Improved antenna phase center models for GLONASS

Abstract

Thanks to the increasing number of active GLONASS satellites and the increasing number of multi-GNSS tracking stations in
the network of the International GNSS Service (IGS), the quality of the GLONASS orbits has become significantly better over
the last few years. By the end of 2008, the orbit RMS error had reached a level of 3–4cm. Nevertheless, the strategy to process
GLONASS observations still has deficiencies: one simplification, as applied within the IGS today, is the use of phase center
models for receiver antennas for the GLONASS observations, which were derived from GPS measurements only, by ignoring the
different frequency range. Geo++ GmbH calibrates GNSS receiver antennas using a robot in the field. This procedure yields
now separate corrections for the receiver antenna phase centers for each navigation satellite system, provided its constellation
is sufficiently populated. With a limited set of GLONASS calibrations, it is possible to assess the impact of GNSS-specific
receiver antenna corrections that are ignored within the IGS so far. The antenna phase center model for the GLONASS satellites
was derived in early 2006, when the multi-GNSS tracking network of the IGS was much sparser than it is today. Furthermore,
many satellites of the constellation at that time have in the meantime been replaced by the latest generation of GLONASS-M
satellites. For that reason, this paper also provides an update and extension of the presently used correction tables for
the GLONASS satellite antenna phase centers for the current constellation of GLONASS satellites. The updated GLONASS antenna
phase center model helps to improve the orbit quality.

KeywordsGLONASS–Multi-GNSS processing–Receiver antenna–Satellite antenna–Phase center modeling–Reference frame–GNSS orbits

Full text

ORIGINAL ARTICLE
Improved antenna phase center models for GLONASS
Rolf Dach
•
Ralf Schmid
•
Martin Schmitz
•
Daniela Thaller
•
Stefan Schaer
•
Simon Lutz
•
Peter Steigenberger
•
Gerhard Wu
¨
bbena
•
Gerhard Beutler
Received: 12 October 2009 / Accepted: 27 March 2010 / Published online: 11 April 2010
 Springer-Verlag 2010
Abstract Thanks to the increasing number of active
GLONASS satellites and the increasing number of multi-
GNSS tracking stations in the network of the International
GNSS Service (IGS), the quality of the GLONASS orbits
has become significantly better over the last few years. By
the end of 2008, the orbit RMS error had reached a level of
3–4 cm. Nevertheless, the strategy to process GLONASS
observations still has deficiencies: one simplification, as
applied within the IGS today, is the use of phase center
models for receiver antennas for the GLONASS observa-
tions, which were derived from GPS measurements only,
by ignoring the different frequency range. Geo?? GmbH
calibrates GNSS receiver antennas using a robot in the
field. This procedure yields now separate corrections for
the receiver antenna phase centers for each navigation
satellite system, provided its constellation is sufficiently
populated. With a limited set of GLONASS calibrations, it
is possible to assess the impact of GNSS-specific receiver
antenna corrections that are ignored within the IGS so far.
The antenna phase center model for the GLONASS satel-
lites was derived in early 2006, when the multi-GNSS
tracking network of the IGS was much sparser than it is
today. Furthermore, many satellites of the constellation at
that time have in the meantime been replaced by the latest
generation of GLONASS-M satellites. For that reason, this
paper also provides an update and extension of the pres-
ently used correction tables for the GLONASS satellite
antenna phase centers for the current constellation of
GLONASS satellites. The updated GLONASS antenna
phase center model helps to improve the orbit quality.
Keywords GLONASS  Multi-GNSS processing 
Receiver antenna  Satellite antenna 
Phase center modeling  Reference frame  GNSS orbits
Introduction
The Globalnaya Navigatsionnaya Sputnikovaya Sistema
(GLONASS; Russian for Global Navigation Satellite
System)—the Russian counterpart of the American Global
Positioning System (GPS)—became important in Global
Navigation Satellite System (GNSS) analyses during the
last few years. Today (May 2009), 20 GLONASS satellites
are active and the satellite constellation has become very
stable with the second generation of GLONASS-M satel-
lites. A number of manufacturers provide combined GPS/
GLONASS receivers. As the GPS/GLONASS tracking
network of the International GNSS Service (IGS, Dow et al.
2009) reached nearly global coverage by the end of 2008, the
quality of the GLONASS orbits is now at a level of 3–4 cm.
R. Dach (&)  D. Thaller  S. Lutz  G. Beutler
Astronomical Institute, University of Bern, Sidlerstrasse 5,
3012 Bern, Switzerland
e-mail: rolf.dach@aiub.unibe.ch
R. Schmid
Forschungseinrichtung Satellitengeoda
¨
sie,
Technische Universita
¨
tMu
¨
nchen, Arcisstrasse 21,
80333 Munich, Germany
M. Schmitz  G. Wu
¨
bbena
Geo?? GmbH, Steinriede 8, 30827 Garbsen, Germany
S. Schaer
Swiss Federal Office of Topography swisstopo,
Seftigenstrasse 264, 3084 Wabern, Switzerland
P. Steigenberger
Institut fu
¨
r Astronomische und Physikalische Geoda
¨
sie,
Technische Universita
¨
tMu
¨
nchen, Arcisstrasse 21,
80333 Munich, Germany
123
GPS Solut (2011) 15:49–65
DOI 10.1007/s10291-010-0169-5

This accuracy level still is about three times lower than
that for the GPS orbits. Dach et al. (2009) showed that the
improvements due to adding GLONASS to GPS observa-
tions are limited to parameters valid for a short time span
(one hour and shorter). For parameters with a longer
validity interval, the uncertainty of the observation mod-
eling absorbs the statistically expected benefit from addi-
tional measurements in the analysis model.
The currently available models for the receiver and
satellite antenna phase center locations limit the achievable
accuracy of GLONASS results. Both categories of anten-
nas will be addressed subsequently, but first of all it is
necessary to describe the data processing strategy used as
the basis for all further experiments in ‘‘Reprocessing of
GLONASS data at CODE’’ .
No distinction is made between the GPS and GLONASS
frequencies for the receiver antennas within the IGS so far.
The GPS-derived corrections are used for the measure-
ments of both GNSS. In ‘‘GNSS-specific receiver antenna
phase center modeling’’, the differences between GNSS-
specific corrections as well as their impact on coordinate
estimates are analyzed.
The phase center corrections (PCC) currently used
within the IGS for the GLONASS satellite antennas
(igs05.atx model, Schmid et al. 2007) also have several
drawbacks. They were computed in early 2006 when
the GLONASS-capable receivers in the IGS network
were mainly located in Europe and when the first two
GLONASS-M satellites were in space only for a short time
span. Since then almost all GLONASS satellites have been
replaced by new generation satellites. Both the number and
the global distribution of GLONASS tracking stations have
been improved significantly since 2006. The number of
different antenna types has also grown significantly. These
developments indicate that an update of the satellite
antenna phase center models for the GLONASS satellites is
badly needed. ‘‘Satellite antenna phase center modeling’’
describes the generation of such models.
The updated receiver and satellite antenna phase center
models are validated in ‘‘Validation of the satellite antenna
phase center models’’ .
Reprocessing of GLONASS data at CODE
CODE, the Center for Orbit Determination in Europe, is a
joint venture of the Astronomical Institute of the University
of Bern (AIUB, Bern, Switzerland), the Swiss Federal
Office of Topography (swisstopo, Wabern, Switzerland),
the Federal Agency for Carthography and Geodesy (BKG,
Frankfurt am Main, Germany), and the Institut fu
¨
r Astro-
nomische und Physikalische Geoda
¨
sie of the Technische
Universita
¨
tMu
¨
nchen (IAPG/TUM, Munich, Germany).
CODE has been one of the global analysis centers of the
IGS since the start of IGS test campaign operations on June
21, 1992. All operational computations are performed at
the AIUB using the development version of the Bernese
GPS Software (Dach et al. 2007). Since May 2003, CODE
has been analyzing GPS and GLONASS data in a com-
bined analysis to achieve the best possible consistency of
the GPS and GLONASS orbit products. This strategy is not
only applied to the CODE contributions to the IGS final
products, but also to its rapid and ultra-rapid products.
CODE also participates in the first reprocessing cam-
paign of the IGS. The IGS decided to limit this activity to a
GPS-only solution. The corresponding computations of
CODE were performed at IAPG/TUM between summer
2008 and spring 2009 (Steigenberger et al. 2009). The
processing strategy of the operational CODE solution from
August 2008 was used for this effort (except that the
reprocessing was limited to GPS). In this way, a consistent
time series of GPS-derived CODE products from January
1994 up to December 2008 could be generated.
The reprocessed GPS-only products were extended to
GLONASS by introducing GLONASS tracking data gath-
ered after May 2003 in addition to the GPS data. The GPS/
GLONASS tracking data were processed using the strategy
applied to the IGS reprocessing. Finally, the additional
observations were combined with the GPS-only part on
the observation level to generate a fully consistent multi-
system time series of products.
For the GLONASS extension of the reprocessed solu-
tions, more GLONASS tracking stations could be included
than in the operational processing (Fig. 1). Even though
most of the stations were still located in Europe (at least till
the end of 2007), the quality of the GLONASS orbits could
be improved by a factor of about two. It reached a level of
about 5–6 cm at the end of 2007 and improved to 3–4 cm
by the end of 2008 (Fig. 2). For comparison, the corre-
sponding values for the GPS satellites are 1–2 cm. This
quality measure is based on an orbit determination process:
apart from the six initial osculating orbital elements, nine
empirical parameters in the Sun-oriented coordinate system
at the satellite consisting of a component (D) pointing from
the satellite to the Sun, of a (Y) component along the solar
panel axis of the satellite, and the (X) component com-
pleting the right-hand system (three constant and six
once-per-revolution parameters, Beutler et al. 1994) were
determined introducing the satellite positions every 15 min
from three independent consecutive daily solutions.
GNSS-specific receiver antenna phase center modeling
The PCC model, as it is used within the IGS consists of two
components. The so-called phase center offset (PCO) is a
50 GPS Solut (2011) 15:49–65
123

vector pointing from a mechanical marker at the antenna
(antenna reference point) to a mean phase center. Addi-
tional azimuth- and elevation-dependent phase center
variations (PCV) are usually provided in grids. Any change
in the PCO can be compensated by the PCV. In conse-
quence, the PCO can be freely defined (e.g., to have no
PCV correction in zenith direction) as long as the PCV are
consistently used.
Update of the igs05.atx phase center model
The set of antenna PCC (contained in the file igs05.atx,
maintained by the IGS) currently used by the IGS was
compiled in 2005/06 when the absolute antenna phase
center model was introduced (Schmid et al. 2007).
According to the rules for the maintenance of that file (IGS
Mail No. 5440 and General antenna file information of the
antenna calibration working group of the IGS, available at
ftp://ftp.igs.org/pub/station/general/antenna_README.pdf)
generally only new antenna/radome combinations are
added. Therefore, many corrections are up to 4 years old.
Many additional antennas were calibrated since that time,
which could help to improve the ‘‘type-mean’’ corrections
of the corresponding antenna types. The calibration values
contained in igs05.atx are based on GPS measurements
only. GLONASS observations were not included due to the
weak GLONASS constellation at that time. This is why the
GPS-derived antenna PCC are also used for the GLONASS
observations made on different frequencies.
More GLONASS satellites are active today than in
2005/06. Therefore, system-specific corrections for GPS
and GLONASS can be determined using a robot (Wu
¨
bbena
et al. 2006). Table 1 lists all antenna/radome combinations
contained in the reprocessed network, for which GNSS-
specific PCC were available. The calibration values resul-
ted in an updated version of igs05.atx, called from now on
10
20
30
40
50
60
70
80
90
100
110
120
Number of multi−GNSS stations
Reprocessed solution
Operational solution
J
OJAJO
J
AJ
O
J
AJ
O
J
AJ
O
JAJ
O
2003 2004 2005 2006 2007 2008
Year
Fig. 1 Number of sites in the
IGS network providing
GLONASS data, which were
used for orbit determination in
the CODE operational (blue)
and reprocessed (red) solutions
Median of RMS in cm
0
5
10
15
20
JOJAJOJAJOJAJOJAJOJAJO
2003 2004 2005 2006 2007 2008
Year
GLONASS satellites (repro.) GLONASS satellites (oper.)
GPS satellites (oper.)
Fig. 2 Median of the RMS for
the fit of a 3-day arc of the
operational (blue) and
reprocessed (red) CODE orbits
for the GLONASS satellites as
well as of the operational GPS
orbits (green)
GPS Solut (2011) 15:49–65 51
123

igs05(upd).atx, which was used for this study. Note that the
new calibration values for GPS replace the existing values
in the IGS file igs05.atx.
As a consequence, all reference frame stations using one
of these antenna types have to be excluded from the datum
definition because an offset in the estimated station coor-
dinates is expected (‘‘Use of GNSS-specific PCC’’).
Therefore, 35 out of 96 IGS reference frame sites were
omitted for the datum definition. This results in a dilemma:
one would like to have the most recent antenna PCC tables
with as many individual calibrations for the ‘‘type-mean’’
values as possible, and one would like to maintain a stable
geodetic reference frame at the same time.
The number of individual antennas and calibration runs
used to obtain the updated GPS-specific antenna ‘‘type-
mean’’ corrections for igs05(upd).atx reveals a strong
imbalance between the different antenna/radome combi-
nations (Table 1). The ‘‘type-mean’’ values for the Ashtech
and NovAtel antennas are both based on only two indi-
vidual antennas. Thus, the redundancy is small. Fortu-
nately, these antenna types did not find widespread use in
the IGS network (except for ASH701945E_M NONE).
Therefore, it is expected this problem to have only mar-
ginal impact on the general results of this study.
There are several antennas with a limited number of
individual antennas contributing to the GLONASS-specific
antenna ‘‘type-mean’’ PCC (Table 1). The conclusions
emerging from this study may be in particular problematic
for the two Javad Regant types, because they dominated
the GLONASS tracking network prior to 2006 (about one-
third of the network was equipped with this combination).
Figure 3 (top), showing the number of stations in the
reprocessed GLONASS tracking network of December
2003 equipped with a specific antenna/radome combina-
tion, illustrates the situation. About 50% of the stations are
equipped with antenna types for which robot calibrations
are available (for the original igs05.atx model before the
update the percentage is only 40%). igs05(upd).atx
includes GLONASS-specific antenna PCC for about half of
the stations (indicated by red-labeled antenna names in
Fig. 3). This situation is more or less stable till the second
half of 2006.
Figure 3 (bottom) illustrates the situation in December
2008, which is very close to the current state of the
GLONASS tracking network used in the operational
CODE processing. Note that there are new antenna types
(in particular from Trimble and Leica) dominating the
network. Most of these antenna types were calibrated with
a robot. By updating the robot calibrations from igs05.atx
to igs05(upd).atx, the percentage of receiver/antenna
combinations with a robot calibration grows from 59 to
72%. About two-thirds of the GLONASS tracking sta-
tions available in December 2008 can be processed with
Table 1 Antenna/radome combinations with updated antenna PCC in igs05(upd).atx
Antenna Radome ‘‘Type-mean’’ values are derived from Number of stations Calibration type
in igs05.atx
Calibration was also used
for the same antenna type
with other radomes
GPS: no.
of antennas
GPS: no.
of calibrations
GLO: no.
of antennas
GLO: no.
of calibrations
Reference GNSS GPS-only
ASH700936D_M NONE 2 27 3 6 3 2 1 ROBOT DOME, JPLA
ASH701945E_M NONE 2 4 1 2 7 2 9 COPIED JPLA
JPSREGANT_DD_E NONE 24 153 1 6 0 8 0 ROBOT
JPSREGANT_SD_E NONE 15 74 1 5 1 7 0 ROBOT
LEIAT504GG NONE 25 49 21 41 2 8 0 ROBOT
LEIAT504GG LEIS 79 157 70 136 1 11 0 ROBOT
LEIAX1202GG NONE 14 28 14 28 0 1 0 FIELD
NOV702GG NONE 2 4 2 4 0 1 0 ROBOT
TPSCR.G3 TPSH 60 120 58 113 1 4 0 ROBOT
TPSCR3_GGD CONE 159 285 47 94 1 13 0 FIELD
TRM29659.00 NONE 18 36 16 31 12 2 12 ROBOT DOME
TRM29659.00 TCWD 6 57 1 2 1 1 2 ROBOT
TRM55971.00 NONE 59 116 59 116 2 11 2 ROBOT
A statistics on how many antennas and calibration runs did contribute to the ‘‘type-mean’’ values for GPS and GLONASS is provided. The number of stations provides an overview on the usage
of the antenna/radome combination within the processed network (on reference frame stations, combined GPS/GLONASS tracking stations, and on GPS-only tracking stations)
52 GPS Solut (2011) 15:49–65
123

GNSS-specific antenna PCC in this study (red labels in
Fig. 3, bottom).
Use of GNSS-specific PCC
Before studying the impact of GNSS-specific antenna PCC,
it is possible to check the impact of the updated GPS
corrections on the resulting station coordinates. Coordinate
estimates from a solution using the original igs05.atx
antenna PCC tables are compared with a solution using the
updated igs05(upd).atx values. In both cases, the GPS-
derived corrections are used for the GPS and GLONASS
measurements. The differences in the up component are
shown in Fig. 4. They reach values of up to 5 mm, even
though both solutions use the same set of reference stations
for the no-net-rotation (NNR) condition in a minimum
constraint solution for the datum definition. As expected,
the differences show systematics for the individual antenna
types, regardless of whether the antenna was used at a
GPS-only or a combined GPS/GLONASS tracking station
(dark blue and red bars). Surprisingly, there are also a few
stations that show differences of [1 mm, although the
same antenna PCC are used in both computations (light
blue and red bars). Most of these stations only observed for
036
91215
Mean number of stations per day, December 2008
ROBOT
COPIED from ROBOT
CONVERTED from igs01
FIELD
ADOPTED from NONE
72%
7%
1%
5%
15%
(IGS: 59%)
(IGS: 9%)
(IGS: 0%)
(IGS: 17%)
(IGS: 15%)
AOAD/M_B DUTD
JPLD/M_R NONE
ASH701073.1 NONE
ASH701945G_M AUST
LEIAT504 NONE
LEIAR25 NONE
ASH701946.3 NONE
TRM29659.00 UNAV
AOAD/M_B OSOD
AOAD/M_T DOME
AOAD/M_T JPLA
ASH700936C_M SNOW
ASH701073.1 SCIS
ASH701073.1 SNOW
ASH701941.B SCIT
ASH701945B_M NONE
ASH701945C_M SNOW
TPSCR3_GGD PFAN
TPSG3_A1 NONE
TRM57971.00 NONE
AOAD/M_T AUST
ASH701941.B SNOW
AOAD/M_T NONE
TPSCR3_GGD NONE
AOAD/M_T OSOD
ASH701945C_M NONE
TRM29659.00 TCWD
ASH700936D_M NONE
TPSCR.G3 TPSH
ASH701945E_M NONE
NOV702GG NONE
LEIAX1202GG NONE
JPSREGANT_SD_E NONE
TRM29659.00 NONE
JPSREGANT_DD_E NONE
TPSCR3_GGD CONE
LEIAT504GG NONE
LEIAT504GG LEIS
TRM55971.00 NONE
036912
15
Mean number of stations per day, December 2003
ROBOT
COPIED from ROBOT
CONVERTED from igs01
FIELD
ADOPTED from NONE
51%
8%
3%
0%
38%
(IGS: 40%)
(IGS: 8%)
(IGS: 3%)
(IGS: 10%)
(IGS: 39%)
ASH701945C_M SNOW
AOAD/M_T JPLA
ASH701073.1 DOME
ASH701073.3 NONE
AOAD/M_B OSOD
AOAD/M_T AUST
ASH701073.1 NONE
ASH701073.1 SCIS
ASH701941.1 SNOW
ASH701941.B NONE
ASH701946.2 NONE
ASH701946.3 SNOW
ASH701073.1 SNOW
ASH701941.B SNOW
AOAD/M_T OSOD
TRM29659.00 NONE
ASH700936D_M NONE
TPSCR3_GGD CONE
JPSREGANT_DD_E NONE
JPSREGANT_SD_E NONE
Fig. 3 Number of combined
GPS/GLONASS tracking
stations in the processed
network equipped with a
specific antenna/radome
combination (top average over
all days in December 2003,
bottom average over all days in
December 2008). The colors
characterize the calibration
types (see ANTEX format
description at
ftp://ftp.igs.org/pub/station/
general/antex13.txt). The per-
centage of the different calibra-
tion types is given in the legend
for igs05(upd).atx and in
parentheses for the original
igs05.atx model. Antenna types
with red labels got updated PCC
in igs05(upd).atx
GPS Solut (2011) 15:49–65 53
123

a limited number of days within the entire period of
6.5 years.
The differences between the elevation- and azimuth-
dependent PCV for the GPS and GLONASS frequencies
are in the range of a few mm for L1 and L2, respectively.
According to Wu
¨
bbena et al. (2006), these values are
reproducible to within 0.3–0.4 mm. The differences
between individual antennas of the same type have abso-
lute values in the range of 2–3 mm for low elevations.
Thus, the differences between GNSS-specific antenna PCC
are significant, at least for those with a ‘‘type-mean’’ value
derived from a suitable number of individual antennas.
When converting the elevation- and azimuth-dependent
PCV for the L1 and L2 frequencies into the ionosphere-free
linear combination (as they are needed for a global network
analysis), the differences between the GPS- and GLONASS-
specific corrections may reach 10 mm in absolute value. The
differences for one of the Ashtech antennas are shown as a
typical example in Fig. 5. Note that the mean difference
between the GPS- and GLONASS-specific PCV corresponds
to a time bias between the GPS and GLONASS measure-
ments. Thus, it is absorbed by the inter-system bias, which
has to be taken into account in the multi-GNSS processing
for each station at least as a constant bias between the
receiver hardware delays of the individual GNSS.
In order to analyze the impact of the GNSS-specific
antenna PCC on the mean station coordinates, the entire
interval of the GLONASS extension of the CODE repro-
cessing (6.5 years) has been analyzed with the updated
antenna PCC table. In a first run, the GPS-derived cor-
rections were used for both GPS and GLONASS mea-
surements, whereas in the second run the GNSS-specific
corrections were used. Two cumulative solutions have been
derived considering mean station coordinates and veloci-
ties. The resulting time series of station positions have been
analyzed with FODITS, a new component of the Bernese
GPS Software. FODITS stands for ‘‘
Find Outliers and
Discontinuities in Time Series’’ (Ostini et al. 2008). The
new tool was used to detect outliers and significant dis-
continuities in the station coordinate time series. The dif-
ferences between the two coordinate sets (introducing
identical outlier and discontinuity definition) in the vertical
component are provided in Fig. 6. They are very small and
reach values of 1 mm at maximum. These differences
show, not unexpectedly, systematic effects as a function of
the antenna type.
The small absolute value of the differences is surprising
in view of the fact that the differences between GLONASS-
and GPS-specific PCV (as, e.g., shown in Fig. 5) are about
twice as large as the PCV differences causing the coordinate
differences in Fig. 4. It was already mentioned that the
average of the difference between GNSS-specific antenna
PCC is absorbed by the inter-system bias. There are, how-
ever, several other reasons for the marginal impact of
GNSS-specific PCC on the estimated station coordinates:
1. The GLONASS constellation consists only of half of
the number of satellites in the GPS constellation during
the analyzed time span (slowly increasing to about
two-thirds toward the end of 2008).
2. A much smaller number of GLONASS ambiguities
were resolved than in the case of GPS, because
ambiguity resolution for GLONASS was only enabled
for baselines shorter than 20 km.
3. Schaer et al. (2009) found evidence that the inter-system
biases between GPS and GLONASS significantly
deviate from a constant. As the current multi-GNSS
processing usually implies this behavior, the solution
cannot benefit in an optimal way from the additional
measurements.
−6
−3
0
3
6
ΔUp in mm
Reference site (PCC only available in igs05.atx) dummy
GPS−only (PCC only available in igs05.atx) GPS+GLONASS (PCC only available in igs05.atx)
GPS−only (new PCC available in igs05(upd).atx)
GPS+GLONASS (new PCC available in igs05(upd).atx)
Fig. 4 Differences of the station heights between solutions using the
original igs05.atx and the updated igs05(upd).atx antenna PCC. The
GPS-derived corrections are used for the GPS and the GLONASS
measurements. The stations are sorted alphabetically, but they are not
labeled. Both coordinate sets are computed from the entire interval of
6.5 years of the GLONASS extension of the CODE reprocessing as
described in ‘‘Reprocessing of GLONASS data at CODE’’
54 GPS Solut (2011) 15:49–65
123

These reasons might explain why the averaged station
coordinates are so clearly dominated by GPS.
In view of the sizable differences between GPS- and
GLONASS-specific antenna PCC and of the continuously
increasing number of available GLONASS satellites,
which enhances the impact of GLONASS on the combined
solution, GNSS-specific antenna PCC should be applied
whenever processing multi-GNSS data sets.
Satellite antenna phase center modeling
The currently used igs05.atx model includes in addition to
the receiver antenna calibrations consistent corrections for
the satellite antennas. The nadir-dependent corrections for
the satellite antenna phase center are mean values for all
satellites of the same type (no azimuth-dependence has
been considered so far). The PCO are provided individually
for each satellite. The values in igs05.atx were determined
in 2005 and in early 2006 (Schmid et al. 2007).
Block mean values were defined and used for the sat-
ellites launched since that time. The following GPS satel-
lites are affected:
SVN52/PRN G31 (launched on September 25, 2006),
SVN58/PRN G12 (November 17, 2006),
SVN55/PRN G15 (October 17, 2007),
SVN57/PRN G29 (December 20, 2007), and
SVN48/PRN G07 (March 15, 2008)
(Satellites launched after December 2008 are not
included because the computations for this paper were
started in early 2009).
This number of satellites corresponds to about 16%
of the entire constellation of 32 GPS satellites in May
2009.
The situation is even more dramatic for the GLONASS
satellites. Due to the short lifetime of the older GLONASS
satellites, in May 2009 there is an almost completely new
GLONASS constellation compared to 2005/06 (only three
satellites from end of 2005 are still active in May 2009,
namely SVNs701, 712, and 795, see Fig. 7). An update of
the satellite antenna phase center model, at least for these
newly launched satellites, is therefore badly needed. The
following sections discuss the process of updating the
satellite antenna phase center model for all GLONASS and
for the youngest GPS satellites.
0
30
60
90
Elevation angle in deg.
0 60 120 180 240 300 360
Azimuth in deg.
−10 mm
−5 mm
0 mm
5 mm
10 mm
Fig. 5 Differences between the
PCV for GLONASS and GPS
from GNSS-specific calibrations
as a function of azimuth and
elevation for the
ASH701945E_M NONE (the
antenna phase center offset is
identical for both GNSS). The
influence on the ionosphere-free
linear combination is shown
−6
−3
0
3
6
ΔUp in mm
Reference site (PCC only available in igs05.atx)
GPS−only (PCC only available in igs05.atx) GPS+GLONASS (PCC only available in igs05.atx)
GPS−only (new PCC available in igs05(upd).atx)
GPS+GLONASS (new PCC available in igs05(upd).atx)
Fig. 6 Differences of the
station heights between
solutions considering and
ignoring GLONASS-specific
PCC, respectively. Both
coordinate sets are computed
from the entire interval of
6.5 years of the GLONASS
extension of the CODE
reprocessing. (Same scale as in
Fig. 4 has been used for
comparison.)
GPS Solut (2011) 15:49–65 55
123

Computation of the satellite antenna model update
The satellite antenna PCC were derived from the
GLONASS extension of the CODE reprocessing. From
the independent 1-day solutions, 3-day solutions were
derived by combining the three corresponding 1-day normal
equations. As the number of orbit parameters is comparable
in the 1- and 3-day orbits, the 3-day orbits are much better
defined than the 1-day orbits. This is in particular true for
those GLONASS satellites, which were observed mainly
over Europe. The step from the 1-day to the 3-day orbits is
essential, because the orbit parameters and the satellite
antenna PCC are highly correlated. Six initial osculating
orbital elements and nine empirical parameters (three
constant and six once-per-revolution parameters in D-, Y-,
and X-directions according to the orbit model described in
Beutler et al. 1994) are set up for each satellite arc, where
the periodic terms of the D- and Y-components are con-
strained to zero. Empirical velocity changes (so-called
pseudo-stochastic pulses) are set up and solved for at 12-h
intervals.
The 3-day solutions ([2,000) were then combined to
generate a cumulative solution. Again FODITS was used to
detect outliers and significant discontinuities in the station
coordinate time series. The reference frame was aligned
with the ITRF2005 using stations provided in the IGS05
(an IGS-specific realization of ITRF2005; Altamimi et al.
2007) together with NNR conditions applied to a minimum
constraint solution. The station coordinates and velocities
resulting from this step were introduced as known when
computing the satellite antenna PCC. The igs05.atx values
for all satellite antennas were kept fixed for datum defini-
tion. Different sets of coordinates and velocities were
computed using the different scenarios for handling the
receiver antenna PCC, but using the same set of reference
stations together with the same list of outliers and
discontinuities.
Update of the satellite antenna PCO
To keep the updated satellite antenna model consistent (in
scale) with igs05.atx, the PCO of the GPS satellites laun-
ched before 2005 were fixed to their igs05.atx values. Only
the Z-offsets for the five new GPS satellites (see to the
introduction to this section) and for the GPS satellite
SVN53, PRN G17 (launched on September 26, 2005) were
estimated, because no or only a very limited amount of data
contributed to the igs05.atx values for these satellites. The
Z-offsets for all GLONASS satellites were recomputed
because of the high uncertainty of these values in igs05.atx,
which was caused by the sparse GLONASS network of
about 30 stations (located moreover mainly in Europe at
that time).
The time series of estimates for the satellite antenna
PCO (Z-component) from the 3-day solutions with respect
to the corresponding igs05.atx value is shown for one of the
GLONASS satellites (SVN791, PRN R22) in Fig. 8. The
shaded areas indicate the eclipse periods. A correlation
between the noise pattern of the estimated antenna PCO
and the eclipse periods is clearly visible. This observation
indicates that the Z-offset is correlated with the orientation
of the orbital plane with respect to the Sun, which in turn
influences the correlation between the Z-offset and the
radiation pressure parameters. The noise of the Z-offsets
increases toward the end of the time series, when the
satellite was no longer reliably tracked by the stations.
The mean satellite antenna PCO computed from this time
series is also plotted in Fig. 8. Three options for handling the
receiver antenna PCC (mainly for the GLONASS observa-
tions) were used for comparison purposes:
701
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
783
784
787
788
789
791
792
793
794
7
95
796
7
97
798
JO
J
AJO
J
A
JO
J
A
J
O
JA
J
O
JA
J
O
2003 2004
2005
2006 2007 2008
Year
Fig. 7 Development of the
GLONASS constellation since
June 2003 until end of 2008
(a satellite is indicated as active
as soon as an orbit determination
was possible in the operational
CODE final solution). The blue
bars indicate the old style
GLONASS satellites whereas
red bars are used for the
modernized GLONASS-M
satellites. SVN711 is a
prototype of the GLONASS-M
series
56 GPS Solut (2011) 15:49–65
123

• Green The original igs05.atx receiver antenna PCC
were applied, implying that the GPS-derived values are
also used for the GLONASS measurements.
• Blue Updated GPS receiver antenna PCC igs05(upd).atx
where applied where available (Table 1), whereas the
igs05.atx corrections were introduced for the other
antennas. The GPS-derived corrections were used for
both the GPS and the GLONASS data.
• Red Updated receiver antenna PCC igs05(upd).atx are
used (Table 1). GNSS-specific corrections were applied
for the GPS and the GLONASS data.
The three mean Z-offsets were estimated using the full
covariance information by combining the corresponding
normal equations. The stated uncertainty is the standard
deviation of the mean offset derived from the time series.
The three Z-offsets significantly differ by about 150 mm
from the currently used igs05.atx value. On the one hand,
the two solutions based on GPS-derived receiver antenna
corrections for GLONASS (‘‘Green’’ and ‘‘Blue’’) agree
very well. The Z-offset emerging from solution ‘‘Red’’
using GNSS-specific corrections, on the other hand, differs
by 22 mm from these two solutions.
Figure 9 gives an overview of the corresponding values
for the complete GLONASS constellation active in the
time span of 6.5 years, where only satellites observed for at
least 90 days are included. The difference of about 20 mm
between using GNSS-specific receiver antenna PCC
(‘‘Red’’) and the other two solutions is approximately the
same for all older GLONASS satellites. The difference is
smaller for the GLONASS-M satellites. For the youngest
satellites, SVN718 up to 726 (SVN716 might also belong
to this group, but only few observations were available till
summer 2007, because many receivers needed a firmware
upgrade to enable tracking of this satellite with frequency
channel zero), it even vanishes. These GLONASS-M sat-
ellites were launched in 2007 or 2008 when most of the
older GLONASS satellites were already inactive. In the
same time period, the number of different GNSS receiver
antenna types in the tracking network grew. Therefore,
either the characteristics of the two satellite antenna types
are different or some of the systematic differences between
GNSS-specific receiver antenna PCC are absorbed by the
satellite antenna Z-offsets. Note that the GLONASS
tracking network was dominated by two Javad Regant
types in the early days, see Fig. 3 (top). A full consistency
of the receiver and satellite antenna corrections is, in any
case, a requirement to achieve high-quality results.
Update of the satellite antenna PCV
Using the previously estimated satellite antenna PCO as
known, consistent nadir-dependent satellite antenna PCV
can now be established. For this purpose, a zero-mean
condition was imposed for the estimated PCV of each
satellite antenna, which is why corrections for all GPS and
GLONASS satellites could be estimated simultaneously.
The nadir-dependent satellite antenna PCV are not
sensitive to the three different scenarios for handling the
receiver antenna PCC. Therefore, only the most sophisti-
cated solution with GNSS-specific receiver antenna PCC
(‘‘Red’’) is subsequently discussed.
Figure 10 compares the yearly solutions for the nadir-
dependent satellite antenna PCV as derived from the
−1000
−500
0
500
1000
Δ Z−offset in mm
SVN 791/PRN R22 (GLONASS)
Nominal value from igs05.atx for SVN 791 2000.9 mm
igs05.atx for receivers, GPS and GLONASS
1856.1 +− 10.1 mm
updated PCC for receivers (see Tab. 1), GPS−PCC for GLONASS 1854.4 +− 10.1 mm
updated PCC for receivers (see Tab. 1), GNSS−specific PCC 1832.8 +− 10.3 mm
JOJAJOJAJOJAJOJAJOJAJO
2003 2004 2005 2006 2007 2008
Year
Fig. 8 Differences between
satellite antenna phase center
Z-offset for GLONASS satellite
SVN791 (PRN R22) from 3-day
solutions of the GLONASS
extension of the CODE
reprocessing and the values in
igs05.atx. The shaded periods
indicate the eclipse periods. The
dashed lines indicate the mean
values of the three scenarios for
handling the receiver antenna
PCC, see text (note, the green
line is located behind the blue
one)
GPS Solut (2011) 15:49–65 57
123

GLONASS extension of the CODE reprocessing. Stable
solutions were obtained for all GPS and GLONASS sat-
ellites. The yearly solutions coincide to within ±1 mm.
Only for nadir angles of 0 (GPS and GLONASS), 14
(GPS), and 15 (GLONASS), the variations are somewhat
larger due to the limited number of observations contrib-
uting at these angles. As opposed to GPS, corrections for
nadir angles up to 15 can be reliably estimated for
GLONASS from ground stations thanks to the lower orbit
height of these satellites. igs05.atx does, however, only
contain corrections up to nadir angles of 14.
For most of the satellites, the nadir-dependent PCV
from igs05.atx (black dots) and from our estimation were
very close (e.g., for SVN60, PRN G23, Fig. 10, top,
right). For some GPS and GLONASS satellites, however,
the new PCV show small, but significant differences
with respect to the values in igs05.atx (e.g., for SVN792,
PRN R21, Fig. 10, bottom, left). Differences of a few
millimeters may be understood because igs05.atx only
contains block-specific mean PCV (Schmid et al. 2007).
The largest differences between our new corrections and
those in igs05.atx are those for SVN56 (Fig. 10, top, left)
for GPS and for SVN714 (Fig. 10, bottom, right) for
GLONASS. In both cases, the new set of nadir-dependent
corrections are almost the same in the available yearly
solutions.
Figure 11 gives an overview of the consistency of the
nadir-dependent satellite antenna PCV for all satellites of
each type and compares them to the block-specific
igs05.atx values.
Schmid et al. (2007) distinguish three satellite groups of
common antenna behavior for the GPS, namely Block II/
IIA, Block IIR-A, and Block IIR-B/IIR-M.
Figure 10 says, however, that the differences of the
corrections between individual satellites of a group are
small, but significant. This results in the proposal that
satellite-specific antenna PCV should be considered for
future antenna phase center models. There are, however,
two important arguments in favor of the current strategy
based on a minimum number of parameters:
• Additional parameters might weaken the normal equa-
tion system.
• As each GPS satellite follows the same ground track
day after day the station-specific observation geometry
is repeated day after day, as well. Therefore, station-
specific effects may cause systematic satellite-specific
errors, e.g., errors in the satellite antenna PCV.
The inclusion of observations from Low Earth Orbiting
(LEO) satellites might mitigate this problem. As opposed
to a terrestrial site, the LEOs track the GNSS satellites
more uniformly. Calibration of the space-borne GPS
antennas is, on the other hand, a challenging task because
of local multipath and cross-talk effects (Ja
¨
ggi et al. 2009).
The impact of station-dependent effects might, e.g., be
studied by comparing satellite-specific PCV derived from
solutions using different and independent tracking
networks.
The older and the modernized GLONASS satellites
obviously show a similar behavior. The scatter of the
−300
−250
−200
−150
−100
−50
0
Δ Z−offset in mm
701/R06
711/R05
712/R07
713/R24
714/R23
715/R14
716/R15
717/R10
718/R17
719/R20
720/R19
721/R13
722/R09
723/R11
724/R18
725/R21
726/R22
783/R18
784/R08
787/R17
788/R24
789/R03
791/R22
792/R21
793/R23
794/R02
795/R04
796/R01
797/R08
798/R22
Receiver antenna modeling:
igs05.atx for receivers, GPS and GLONASS
updated PCC for receivers (see Tab. 1), GPS−PCC for GLONASS
updated PCC for receivers (see Tab. 1), GNSS−specific PCC
igs05.atx PCO
values are
estimated
defined
Satellite type
GLONASS
GLONASS−M
Fig. 9 Differences of the new mean satellite antenna phase center
Z-offsets for the GLONASS satellites with respect to igs05.atx
(diamonds). The receiver antenna phase centers: original igs05.atx
corrections (green); igs05(upd).atx with GPS-derived corrections for
GLONASS (blue); igs05(upd).atx with GNSS-specific corrections for
GPS and GLONASS observations (red). The error bars indicate the
uncertainty of the mean offset as derived from the entire time series of
3-day solutions. (SVN711 is a prototype of the GLONASS-M series;
SVN714 outside of the diagram)
58 GPS Solut (2011) 15:49–65
123

nadir-dependent GLONASS PCV is comparable to that of
the two older generations of GPS satellites (Fig. 11).
The satellite-specific PCV for GLONASS show a similar
behavior as in the case of GPS. The scatter between the
individual satellites in Fig. 11 is, on one hand, larger than the
scatter between the yearly solutions for the individual satel-
lites (see Block II/IIA and Block IIR-A in Fig. 10). On the
other hand, the GLONASS satellites are not observed as
intensely as the GPS satellites (fewer stations, not well glob-
ally distributed). The GLONASS constellation has, however,
the advantage that each satellite is observed by the complete
tracking network within 17 revolutions corresponding to
eight sidereal days. Therefore, the derived GLONASS
parameters are less dependent on the tracking network.
One GLONASS-M satellite, namely SVN714, PRN R23,
shows a significantly different behavior in the satellite
antenna phase center (PCO in Fig. 9 and PCV in Figs. 10,
11). The mean Z-offset is, however, only 3 cm larger than
the mean value of all GLONASS-M satellites. As this
satellite became active in February 2006, the time slot for
computing the corresponding igs05.atx corrections was
(in particular in view of the sparse tracking network) not
long enough to detect the anomalous behavior of that
particular satellite. The assumption that all GLONASS
satellites had the same nadir-dependent PCV led to an
igs05.atx value for the PCO which was off by about
40 cm. Recently, the value for PRN R23 was corrected
(see IGS Mail No.5970).
−15
−10
−5
0
5
10
15
Satellite PCV in mm
0
1
2
3
4
5
6
789
10
11
12
13
14
15
Nadir in degree
SVN 792
PRN R21
GLONASS
from year 1980
from year 2003
from year 2004
from year 2005
from year 2006
from year 2007
from year 2008
−15
−10
−5
0
5
10
15
Satellite PCV in mm
012
3
45678
9
10 11 12 13 14 15
Nadir in degree
SVN 714
PRN R23
GLONASS−M
from year 1980
from year 2003
from year 2004
from year 2005
from year 2006
from year 2007
from year 2008
−15
−10
−5
0
5
10
15
Satellite PCV in mm
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Nadir in degree
SVN 56
PRN G16
Block IIR−A
from year 1980
from year 2003
from year 2004
from year 2005
from year 2006
from year 2007
from year 2008
−15
−10
−5
0
5
10
15
Satellite PCV in mm
0123456789101112131415
Nadir in degree
SVN 60
PRN G23
Block IIR−B
from year 1980
from year 2003
from year 2004
from year 2005
from year 2006
from year 2007
from year 2008
Fig. 10 Examples of yearly solutions for the nadir-dependent satellite antenna PCV for individual GPS (top) and GLONASS (bottom) satellites.
The colors refer to the individual yearly solutions. The black dots mark the igs05.atx corrections
−15
−10
−5
0
5
10
15
Satellite PCV in mm
0123
4
5 6 7 8 9 101112131415
Nadir in degree
R23
GLONASS−
Satellite type
GLONASS
GLONASS−M
−15
−10
−5
0
5
10
15
Satellite PCV in mm
012
34
56789
10 11
12 13 14 15
Nadir in degree
GPS−
Satellite type
Block II
Block IIA
Block IIR−A
Block IIR−B
Block IIR−M
Fig. 11 Nadir-dependent satellite antenna PCV for all GPS (top) and
GLONASS (bottom) satellites observed for [90 days during the
GLONASS extension of the CODE reprocessing. The colors indicate
the different satellite types, the dots illustrate the corresponding
igs05.atx corrections
GPS Solut (2011) 15:49–65 59
123

Validation of the satellite antenna phase center models
In ‘‘Use of GNSS-specific PCC’’, it was suggested that
GNSS-specific receiver antenna PCC should be used as
soon as reliable values would become available. The
satellite antenna phase center model for the GLONASS
satellites was also updated whereas the igs05.atx values for
the old GPS satellites were fixed (‘‘Satellite antenna phase
center modeling’’).
To validate these two conclusions, the following solu-
tions have been generated:
• S
1
The IGS convention for the GPS-derived receiver
antenna PCC for GPS and GLONASS measurements is
used. The values in the file igs05.atx are used for the
satellite antennas.
• S
2
The GNSS-specific PCC for the receiver antennas
igs05(upd).atx (as available in Table 1) and the new
satellite antenna PCC are used (derived in ‘‘Satellite
antenna phase center modeling’’).
The differences of the results from both solutions are
discussed in this section by studying the arc overlaps, the
residuals of Satellite Laser Ranging (SLR) measurements,
the station coordinates estimated over long time periods,
and the results of the kinematic positioning method.
Impact of the updated antenna phase center model
on the GLONASS satellite orbits
The orbits of two consecutive days, i and i ? 1 should
provide identical positions for each satellite for the midnight
epoch t
i ? 1
: r
*
i
ðt
iþ1
Þ¼r
*
iþ1
ðt
iþ1
Þ. The resulting disconti-
nuities r
*
i
ðt
iþ1
Þr
*
iþ1
ðt
iþ1
Þ may serve as quality indicators
of a particular series of orbits. In an analogous manner,
discontinuities may be calculated for the velocity vectors.
The orbits r
*
i
ðtÞ actually used here for this purpose are
those corresponding to the middle day of 3-day arcs, in the
way they are generated by the CODE analysis center, see
Ineichen et al. (2001). Consecutive 3-day arcs are not
independent but they are required because of the poor
GLONASS tracking geometry outside Europe.
The differences between the solutions S
1
and S
2
at the
day boundaries were computed for the position and for the
velocity vectors:
Dr
i
¼þr
*
s
1
;i
ðt
iþ1
Þr
*
s
1
;iþ1
ðt
iþ1
Þ




 r
*
s
2
;i
ðt
iþ1
Þr
*
s
2
;iþ1
ðt
iþ1
Þ




Dv
i
¼þv
*
s
1
;i
ðt
iþ1
Þv
*
s
1
;iþ1
ðt
iþ1
Þ




 v
*
s
2
;i
ðt
iþ1
Þv
*
s
2
;iþ1
ðt
iþ1
Þ




ð1Þ
The differences Dr
i
and Dv
i
are summed up for each
satellite over the entire time span of the comparison. The
result for the GLONASS satellites is provided in Table 2.
A positive sum of differences indicates on the average
larger discontinuities for the solution S
1
, implying that the
more sophisticated GLONASS antenna phase center model
from solution S
2
is preferable.
The mean position discontinuity per day, averaged over
all GLONASS satellites, is only reduced from 63.8 to
63.0 mm due to the use of updated antenna PCC. For the
GLONASS-M satellites, the benefit is even smaller (from
62.8 to 62.4 mm). The improvement thus amounts to about
1% for the complete constellation (from 63.3 to 62.7 mm).
The benefit is small, but the orbit quality consistently
improves for all satellites, except for SVN715.
Validating the GLONASS orbits using SLR data
The quality of GLONASS orbits may also be validated
using the SLR measurements (normal points) provided by
the International Laser Ranging Service (ILRS, Pearlman
et al. 2002) and the distances between the satellite and the
microwave tracking station at the epoch of the SLR mea-
surement. The differences between the two observations
are called SLR residuals in this paper. The coordinates
of the ILRS sites were taken from the file SLRF2005
(a special reference frame currently used within the ILRS)
to generate the residuals for the two sets of GLONASS
orbits. Four GLONASS satellites were tracked by ILRS
stations in 2008: SVN712/PRN R07 (only from January to
May), SVN723/PRN R11 (only from June to December),
SVN716/PRN R15, and SVN713/PRN R24 (both through-
out the year). Figure 12 shows the mean differences of the
absolute values of the residuals between the orbit solutions
S
1
- S
2
.
Most of the mean differences are positive, implying that
the residuals were reduced by the updated antenna phase
center model. Satellite SVN712 is an exception, showing
negative differences for some of the SLR stations, namely
7810 Zimmerwald, 7237 Changchun, and 7090 Yarragadee.
Stations located in the vicinity of the three sites do, how-
ever, show a different behavior. This is in particular true
for Zimmerwald (7810) and Wettzell (8834) (for a few
time periods) when tracking SVN712 at the same time. The
effect is probably related to station problems, which were
not taken into account in our validation procedure,
described in Urschl (2007). There was, e.g., no attempt to
consider station-specific range biases.
Impact of the updated satellite antenna phase center
model on station coordinates
In order to study the impact of the updated satellite
antenna PCC on the reference frame, the updated PCC for
60 GPS Solut (2011) 15:49–65
123

the GLONASS satellites from ‘‘Satellite antenna phase
center modeling’’ were used to generate a new set of
station coordinates and velocities for the full interval of
the GLONASS extension of the CODE reprocessing. The
resulting coordinates were compared to the coordinates
obtained with the original igs05.atx corrections for the
GLONASS satellites. Both solutions were based on
the same corrections for the GPS satellites and for
the receiver antennas (igs05(upd).atx). The differences
between the vertical components of the two solutions are
below the 1-mm limit—the horizontal ones are even
smaller.
Obviously, the updated GLONASS satellite antenna
PCC do not have a significant influence on the coordinates.
This is consistent with the findings in ‘‘Use of GNSS-
specific PCC’’, where it was already shown that GLONASS
has only a small impact on the estimated coordinates. One
may also draw the conclusion that the updated satellite
antenna corrections do not have a negative impact on the
reference frame.
Impact of the updated antenna phase center model
on kinematic positioning
Dach et al. (2009) and Ineichen et al. (2008) showed that
GLONASS observations used in addition to GPS mea-
surements have a significant impact on coordinates esti-
mated in the rapid-static mode (based on short data spans).
One may therefore expect that the coordinates calculated in
the kinematic mode are also prone to the use of different
phase center models.
The global network was processed with a sampling
rate of 30 s over 10 days in December 2008 (days of year
350–359) to study the impact of the antenna phase centers.
A few stations representing the antennas with updated
PCC (Table 1) on different continents were treated as
kinematic. The coordinates of all the remaining stations,
the satellite orbits, and the Earth rotation parameters were
introduced as known values from the daily processing of
the static network.
Approximately 28,800 positions for each of the kine-
matic stations were assigned to adjacent subintervals with
lengths of either 15 or 60 min. The 30 or 120 positions
within each interval were used to compute the standard
deviation of the mean values of the coordinates. The
arithmetic mean of the standard deviations from all 960 or
240 intervals is provided in Table 3. Four sets of solutions
(experiments) are discussed subsequently. The first set is
represented by columns 4 and 5, the second by columns 6,
7, and 8, the third by columns 9 and 10, and the fourth by
columns 11 and 12.
The first set of solutions in Table 3, based on 15-min
intervals, compares the GPS-only and the combined GPS/
GLONASS solution applying identical receiver antenna
PCC for the GPS and GLONASS measurements—corre-
sponding to current practice in the IGS. Despite this
deficiency, the standard deviation of the mean station
height for intervals of 15 min is improved. 32-GPS and
16-GLONASS satellites were active in December 2008.
Assuming a white noise law, one would expect an
improvement by a factor of
ffiffiffiffiffiffiffi
1:5
p
 1:22 due to the addi-
tional GLONASS observations. This value was achieved
for many of the analyzed sites.
The updated GNSS-specific receiver antenna PCC
model igs05(upd).atx was used for a second set of solu-
tions, also based on 15-min intervals. The GPS-only and
the combined GPS/GLONASS solution (first two solutions
of the second set) are compared as in the previous exper-
iment and the results are the same. The third of the second
set of solutions used the updated satellite antenna PCC
from ‘‘Satellite antenna phase center modeling’’ for the
GLONASS satellites and was based on a combination of
GPS and GLONASS. Compared to the solution using the
IGS satellite antenna PCC, the differences are \0.1 mm.
Table 2 Sum of differences according to Eq. 1 at the day boundaries
using the IGS standard and the updated satellite antenna PCC from
‘‘Satellite antenna phase center modeling’’, respectively
PRN SVN Number of arc
boundaries
Differences in the
Position in mm Velocity in mm/s
R06 701 1,518 944 288
R05 711 979 326 75
R07 712 1,263 1,350 240
R24 713 929 424 59
R23 714 957 1,285 197
R14 715 684 47 -15
R15 716 482 97 7
R10 717 682 122 47
R20 719 407 103 13
R19 720 418 276 27
R18 783 1,208 671 73
R17 787 1,164 658 184
R24 788 827 891 221
R03 789 1,428 85 203
R22 791 1,399 1,644 336
R21 792 1,539 2,456 343
R23 793 952 871 223
R02 794 1,160 680 196
R04 795 1,792 1,082 264
R01 796 1,224 997 238
R08 797 1,207 953 163
R19 798 519 448 126
Only satellites with at least 400-day boundary values are included.
The GLONASS-M satellites are in the upper, the first generation of
GLONASS satellites in the lower part
GPS Solut (2011) 15:49–65 61
123

This result could be expected, because the satellite geom-
etry does not change substantially during the 15-min
intervals. The antenna phase center model, therefore, has
only a systematic influence on the mean value of a rapid-
static solution, but does not show up in the standard
deviation of the mean coordinates.
The third set of solutions in Table 3 is based on
GLONASS-only. The impact of the updated antenna PCC
on the standard deviations of the coordinates is slightly
larger than in the combined case. It is, on one hand,
remarkable that a rapid-static solution is at all possible
with the limited number of active GLONASS satellites
(16 December 2008). The noise of these solutions is, on the
other hand and not unexpectedly, larger than the corre-
sponding noise of the GPS-only solution, in particular for
stations with a weak satellite geometry during a significant
part of the day (e.g., CONZ and REUN).
As the effect of the antenna PCC on the 15-min solutions
is limited, the fourth set of solutions (corresponding to the
last two columns in Table 3) are fictitious 60-min coordi-
nate solutions. As the satellite geometry changes signifi-
cantly within 60 min, the antenna phase center model
should have more influence on the standard deviations of
the hourly solutions. Two GLONASS-only solutions are
compared in Table 3 both using the GLONASS-specific
receiver antenna PCC from igs05(upd).atx. The first solu-
tion uses the igs05.atx GLONASS satellite antenna cor-
rections, the second one the updated values provided in
‘‘ Satellite antenna phase center modeling’’. A small benefit
of using the improved antenna phase center model results in
the case of the 60-min solution (10 stations have smaller,
5 larger standard deviations, and 7 are on the same level).
Note that other effects like near-field multipath also have an
impact on these values. Such site-specific issues play a more
important role for the 60-min solutions because of the
reduced redundancy of the kinematic GLONASS-only
solution when compared with GPS-only (double number of
satellites) or a combined GPS/GLONASS (triple number of
satellites) solution.
For the latter two GLONASS-only solutions, the varia-
tions of the fictitious hourly solutions were analyzed. For
this purpose, the mean coordinates for intervals of 60 min
were extracted from the kinematic solutions. The RMS of
these time series of hourly coordinates is shown in Table 4.
The updated satellite antenna PCC-only cause a minor
impact on the hourly coordinate solutions (excluding the
stations CONZ and REUN, the mean of the RMS values of
all stations is identical on the sub-mm level). This confirms
the conclusions drawn from Table 3 and in ‘‘Impact of the
updated satellite antenna phase center model on station
coordinates’’ that the updated satellite antenna phase center
model for the GLONASS satellites does not ‘‘disturb’’ the
coordinate solution. The solution is dominated by envi-
ronmental effects, which are difficult to be eliminated in
the case of a GLONASS-only solution due to the small
redundancy.
Summary and conclusions
The CODE reprocessing solution for the IGS based on
GPS-only, performed at the Technische Universita
¨
tMu
¨
n-
chen, has been expanded to a combined GPS/GLONASS
solution for the time period from May 2003 to December
2008. Due to improved modeling and additional tracking
sites, the GLONASS orbits could be improved by up to a
factor of about two compared to the operational solution (in
particular prior to 2007) achieved by the CODE Analysis
−10
0
10
20
7839
−10
0
10
20
1893
−10
0
10
20
7840
−10
0
10
20
7810
−10
0
10
20
8834
−10
0
10
20
7832
−10
0
10
20
7237
−10
0
10
20
7105
−10
0
10
20
7110
−10
0
10
20
7406
−10
0
10
20
7405
−10
0
10
20
7090
−10
0
10
20
7825
United Kingdom
Germany
Switzerland
Austria
Ukraine
Saudi Arabia
China
Australia
Australia
USA
USA
USA
Chile
Station location
Herstmonceux
Wettzell
Zimmerwald
Graz
Katzively
Riyadh
Changchun
Yarragadee
Mt. Stromlo
Monument
Peak
Greenbelt
Concepcion
ILRS ID
7840
8834
7810
7839
1893
7832
7237
7090
7825
7110
7110
7105
7405
0
500
1000
1500
2000
Number of normal points
Fig. 12 Mean differences of the absolute values of the SLR residuals
between the 3-day GLONASS orbits computed with original igs05.atx
or updated antenna PCC (Table 1;‘‘Satellite antenna phase center
modeling’’) in mm. Only SLR stations (green dots) with at least
400 normal points in 2008 were included. The four bars per tracking
station indicate the residual differences for the GLONASS satel-
lites 712 (PRN R07), 723 (PRN R11), 716 (PRN R15), and 713
(PRN R24), respectively. The colors of the bars indicate the number
of normal points contributing to this statistics
62 GPS Solut (2011) 15:49–65
123

Table 3 Standard deviation of the mean station height over a certain time interval (15 or 60 min) derived from a kinematic coordinate estimation
Station Antenna Radome GPS-only
igs05.atx
for rec.
igs05.atx
for sat.
GPS/
GLONASS
igs05.atx
for rec.
igs05.atx
for sat.
GPS-only
igs05(upd).atx
for rec.
igs05.atx for
sat.
GPS/
GLONASS
igs05(upd).atx
for rec.
igs05.atx for
sat.
GPS/
GLONASS
igs05(upd).atx
for rec.
igs05(upd).atx
for sat.
GLONASS-
only
igs05.atx
for rec.
igs05.atx
for sat.
GLONASS-
only
igs05(upd).atx
for rec.
igs05(upd).atx
for sat.
GLONASS-
only
igs05(upd).atx
for rec.
igs05.atx
for sat.
GLONASS-
only
igs05(upd).atx
for rec.
igs05(upd).atx
for sat.
15 min 15 min 15 min 60 min
MAS1 ASH701945E_M NONE 1.7 1.5 1.7 1.5 1.5 7.0 8.0 14.9 16.1
CAGZ JPSREGANT_DD_E NONE 1.3 1.1 1.3 1.1 1.1 2.9 2.9 3.1 3.2
CRAR JPSREGANT_DD_E NONE 2.5 1.7 2.5 1.7 1.7 3.6 3.6 2.9 2.9
UNB3 JPSREGANT_DD_E NONE 1.1 0.9 1.1 0.9 0.9 2.0 2.0 2.0 2.0
IRKJ JPSREGANT_SD_E NONE 1.3 1.0 1.3 1.0 1.0 3.6 3.5 4.2 4.1
ZIMJ JPSREGANT_SD_E NONE 1.2 1.0 1.2 1.0 1.0 2.7 2.8 2.3 2.4
BZRG LEIAT504GG LEIS 1.4 1.1 1.4 1.1 1.1 6.8 6.8 14.0 14.0
RCMN LEIAT504GG LEIS 1.7 1.5 1.7 1.5 1.5 3.8 3.8 3.6 3.6
TSEA LEIAT504GG LEIS 2.1 1.6 2.1 1.6 1.6 3.3 3.3 3.1 3.0
HYDE LEIAT504GG NONE 1.7 1.5 1.7 1.5 1.5 4.3 4.4 8.5 8.4
JOZ2 LEIAT504GG NONE 1.2 0.9 1.2 0.9 0.9 2.5 2.4 2.5 2.3
PDEL LEIAT504GG NONE 1.5 1.2 1.5 1.2 1.2 3.2 3.2 3.3 3.2
BARH LEIAX1202GG NONE 1.8 1.4 1.8 1.4 1.4 4.3 4.4 7.0 7.2
REYK TPSCR.G3 TPSH 1.6 1.3 1.6 1.3 1.3 2.6 2.5 2.1 2.1
AZCO TPSCR3_GGD CONE 2.7 2.1 2.7 2.1 2.1 7.0 6.9 10.1 10.6
CONZ TPSCR3_GGD CONE 1.8 1.5 1.8 1.4 1.5 7.5 7.4 20.3 20.0
FFMJ TPSCR3_GGD CONE 1.2 1.0 1.2 1.0 1.0 2.2 2.2 1.8 1.8
WTZJ TRM29659.00 NONE 1.2 1.1 1.2 1.1 1.1 2.6 2.6 2.1 2.0
GANP TRM55971.00 NONE 1.6 1.2 1.6 1.2 1.2 3.0 3.1 2.8 2.8
REUN TRM55971.00 NONE 3.0 2.4 3.0 2.4 2.4 14.8 14.3 25.5 22.5
ROSA TRM55971.00 NONE 3.0 2.3 3.0 2.4 2.3 7.0 6.9 9.4 9.1
ZIM2 TRM55971.00 NONE 1.5 1.2 1.5 1.2 1.2 3.1 3.1 2.6 2.5
Mean over all stations 1.7 1.4 1.7 1.4 1.4 4.5 4.6 6.7 6.6
Different observations were processed (GPS-only, GLONASS-only, and fully combined GPS/GLONASS); in addition, the modeling of the antenna PCC for the receiver and satellite antennas
was varied
igs05.atx for rec. IGS standard receiver antenna PCC from igs05.atx derived from GPS observations are used for both GPS and GLONASS measurements, igs05(upd).atx for rec., igs05.atx was
updated with GNSS-specific receiver antenna PCC (Table 1), igs05.atx for sat. IGS standard antenna PCC from igs05.atx are used for all satellites, igs05(upd).atx for sat. IGS standard antenna
PCC from igs05.atx are only used for GPS satellites, whereas for the GLONASS satellites the PCC derived in ‘‘Satellite antenna phase center modeling’’ are introduced. The values are given
in mm
GPS Solut (2011) 15:49–65 63
123

Center. The time series of combined GPS/GLONASS
solutions was used as the basis for this study and to update
the antenna phase center model.
An updated antenna PCC file, called igs05(upd).atx, was
generated containing all receiver antenna/radome combi-
nations available with reliable GNSS-specific corrections.
Some converted field calibrations could be replaced by
robot calibrations in the updated file. These updated cor-
rections affect the station coordinates by up to 5 mm, even
if the GPS-derived values are used for both, the GPS and
the GLONASS observations. This result underlines the
problem of a stable reference frame realization on one hand
and the necessity to update the receiver antenna PCC on the
other hand.
GNSS-specific receiver antenna corrections became
available for many antenna types since 2005/06. The dif-
ferences between GPS and GLONASS PCV reach values
of up to 10 mm for the ionosphere-free linear combination.
The introduction of these GNSS-specific corrections has a
systematic impact of only up to 1 mm on the estimated
station coordinates in a multi-year solution. In some cases,
the GLONASS-specific ‘‘type-mean’’ values show larger
uncertainties than the GPS-specific values, because of the
smaller number of calibrated antennas. As soon as the
uncertainty is small enough, the GNSS-specific corrections
should be used, because the impact of GLONASS on a
combined GPS/GLONASS solution currently grows from
month to month thanks to the continuous growth of the
multi-GNSS tracking sites in the global IGS network and
thanks to the growing number of GLONASS satellites. The
differences between GPS- and GLONASS-specific receiver
antenna PCV are typically twice as large as the difference
between igs05.atx values and the updated receiver antenna
PCC for GPS. The latter differences caused 5-mm changes
in the estimated station heights.
An update of the currently used GNSS satellite antenna
phase center model is also necessary for at least formal
reasons. More or less the complete GLONASS constella-
tion has been replaced since the computation of the cur-
rently used igs05.atx values. The GLONASS tracking
situation has, moreover, dramatically improved since that
time. Today, the uncertainties of the GLONASS satellite
antenna corrections, as documented here, are comparable
to those of the GPS satellites.
Some satellite antennas show significant deviations from
the nadir-dependent block-specific PCV. Examples for
both GPS and GLONASS satellites were provided.
Exceptions from the block-specific PCC should therefore
be allowed for specific satellites. Satellite-specific correc-
tions should be considered for future satellite antenna
phase center models.
The updated satellite antenna phase center model does
not degrade the reference frame of combined GPS/
GLONASS solutions. GLONASS-only rapid-static or
kinematic solutions benefit most from the updated satellite
antenna corrections. The new coefficients will be provided
as a contribution to the next generation of standard IGS
antenna PCC.
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Station GLONASS-only
igs05(upd).atx for rec.
igs05.atx for sat.
GLONASS-only
igs05(upd).atx for rec.
igs05(upd).atx for sat.
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CAGZ 5.2 12.7 0.8 4.7 12.3 0.6
CRAR 0.7 1.1 0.7 0.6 1.4 0.0
UNB3 0.7 0.0 0.8 0.4 0.0 0.6
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RCMN 1.7 3.7 2.0 1.6 3.7 2.0
TSEA 2.9 3.0 6.2 3.5 1.5 6.8
HYDE 1.3 4.7 16.5 3.5 5.2 19.4
JOZ2 0.5 0.8 0.9 0.5 0.6 0.9
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