna z-PCOs from combined ground/space-based data processing vs. IGS standards.