11institutetext:  Technische Universität Wien (TU Wien), Department of Geodesy
and Geoinformation, Wiedner Hauptstraße 8-10, 1040 Vienna, Austria
11email<EMAIL_ADDRESS>22institutetext: Federal Office of Metrology
and Surveying (BEV), Schiffamtsgasse 1-3, 1020 Vienna, Austria

# VLBI Celestial and Terrestrial Reference Frames VIE2022b

H. Krásná 11 L. Baldreich 11 J. Böhm 11 S. Böhm 11 J. Gruber 11 A.
Hellerschmied 22 F. Jaron 11 L. Kern 11 D. Mayer 22 A. Nothnagel 11 O.
Panzenböck 11 H. Wolf 11

(Received ; accepted )

###### Abstract

Context. We introduce the computation of global reference frames from Very
Long Baseline Interferometry (VLBI) observations at the Vienna International
VLBI Service for Geodesy and Astrometry (IVS) Analysis Center (VIE) in detail.
We focus on the celestial and terrestrial frames from our two latest solutions
VIE2020 and VIE2022b.

Aims. The current International Celestial and Terrestrial Reference Frames,
ICRF3 and ITRF2020, include VLBI observations until spring 2018 and December
2020, respectively. We provide terrestrial and celestial reference frames
including VLBI sessions until June 2022 organized by the IVS.

Methods. Vienna terrestrial and celestial reference frames are computed in a
common least squares adjustment of geodetic and astrometric VLBI observations
with the Vienna VLBI and Satellite Software (VieVS).

Results. We provide high-quality celestial and terrestrial reference frames
computed from 24-hour IVS observing sessions. The CRF provides positions of
5407 radio sources. In particular, positions of sources with few observations
at the time of the ICRF3 calculation could be improved. The frame also
includes positions of 870 new radio sources, which are not included in ICRF3.
The additional observations beyond the data used for ITRF2020 provide a more
reliable estimation of positions and linear velocities of newly established
VLBI Global Observing System (VGOS) telescopes.

###### Key Words.:

astrometry – reference systems – techniques: interferometric

##  1 Introduction

Geodetic and astrometric Very Long Baseline Interferometry (VLBI) observations
have been carried out since 1979. Since 1999, the VLBI sessions – from
scheduling to analyses – have been organized by the International VLBI Service
for Geodesy and Astrometry (IVS; Nothnagel et al. 2017). The Vienna IVS
Analysis Center (VIE), jointly operated by TU Wien and the Federal Office of
Metrology and Surveying (BEV) in Austria, is one of the eight international
institutions worldwide which actively contributed to studies needed for the
latest update of the International Celestial Reference Frame (ICRF) generating
one of the prototype realizations of the current ICRF3 (Charlot et al. 2020),
which was adopted by the International Astronomical Union in August 2018.

Furthermore, VIE, as one of the IVS Analysis Centers, participated in recent
international efforts of calculating an updated realization of the
International Terrestrial Reference System (ITRS). We analyzed a complete set
of individual VLBI observing sessions and provided pre-reduced normal equation
systems (NEQ) for combination with results of other IVS Analysis Centers at
the IVS Combination Center (Hellmers et al. 2022). The final International
Terrestrial Reference Frame (ITRF) originates from a further combination of
reprocessed solutions from four space geodetic techniques (Doppler
Orbitography by Radiopositioning Integrated on Satellite (DORIS), Global
Navigation Satellite Systems (GNSS), Satellite Laser Ranging (SLR), and VLBI).
This final combination allows to overcome the weaknesses of individual
techniques taking advantage of the strength of a combined solution. The
current version of the International Terrestrial Reference Frame, the ITRF2020
(Altamimi et al. 2022), was published in April 2022.

Besides our support of the international efforts towards conventional
reference frame realizations, we generate our own global VLBI reference
frames. The celestial and terrestrial reference frames, together with the
connecting Earth Orientation Parameters (EOP), are created in a common least
squares adjustment of VLBI observations using the Vienna VLBI and Satellite
Software version 3.3 (VieVS; Böhm et al. 2018). In this paper, we introduce
our global reference frame solution VIE2020 generated with VLBI observing
sessions as provided for the ITRF2020 computations. Furthermore, we also focus
on our recent global solution VIE2022b, which involves VLBI experiments
released after the ITRF2020 data deadline. In total, this solution includes
VLBI data from additional 18 months compared to ITRF2020. In Section 2, we
describe the VLBI data in detail and give information about the a priori
models and parametrization of the solutions. Extensive descriptions of the
estimated terrestrial and celestial reference frames, including comparisons to
the most recent international reference frames, are given in Sections 3 and 4,
respectively.

##  2 Data and analysis settings

We analyze VLBI group delays, which are fundamental observables of geodetic
and global astrometric VLBI. In the IVS operation scheme (Nothnagel et al.
2017), after correlation, fringe fitting and pre-processing, the group delays
are provided in so-called databases in the IVS vgosDB format via IVS Data
Centers for Level 2 data analysis. Databases of version 4 include group delays
at X-band (8.4 GHz) with ambiguities resolved and the ionospheric delay
calibrated with a linear combination with simultaneous S-band (2.3 GHz)
measurements.

Table 1: Overview of solutions described by this publication. |  | no. of | no. of
---|---|---|---
solution | data span | sessions | observations
VIE2020 | 1979.5 - 2021.0 | 6786 | $20.0\cdot 10^{6}$
VIE2020-sx | 1979.5 - 2021.0 | 6748 | $19.7\cdot 10^{6}$
VIE2022b | 1979.5 - 2022.5 | 7148 | $22.4\cdot 10^{6}$
VIE2022b-sx | 1979.5 - 2022.5 | 7058 | $21.6\cdot 10^{6}$
Table 2: A priori models used in the VIE2020 and VIE2022b solutions. The asterisk symbol denotes parameters modeled differently from our ITRF2020 contribution. A priori modeling |
---|---
Station a priori position |
TRF with post-seismic deformation | ITRF2014 model (Altamimi et al. 2016) for VIE2020
| ITRF2020 model (Altamimi et al. 2022) for VIE2022b
Station displacement |
solid Earth tides | IERS Conventions 2010 (Petit & Luzum 2010)
rotational deformation due to polar motion | secular polar motion (updated IERS Conventions 2010, https://iers-conventions.obspm.fr/content/chapter7/icc7.pdfversion 2018-02-01)
ocean pole tide loading | IERS Conventions 2010
ocean tidal loading | TPXO72 (Egbert & Erofeeva 2002)
atmospheric tidal and non-tidal loading | APL-VIENNA (Wijaya et al. 2013)
Earth orientation parameters |
∗daily EOP | IERS Bulletin A, https://maia.usno.navy.mil/ser7/finals2000A.allfinals2000A.all
subdaily EOP model |  Desai & Sibois (2016) (ocean tides + libration; linear interpolation)
tidal UT variations | IERS Conventions 2010, UT1S all constituents
precession/nutation model | IAU 2006/2000A (Mathews et al. 2002; Capitaine et al. 2003)
Troposphere |
hydrostatic delay | in situ pressure (Saastamoinen 1972)
hydrostatic mapping function | VMF3 (Landskron & Böhm 2018)
hydrostatic gradients | DAO gradients (MacMillan & Ma 1997)
∗wet mapping function | VMF3 (Landskron & Böhm 2018)
VLBI specific effects |
thermal antenna deformation |  Nothnagel (2009) with in situ temperature and GPT3 as backup
antenna axis offsets |  Nothnagel (2009), antenna-info.txt version 2020-04-23
station eccentricities |  https://ivscc.gsfc.nasa.gov/IVS_AC/apriori/ECCDAT_v2019Dec19.eccECCDAT_v2019Dec19.ecc
gravitational antenna deformation | Artz et al. (2014)
CRF | ICRF3 (Charlot et al. 2020)
galactic aberration | modeled with $\alpha_{GC}=266.4^{\circ},\delta_{GC}=-28.94^{\circ},A_{G}=5.8\leavevmode\nobreak\ $µas/yr, epoch 2015.0
Table 3: Parametrization of the VIE2020 and VIE2022b solutions. The asterisk symbol denotes a different analysis setting compared with our ITRF2020 contribution. Parametrization options |
---|---
clocks | piece-wise linear offsets (PWLO) with time interval 1 hour with relative constraints 43 ps (1.3 cm)
| between offsets, one rate and quadratic term
baseline clock offsets | offset without constraints at selected baselines
zenith wet delay | PWLO with time interval 30 min with relative constraints 50 ps (1.5 cm) between offsets
tropo. gradients | PWLO with time interval 3 hours with relative constraints 0.5 mm between offsets
∗ERP | PWLO with time interval 24 hours with relative constraints 10 mas
| fixed for networks with less than four telescopes
∗celestial pole offsets | PWLO with time interval 24 hours with relative constraints 0.1 µas
| fixed for networks with less than four telescopes
∗weighting | database weights (1/uncertainties) + elevation dependent weighting
Datum definition |
CRF | NNR w.r.t. ICRF3 defining sources except 0700-465, 0809-493
TRF | NNT/NNR on coordinates and velocities w.r.t. ITRF2014 on 21 stations for VIE2020
| NNT/NNR on coordinates and velocities w.r.t. ITRF2020 on 21 stations for
VIE2022b
Figure 1: Antenna participation in VLBI experiments in solution VIE2022b. Red
crosses depict the placement of position breaks. Only antennas with more than
50 experiments are plotted.

The solution VIE2020 is based on VLBI experiments observed at S/X frequencies,
which were analyzed for the ITRF2020 contribution111
https://ivscc.gsfc.nasa.gov/IVS_AC/ITRF2020/itrf2020_sx_sessionTable_v2021Feb10.txtitrf2020_sx_sessionTable_v2021Feb10.txt
by the IVS. In addition, 467 S/X experiments, scheduled mainly for astrometric
purposes to strengthen the ICRF in the Southern Hemisphere, were added to the
VIE2020 solution.

In recent years the geodetic VLBI technique has been undergoing a transition
phase from a legacy S/X era to a novel VLBI Global Observing System (VGOS;
Petrachenko et al. 2009). The VGOS system is based on the so-called broadband
delay, which uses several frequency bands in the range from 2.5 GHz to 14 GHz.
It had been decided that also the VGOS observations222
https://ivscc.gsfc.nasa.gov/IVS_AC/ITRF2020/itrf2020_vgos_sessionTable_v2021Feb10.txtitrf2020_vgos_sessionTable_v2021Feb10.txt
were included in the ITRF2020 solution. This enables a consistent estimation
of the coordinates for newly built VGOS telescopes within the international
terrestrial reference frame. On the other hand, if a global solution is
computed with a primary focus on the celestial reference frame, the mixture of
observations at different frequencies is not desirable. Therefore, we provide
two solutions, with and without VGOS sessions, denoted further as VIE2020 and
VIE2020-sx, respectively. Finally, both datasets have been extended by
sessions which arrived after the ITRF2020 data deadline, i.e., from January
2021 until June 2022. The solutions are denoted as VIE2022b and VIE2022b-sx
(see Table 1). There are 7148 VLBI sessions in the VIE2022b solution providing
22.4 million observations in total. The solution VIE2022b-sx is built by 21.6
million observations which makes a difference of 0.8 million observations
generated by 90 24-hour VGOS experiments.

In Table 2, we provide an overview of the a priori models used for the
calculation of the VLBI theoretical delays in the VIE2020 and VIE2022b
solutions. The only difference is the choice of the a priori terrestrial
reference frame: VIE2020 is modeled with ITRF2014 whereas VIE2022b is based on
the recently available ITRF2020. The asterisk symbol in Table 2 highlights the
application of a different model compared to our submission for the ITRF2020.
At this point, we want to stress the importance of a consistent use of
tropospheric mapping functions, more specifically, the same version of the
Vienna mapping functions (VMF). Mixing VMF3 (Landskron & Böhm 2018) and VMF1
(Böhm et al. 2006) for modeling the hydrostatic and wet part of the
tropospheric delays, respectively, leads to an estimated baseline length that
is on average 2 mm shorter compared to using VMF1 or VMF3 for both
constituents. In-depth analyses on that matter are ongoing.

In contrast to our ITRF2020 submission, the stochastic model, consisting of
the standard deviations derived from the fringe fitting process and elevation-
dependent observational noise $\sigma_{obs}$ (Eq. (1); Gipson et al. 2008), is
applied as a diagonal covariance matrix in the adjustment:

$\sigma^{2}_{obs}=\sigma^{2}_{0}+\sigma^{2}_{i}+\sigma^{2}_{j}=\sigma^{2}_{0}+\bigg{(}\frac{x_{i}}{\sin(\varepsilon_{i})}\bigg{)}^{2}+\bigg{(}\frac{x_{j}}{\sin(\varepsilon_{j})}\bigg{)}^{2},$
(1)

where $\sigma_{0}$ consists of a measurement noise $\sigma_{m}$ together with
an ionospheric delay formal error $\sigma_{ion}$:
$\sigma_{0}^{2}=\sigma_{m}^{2}+\sigma_{ion}^{2}$. The elevation-dependent
noise terms for stations $i$ and $j$, $\sigma_{i}$ and $\sigma_{j}$, are
computed with a constant $x$ = 6 ps for each station divided by the sine of
the associated elevation angle $\varepsilon$. Hence, observations at lower
averaged elevations obtain a lower weight in the least squares adjustment.

In the so-called first solution, a pre-analysis of the VLBI experiments with a
basic parametrization is carried out to check for possible problematic
behavior of the data. In the majority of cases, this can be solved with an
individual single session parametrization, e.g., the definition of clock
breaks, exclusion of cable calibration signals at stations, removal of large
outliers and removal of measurements at individual antennas or baselines, if
unavoidable. This configuration with even more possible options for each VLBI
experiment is stored in the VieVS-internal OPT-files333https://github.com/TUW-
VieVS/VLBI_OPThttps://github.com/TUW-VieVS/VLBI_OPT which we provide to the
public.

As a next step, the parametrization of the so-called main solution is
configured (see Table 3). In the software package VieVS the parametrization of
the time-variable unknowns is realized with piece-wise linear offsets (PWLO)
with certain time intervals and relative constraints between the offsets. The
single session least-squares adjustment is also important for identifying
baseline-dependent clock offsets (BCO; Krásná et al. 2021) in the network. The
baselines with an estimated clock offset larger than three times its formal
error are listed in the OPT-files for estimation in the final solution.

Next, session-wise normal equation systems (NEQ) are prepared for the final
global adjustment. After the reduction, these NEQ contain only parameters
constant over several VLBI experiments, which will be estimated globally. The
remaining parameters, which are time-dependent and do not profit from long
time series of observation, are squeezed out from the NEQ. In our solutions,
we estimate session-wise (baseline-dependent) clock parameters, zenith wet
delays, tropospheric gradients in north and east direction at individual
stations, and coordinates of telescopes which observed only occasionally
within our dataset. The Earth rotation parameters (ERP, i.e., polar motion and
UT1-UTC) are estimated session-wise for networks with more than three
telescopes. For the small networks of three stations or single baselines, all
five Earth orientation parameters (EOP) are fixed to a priori International
Earth Rotation and Reference Systems Service (IERS) Bulletin A values issued
by the IERS Rapid Service/Prediction Center at the U.S. Naval Observatory
(USNO).

The adjustment of the ensemble of sessions is applied to a normal equation
system which results from stacking the individual NEQ according to the theorem
of stacking pre-reduced normal equation systems by Helmert. The set of global
parameters determined by the common inversion of the stacked NEQ then only
contains coordinates and velocities of telescopes, amplitudes of annual and
semi-annual displacements in the station height of selected stations, and
positions of radio sources.

##  3 Vienna terrestrial reference frame

Producing a new global terrestrial reference frame (TRF) requires detailed
information about the underlying dataset and in particular about the
observation time of telescopes taking part in the observation schedules. A
traditional TRF catalog consists of station coordinates at a given epoch and
the linear velocity. The velocity determination requires a sufficiently long
observation time series of the telescope in order to enable a confident
approximation of the antenna linear movement caused predominantly by the
underlying plate tectonics. For this reason, we set a lower limit of 15 VLBI
experiments including the particular station and a minimum time span of five
years between the first and last experiment. For telescopes, which do not
fulfill these conditions, the position is estimated as time series from
individual sessions which is averaged a posteriori to the final single
position. Exceptions to this rule are telescopes at co-location sites with
older VLBI telescopes. In this case, the corrections to the a priori velocity
for both (all) telescopes are tied together with a relative constraint which
forces the velocity corrections at the specified telescopes to be identical.
The approach requires that the same a priori velocity is used for all involved
telescopes. The definition of interval breaks because of discontinuous station
movements, as well as the modeling of the non-linear motion caused by post
seismic deformation, is taken from the underlying a priori catalog, i.e.,
ITRF2014 and ITRF2020 for VIE2020 and VIE2022b solutions, respectively. Table
4 summarizes the pairs (groups) of telescopes tied together in solution
VIE2022b.

Table 4: Co-located VLBI telescopes in VIE2022b where velocity ties are
applied. telescopes - location
---
DSS15, DSS13 - CA, USA
DSS65, DSS65A, ROBLED32 - Spain
FD-VLBA, MACGO12M - TX, USA
FORTORDS, FORT_ORD - CA, USA
GGAO7108, GORF7102, GGAO12M - MD, USA
HARTRAO, HART15M - South Africa
HOBART26, HOBART12 - TAS, Australia
HRAS_085, FTD_7900 - TX, USA
KASHIM34, KASHIM11, KASHIMA - Japan
KAUAI, KOKEE, KOKEE12M - HI, USA
METSAHOV, METSHOVI - Finland
MIZNAO10, VERAMZSW - Japan
MOJAVE12, MOJ_7288 - CA, USA
NRAO20, NRAO_140, NRAO85_1, NRAO85_3 - WV, USA
NYALES20, NYALE13S - Norway
ONSALA60, ONSA13NE, ONSA13SW - Sweden
OV-VLBA, OVRO_130, OVR_7853 - CA, USA
PIETOWN, VLA-N8 - NM, USA
RICHMOND, MIAMI20 - FL, USA
SVETLOE, SVERT13V - Russia
WETTZELL, TIGOWTZL, WETTZ13N, WETTZ13S - Germany
YEBES, YEBES40M, RAEGYEB - Spain
YLOW7296, YELLOWKN - Canada
Table 5: Annual and semi-annual signal (described with amplitude $A$ and phase $\phi$) in station height of new VGOS antennas and of appertaining legacy antennas at the common sites observing in more than 50 sessions in VIE2022b distributed uniformly over the year. For comparison, the harmonic signal in height from ITRF2020 for the entire site is noted in the respective last rows. antenna | TRF |  $A$ [mm] |  $\phi$ [∘] |  $A$ [mm] |  $\phi$ [∘] | no. of sessions | data span [yr:doy]
---|---|---|---|---|---|---|---
|  | annual signal | semi-annual signal |  |
GGAO12M | VIE2022b | 2.7 $\pm$ 0.3 | 240 $\pm$ 05 | 0.3 $\pm$ 0.3 | 130 $\pm$ 47 | 85 | 2017:338 - 2022:098
GGAO7108 | VIE2022b | 7.9 $\pm$ 3.3 | 187 $\pm$ 21 | 2.0 $\pm$ 3.3 | 149 $\pm$ 86 | 65 | 1993:118 - 2002:219
| ITRF2020 | 3.1 $\pm$ 0.2 | 226 $\pm$ 04 | 0.2 $\pm$ 0.2 | 105 $\pm$ 75 |  |
KOKEE12M | VIE2022b | 2.1 $\pm$ 0.5 | 123 $\pm$ 13 | 2.3 $\pm$ 0.5 | 145 $\pm$ 12 | 86 | 2017:338 - 2022:098
KOKEE | VIE2022b | 2.4 $\pm$ 0.2 | 172 $\pm$ 05 | 0.6 $\pm$ 0.2 | 37 $\pm$ 20 | 2790 | 1993:160 - 2022:175
| ITRF2020 | 1.1 $\pm$ 0.3 | 160 $\pm$ 17 | 0.4 $\pm$ 0.3 | 115 $\pm$ 47 |  |
MACGO12M | VIE2022b | 2.6 $\pm$ 0.3 | 325 $\pm$ 07 | 0.9 $\pm$ 0.3 | 30 $\pm$ 22 | 56 | 2020:022 - 2022:102
FD-VLBA | VIE2022b | 1.3 $\pm$ 0.2 | 220 $\pm$ 11 | 1.0 $\pm$ 0.2 | 156 $\pm$ 14 | 405 | 1992:014 - 2022:048
HRAS_085 | VIE2022b | 3.1 $\pm$ 2.6 | 177 $\pm$ 40 | 3.7 $\pm$ 2.4 | 39 $\pm$ 37 | 729 | 1980:103 - 1990:303
| ITRF2020 | 3.1 $\pm$ 0.4 | 176 $\pm$ 06 | 0.5 $\pm$ 0.3 | 151 $\pm$ 39 |  |
NYALE13S | VIE2022b | 7.3 $\pm$ 1.0 | 336 $\pm$ 09 | 8.0 $\pm$ 1.1 | 137 $\pm$ 08 | 176 | 2020:049 - 2022:175
NYALES20 | VIE2022b | 3.1 $\pm$ 0.1 | 254 $\pm$ 03 | 2.2 $\pm$ 0.1 | 98 $\pm$ 04 | 2282 | 1994:278 - 2022:173
| ITRF2020 | 2.3 $\pm$ 0.5 | 295 $\pm$ 13 | 1.6 $\pm$ 0.5 | 121 $\pm$ 19 |  |
ONSA13SW | VIE2022b | 3.9 $\pm$ 0.3 | 207 $\pm$ 05 | 1.8 $\pm$ 0.3 | 177 $\pm$ 10 | 85 | 2019:008 - 2022:014
ONSA13NE | VIE2022b | 5.4 $\pm$ 0.3 | 213 $\pm$ 03 | 2.4 $\pm$ 0.3 | 179 $\pm$ 07 | 104 | 2019:008 - 2022:098
ONSALA60 | VIE2022b | 4.3 $\pm$ 0.2 | 211 $\pm$ 03 | 1.7 $\pm$ 0.2 | 16 $\pm$ 07 | 1162 | 1980:208 - 2022:144
| ITRF2020 | 3.5 $\pm$ 0.3 | 203 $\pm$ 05 | 0.4 $\pm$ 0.3 | 117 $\pm$ 49 |  |
RAEGSMAR | VIE2022b | 0.9 $\pm$ 0.8 | 249 $\pm$ 42 | 2.6 $\pm$ 0.6 | 45 $\pm$ 14 | 89 | 2018:352 - 2022:173
| ITRF2020 | 0.7 $\pm$ 1.3 | 110 $\pm$ 106 | 0.7 $\pm$ 1.3 | 116 $\pm$ 108 |  |
RAEGYEB | VIE2022b | 0.9 $\pm$ 0.3 | 254 $\pm$ 27 | 0.6 $\pm$ 0.3 | 69 $\pm$ 37 | 80 | 2015:048 - 2022:098
YEBES40M | VIE2022b | 5.4 $\pm$ 0.3 | 242 $\pm$ 03 | 3.8 $\pm$ 0.3 | 6 $\pm$ 04 | 391 | 2008:256 - 2022:116
| ITRF2020 | 3.4 $\pm$ 0.4 | 229 $\pm$ 07 | 1.1 $\pm$ 0.4 | 1 $\pm$ 23 |  |
WETTZ13S | VIE2022b | 4.3 $\pm$ 0.3 | 227 $\pm$ 04 | 0.9 $\pm$ 0.3 | 4 $\pm$ 17 | 88 | 2017:338 - 2022:102
WETTZ13N | VIE2022b | 6.0 $\pm$ 0.3 | 243 $\pm$ 03 | 1.8 $\pm$ 0.3 | 127 $\pm$ 09 | 418 | 2015:161 - 2022:173
WETTZELL | VIE2022b | 5.4 $\pm$ 0.1 | 232 $\pm$ 01 | 0.5 $\pm$ 0.1 | 143 $\pm$ 13 | 4080 | 1983:321 - 2022:175
| ITRF2020 | 4.1 $\pm$ 0.2 | 219 $\pm$ 03 | 0.6 $\pm$ 0.2 | 17 $\pm$ 22 |  |
Table 6: Difference in height and in height velocity of VIE2022b w.r.t. ITRF2020 for telescopes listed in Table 5. antenna |  $\Delta h$ [mm] |  $\Delta\dot{h}$ [mm/yr]
---|---|---
FD-VLBA | 1.6 $\pm$ 1.4 | 0.21 $\pm$ 0.08
GGAO12M | 7.7 $\pm$ 3.5 | -0.28 $\pm$ 0.11
GGAO7108 | -77.3 $\pm$ 30.6 | -0.28 $\pm$ 0.11
HRAS_085 | 33.0 $\pm$ 17.4 | 1.74 $\pm$ 0.63
KOKEE | -0.8 $\pm$ 1.2 | -0.16 $\pm$ 0.08
KOKEE12M | -1.6 $\pm$ 3.6 | -0.16 $\pm$ 0.08
MACGO12M | 16.3 $\pm$ 11.2 | 0.21 $\pm$ 0.08
NYALE13S | -2.2 $\pm$ 27.3 | 0.42 $\pm$ 5.49
NYALES20 | 4.7 $\pm$ 1.1 | 0.38 $\pm$ 0.09
ONSA13NE | 2.6 $\pm$ 3.1 | 0.01 $\pm$ 0.07
ONSA13SW | 4.2 $\pm$ 4.0 | 0.01 $\pm$ 0.07
ONSALA60 | 1.4 $\pm$ 1.0 | 0.01 $\pm$ 0.07
RAEGSMAR | -21.7 $\pm$ 390.9 | 7.52 $\pm$ 96.93
RAEGYEB | 9.9 $\pm$ 2.0 | -0.43 $\pm$ 0.28
WETTZ13N | 3.2 $\pm$ 1.1 | 0.20 $\pm$ 0.06
WETTZ13S | 4.0 $\pm$ 1.5 | 0.20 $\pm$ 0.06
WETTZELL | 4.2 $\pm$ 0.9 | 0.20 $\pm$ 0.06
YEBES40M | 2.2 $\pm$ 1.3 | -0.43 $\pm$ 0.28
Table 7: Transformation parameters from ITRF2020 to VIE2020 (top of the table) and from ITRF2020 to VIE2022b (bottom of the table) computed from stations with mean coordinate errors below 10 mm in Vienna TRFs. In each second row the rate per year is given. $T_{x}$ [mm] |  $T_{y}$ [mm] |  $T_{z}$ [mm] |  $R_{x}$ [µas] |  $R_{y}$ [µas] |  $R_{z}$ [µas] | scale s [ppb] ([mm])
---|---|---|---|---|---|---
$\dot{T}_{x}$ [mm/yr] |  $\dot{T}_{y}$ [mm/yr] |  $\dot{T}_{z}$ [mm/yr] |  $\dot{R}_{x}$ [µas/yr] |  $\dot{R}_{y}$ [µas/yr] |  $\dot{R}_{z}$ [µas/yr] |  $\dot{s}$ [ppb/yr] ([mm/yr])
-0.8 $\pm$ 1.7 | -3.4 $\pm$ 1.7 | -2.0 $\pm$ 1.7 | 60.5 $\pm$ 69.2 | 21.6 $\pm$ 68.5 | -5.4 $\pm$ 54.2 | 0.56 $\pm$ 0.26 ( 3.6 $\pm$ 1.7)
0.0 $\pm$ 0.0 | -0.2 $\pm$ 0.0 | 0.0 $\pm$ 0.0 | 6.0 $\pm$ 1.7 | 0.8 $\pm$ 1.8 | 4.4 $\pm$ 1.5 | 0.02 $\pm$ 0.01 ( 0.1 $\pm$ 0.0)
1.9 $\pm$ 0.7 | -1.0 $\pm$ 0.7 | -2.3 $\pm$ 0.7 | 35.4 $\pm$ 29.4 | 36.2 $\pm$ 29.0 | 21.4 $\pm$ 23.2 | 0.59 $\pm$ 0.11 ( 3.7 $\pm$ 0.7)
0.2 $\pm$ 0.0 | -0.2 $\pm$ 0.0 | -0.2 $\pm$ 0.0 | 5.6 $\pm$ 0.7 | 4.3 $\pm$ 0.7 | 1.8 $\pm$ 0.6 | 0.03 $\pm$ 0.00 ( 0.2 $\pm$ 0.0)

To align the solutions on the a priori frame, no-net-translation (NNT) and no-
net-rotation (NNR) conditions were applied to the coordinates and velocities
of a set of 21 stable long operating telescopes: ALGOPARK, BR-VLBA, FD-VLBA,
FORTLEZA, HARTRAO, HN-VLBA, HOBART26, KASHIMA, KOKEE, KP-VLBA, LA-VLBA,
MATERA, NL-VLBA, NOTO, NYALES20, ONSALA60, OV-VLBA, SC-VLBA, SVETLOE,
WESTFORD, WETTZELL. The reference epoch was set to January 1st, 2015 for both
frames, VIE2020 and VIE2022b. Figure 1 shows the active telescope
participation in the solution VIE2022b of telescopes which took part in more
than 50 experiments as a function of time. The red crosses indicate the
defined breaks in position or velocity.

Figure 2: Annual (blue) and semi-annual (red) height signal in VIE2022b. The
amplitude is depicted by the arrow length. The phase of the maximum
displacement is represented by the orientation of the arrow. If the arrow
points towards north, the maximum appears in January and it continues
clockwise further. The maximum of the semi-annual signal is depicted in the
first half year. Figure 3: Session-wise scale factor computed with VIE2022b
parametrization w.r.t. ITRF2020. The black line represents the smoothed scale
factor obtained by local regression using a span of 5% of the total number of
data points.

In addition, the seasonal displacement in the height component at annual and
semi-annual periods $P_{i}$ ($P_{1}=365.25$ days, $P_{2}=182.63$ days) at
chosen stations were estimated. The station height displacement $\Delta
h=\Delta h_{1}+\Delta h_{2}$ is parametrized in a form of sine and cosine
amplitude ($A_{si},A_{ci}$):

$\Delta h_{i}=A_{ci}\cdot\cos\bigg{(}\frac{mjd-\mathrm{mjd_{0}}}{P_{i}}\cdot
2\pi\bigg{)}+A_{si}\cdot\sin\bigg{(}\frac{mjd-\mathrm{mjd_{0}}}{P_{i}}\cdot
2\pi\bigg{)},$ (2)

where the reference epoch $\mathrm{mjd_{0}}$ was set to January 1st, 2000 and
$mjd$ is the modified Julian date of the experiment. The amplitude $A_{i}$ and
phase $\phi_{i}$ of the seasonal wave is obtained with the basic mathematical
relation as:

$A_{i}=\sqrt{A_{ci}^{2}+A_{si}^{2}},\qquad\phi_{i}=\arctan{\bigg{(}\frac{A_{si}}{A_{ci}}\bigg{)}}.$
(3)

For these parameters, we selected 74 antennas which observed in at least 50
experiments distributed uniformly over a year. To estimate the seasonal
variation of the signal, the measurements have to cover the changing seasons.
For this reason, we did not estimate the seasonal displacement for EFLSBERG,
OHIGGINS, PARKES, SYOWA and YLOW7296 because their participation in VLBI
sessions is rather episodic (compare with Fig. 1). The estimation of the
amplitude for a semi-annual signal is relevant especially for telescopes in
the subtropical zones where the sum of the annual and semi-annual signal fits
the changes in the telescope height over a year best. The estimated annual and
semi-annual signals for all 74 telescopes are plotted in Fig. 2 as arrows
representing the amplitude (length) and phase (direction, azimuth 0 = Jan 1)
of the height displacement at the respective periods. In Table 5, we highlight
the estimates of the harmonic signal at the newly established VGOS antennas
and complete the information with the co-located legacy telescopes. The
accuracy of the estimated signal depends on the number and distribution of the
experiments allowing the correct tracing of the height change over the year.
For example, in Europe, the maximum reading of the annual signal in the height
occurs in the summer months July and August, which means that the crust goes
up. At observatories in Onsala or Wettzell, there is an agreement between the
harmonic height changes estimated at all telescopes with a positive maximum of
4-6 mm occurring in July. This can be explained by the minimal water content
in the ground and no snow load since we applied neither the harmonic signal
provided for ITRF2014 or ITRF2020 nor any hydrology loading modeling in the
data analysis. These results agree with former findings published, e.g., by
Tesmer et al. (2009) or Krásná et al. (2015). For comparison, Table 5 includes
the amplitude and phase for annual and semi-annual signals in height computed
from the sine and cosine amplitudes as they are provided with ITRF2020444
https://itrf.ign.fr/ftp/pub/itrf/itrf2020/ITRF2020-Frequencies-ENU-
CF.snxITRF2020-Frequencies-ENU-CF.snx. In ITRF2020 an identical signal at all
telescopes within each geodetic site is given. We would like to point out,
that for telescope NYALE13S an erroneous harmonic signal of zero amplitude is
given in ITRF2020, which should be treated carefully in a potential VLBI
analysis.

To complete the information about the difference in height at VGOS antennas
from Table 5 in VIE2022b and ITRF2020, the height differences for the epoch
2015 and the differences in height velocity computed as VIE2022b minus
ITRF2020 are listed in Table 6. The formal errors are computed as propagation
of uncertainties of both catalogs. At most telescopes the estimated heights
are higher in VIE2022b compared to ITRF2020. In particular, it is true for all
differences exceeding their formal error and telescopes observing in the final
years. Differences in the estimated height which lie above the three-fold
formal error occur at NYALES20 (4.7 $\pm$ 1.1 mm), RAEGYEB (9.9 $\pm$ 2.0 mm)
and WETTZELL (4.2 $\pm$ 0.9 mm). This agrees with the fact that the scale
factor of the VIE2022b is higher than the scale factor of ITRF2020. Table 7
summarizes 14 transformation parameters (three translation parameters
($T_{x}$, $T_{y}$, $T_{z}$), three rotation parameters ($R_{x}$, $R_{y}$,
$R_{z}$) and one scale factor with their time derivatives) computed from
stations with mean coordinate error $m_{xyz}$ (Eq. (4)) lower than 10 mm in
VIE2020 and VIE2022b, respectively:

$m_{xyz}=\sqrt{\big{(}m_{x}^{2}+m_{y}^{2}+m_{z}^{2}\big{)}/3},$ (4)

where $m_{x}^{2},m_{y}^{2},$ and $m_{z}^{2}$ are formal errors of the
coordinates. The top lines of the table include parameters describing the
transformation from ITRF2020 to VIE2020, and the bottom part lists parameters
from ITRF2020 to VIE2022b. The maximum translation of $-3.4\pm 1.7$ mm occurs
in y-direction between VIE2020 and ITRF2020 but it is still within the three-
fold of its formal error. The remaining translation parameters are negligible.
All rotations are close or below their formal errors and the maximum value of
$60.5\pm 69.2\leavevmode\nobreak\ $µas appears in x-direction between VIE2020
and ITRF2020. The scale factors from the Vienna VLBI TRFs VIE2020 and VIE2022b
show a difference of $0.56\pm 0.26$ ppb and $0.59\pm 0.11$ ppb w.r.t.
ITRF2020, respectively. The ITRF2020 relies by its scale definition on two
space geodetic techniques, namely VLBI and SLR. The scale of the ITRF2020
long-term frame was determined using internal constraints in such a way that
there are zero scale and scale rate between ITRF2020 and the scale and scale
rate averages of VLBI selected sessions up to 2013.75 (see ITRF2020
webpage555https://itrf.ign.fr/en/solutions/ITRF2020https://itrf.ign.fr/en/solutions/ITRF2020).
After 2014 there is an increase in the scale determined from the VLBI
technique w.r.t. ITRF2020 as can be seen in Fig. 3.

##  4 Celestial reference frame

Celestial reference frames (CRF) are estimated in common global solutions
together with the terrestrial reference frames. We focus on the CRF including
the most recent geodetic and astrometric VLBI experiments until June 2022
observed at S/X frequencies. The catalog VIE2022b-sx consists of 5407 radio
sources. All sources present in the underlying data are kept in the analysis
and their positions are estimated as global parameters. This means that we
neither remove gravitational lenses from the solution, as it was done in
ICRF3, nor do we estimate sources with non-linear motions as session-wise
parameters (so-called special handling sources in ICRF2 (Fey et al. 2015)). We
use ICRF3 as a priori frame and model the galactic acceleration correction
with the adopted ICRF3 value of $A_{G}=5.8\leavevmode\nobreak\ $µas/yr for the
amplitude of the solar system barycenter acceleration vector in direction to
the Galactic center (right ascension $\alpha_{GC}=266.4^{\circ}$, declination
$\delta_{GC}=-28.94^{\circ}$) for the epoch 2015.0.

The alignment of the frame is accomplished by unweighted no-net-rotation
constraints (NNR; Jacobs et al. 2010) to the positions of 301 ICRF3 defining
sources. In ICRF3, a new set of defining sources was selected (independent of
ICRF2 defining sources) based on several criteria, one of them being a uniform
distribution on the sky. Because of the generally sparser distribution of the
observed radio sources in the far south, sources with lower position stability
or a low number of observations had to be included in the set of defining
sources. However, after several tests, we excluded two ICRF3 defining sources
(0700-465 and 0809-493) from the NNR condition since their observations led to
a large distortion of the newly estimated frame. In Fig. 4, we show results of
one of our tests regarding the ICRF3 datum sources. We divided the 303 ICRF3
datum sources into three groups so that we included every third source from
the ICRF3 datum source list sorted in ascending order according to their right
ascension. Then we computed three global solutions which we aligned to ICRF3
with NNR applied to coordinates of the 101 ICRF3 datum sources included in the
three independent lists. Fig. 4 shows the estimated source coordinates
$\alpha^{*}$ and $\delta$ with respect to a solution where all 303 ICRF3 datum
sources were in the NNR condition. We use the designation $\alpha^{*}$ for
right ascension scaled by declination of the source, i.e.,
$\alpha^{*}=\alpha\cdot\cos{\delta}$. Each color represents one of the global
solutions aligned with the subgroup of 101 ICRF3 defining sources. A
systematic difference in the estimated coordinates when excluding 202 radio
sources from the NNR condition is evident with the peak of the differences at
around 20 µas for both coordinates. In particular, we identified two radio
sources with a difference in the estimated coordinates above 1 mas when
dropped from the NNR condition (0700-465, $\Delta\alpha^{*}=3.9$ mas,
$\Delta\delta=3.5$ mas; 0809-493, $\Delta\alpha^{*}=4.2$ mas,
$\Delta\delta=1.7$ mas). Therefore we did not use them to align our Vienna
celestial reference frames (described below) to ICRF3. With more observations
of these sources, their position variability can be studied in the future.

Figure 4: Radio source coordinate estimates from three solutions applying the
NNR condition on three different subgroups of 101 ICRF3 defining sources each.
The differences are plotted w.r.t. a solution aligned with all 303 ICRF3
defining sources. Figure 5: Increase in number of observations for the ICRF3
defining sources by 2022.5 after the release of ICRF3. The black dashed line
depicts the ecliptic plane and the red line represents the galactic plane with
the Galactic center denoted as an empty black circle. Figure 6: Increase in
number of observations for the ICRF3 non-defining sources by 2022.5 after the
release of ICRF3. Figure 7: Number of observations for new sources after the
release of ICRF3 until 2022.5.

We depict the number of new observations for ICRF3 defining sources in Fig. 5
and non-defining sources in Fig. 6 after the ICRF3 cutoff date June 2022. The
majority of new observations for the deep south sources ($\delta<-45^{\circ}$)
come from three dedicated programs: astrometric IVS Celestial Reference Frame
Deep South sessions (IVS-CRDS; de Witt et al. 2019), sessions performed under
the umbrella of the Asia-Oceania VLBI Group for Geodesy and Astrometry (AOV;
McCallum et al. 2019), and sessions conducted with the geodetic Australian
mixed-mode program (McCallum et al. 2022). In addition, Fig. 7 shows the 870
sources which were observed in geodetic/astrometric VLBI experiments after the
ICRF3 release for the first time. The majority of the new sources was observed
in dedicated astrometry experiments conducted by the AOV and by the Very Long
Baseline Array (VLBA; Zensus et al. 1995). In particular, the goal was to
increase the number of sources at the ecliptic plane available for the
navigation of interplanetary spacecrafts (de Witt et al. 2022). Since the VLBA
is located on United States territory, the network is able to observe radio
sources only down to approximately -45∘ declination. Table 8 summarizes the
statistics on observations from the Figs. 5 \- 7. It is evident that despite
the great international effort (de Witt et al. 2021), the increase of
observations to southern sources is still slower than the increase to northern
sources, mainly due to the lack of large geodetic VLBI dishes in the Southern
Hemisphere needed for observations of faint sources.

Table 8: Statistics on observations in VIE2022b-sx since the ICRF3 cutoff date. The values are divided for ICRF3 defining sources (def), ICRF3 non-defining sources (non-def) and sources not included in ICRF3 (new). The number of sources, number of observations and a median value for observations per source is given separately for three declination zones separated by $\delta=0^{\circ}$ and $\delta=-45^{\circ}$. | $\delta$ | no. of | no. of | median of
---|---|---|---|---
|  | sources | obs. | obs. per sou.
def | ¡0∘, 90∘¿ | 149 | $1.6\cdot 10^{6}$ | 3395
| ¡-45∘, 0∘¿ | 105 | $7.3\cdot 10^{5}$ | 2111
| ¡-90∘, -45∘¿ | 46 | $4.5\cdot 10^{4}$ | 273
non-def | ¡0∘, 90∘¿ | 2467 | $1.5\cdot 10^{6}$ | 205
| ¡-45∘, 0∘¿ | 1561 | $4.6\cdot 10^{5}$ | 125
| ¡-90∘, -45∘¿ | 209 | $5.7\cdot 10^{4}$ | 62
new | ¡0∘, 90∘¿ | 493 | $1.0\cdot 10^{5}$ | 198
| ¡-45∘, 0∘¿ | 364 | $5.6\cdot 10^{4}$ | 140
| ¡-90∘, -45∘¿ | 13 | $5.4\cdot 10^{2}$ | 28

The histogram of VIE2022b-sx formal errors (Fig. 8) gives an overview of the
distribution of uncertainties in $\alpha^{*}$ and $\delta$. The median formal
error computed over all sources is 143 µas for $\alpha^{*}$ and 250 µas for
$\delta$ corresponding to the peaks of the histogram. The ratio between the
median formal error for $RA^{*}$ and $De$ of a factor of two remains similar
to that in ICRF3 (i.e., 127 µas / 218 µas). In the VIE2022b-sx CRF catalog, we
follow the recommendation of the ICRF3 which advises inflating the formal
errors of the source coordinates from the global least squares adjustment by a
factor of 1.5 and then adding a noise floor of 30 µas in quadrature to avoid
the dropping of the uncertainties to unrealistic values for frequently
observed sources (Charlot et al. 2020). The individual formal errors of source
coordinates in VIE2022b-sx (black dots) and in ICRF3 (light blue dots) with
respect to the number of observations are shown in Fig. 9. Theoretically, if
there were no correlations between individual observations, the estimated
formal errors would drop with the square root of observations, represented as
the red line in Fig. 9. The deviation from this rule, as can be seen in the
figure, is caused by accounting of the elevation dependent weighting of
observations in VIE2022b-sx which changes the stochastic model and by applying
the noise floor which influences the formal errors of the most frequently
observed sources.

Figure 8: Distribution of source coordinate formal errors in VIE2022b-sx.

Figure 9: Formal errors in $\alpha^{*}$ (upper plot) and $\delta$ (lower plot)
with respect to number of observations in VIE2022b-sx (black dots) and ICRF3
(light blue dots). The red line depicts the hypothetical decrease of formal
errors with the square root of the number of observations.

Fig. 10 shows the formal errors of VIE2022b-sx source coordinates (grey dots)
with respect to declination. The red crosses depict the median formal error
computed over 2∘ wide declination zones. Especially uncertainties in
declination are showing a growth starting at 30∘ declination (median $\sigma
De$ = 150 µas) which accelerates until $-45^{\circ}$ declination (median
$\sigma De$ = 700 µas). Further south, the formal errors jump back to values
around 250 µas. The explanation can be found in the station network. The
majority of sources was observed in campaigns of Very Long Baseline Array
Calibrator Survey (VCS; Beasley et al. 2002; Fomalont et al. 2003; Petrov et
al. 2005, 2006, 2008; Kovalev et al. 2007) or VCS-II (Gordon et al. 2016)
conducted by the VLBA network which, based on its location, observes the
southern sources under rather low elevation angles. This means that the path
of the signal in the atmosphere is longer, which leads to larger formal errors
of the estimated position of the emitting radio sources.

Figure 10: VIE2022b-sx formal errors (grey dots) in $\alpha^{*}$ (upper plot)
and $\delta$ (lower plot) with respect to declination. Crosses depict median
formal errors computed over 2∘ declination in red for VIE2022b-sx and in blue
for ICRF3.

In Fig. 11, we plot the correlation coefficient between $\alpha^{*}$ and
$\delta$ in VIE2022b-sx with respect to the number of observations of the
respective source. The median absolute correlation coefficient is 0.15 which
implies a weak correlation between the two coordinates. Nevertheless, the plot
shows that the correlation for sources with a lower number of observations can
be strong and the correlation coefficient can be close to 1. With an
increasing number of observations, the maximal possible correlation between
the two estimated source coordinates decreases to about 0.3 for $10^{3}$
observations and stays below 0.1 for the most observed sources.

Figure 11: Correlation coefficients between $\alpha^{*}$ and $\delta$ with
respect to number of observations in VIE2022b-sx.

The difference between VIE2022b-sx and ICRF3 is further analyzed with a vector
spherical harmonics decomposition (VSH; Mignard, F. & Klioner, S. 2012; Titov,
O. & Lambert, S. 2013; Mayer & Böhm 2020). Table 9 shows 16 estimated
parameters relevant to the second degree VSH, i.e., rotation
($R_{1},R_{2},R_{3}$), dipole ($D_{1},D_{2},D_{3}$), and ten coefficients
($a$) for the quadrupole harmonics of magnetic ($m$) and electric ($e$) type.
Prior to the comparison, outliers from the VIE2020b-sx CRF were removed. As
outliers, we defined sources with an angular separation to ICRF3 larger than
10 mas or with a position formal error higher than 10 mas. In total, 46
outliers were removed from the VSH computation. The list of sources with
angular separation to ICRF3 ¿ 10 mas is given in Table 10. The non-linear
change in position after the ICRF3 release for some of them (3C48, CTA21,
1328+254) was reported by e.g., Frey & Titov (2021) or Titov et al. (2022).
The causes for the position change of the remaining sources are subject to
further investigation.
The VSH between two catalogs ($cat1$ and $cat2$) is obtained with a least
squares adjustment for the common radio sources. Unlike the NNR condition in
the Vienna global solution, the least squares adjustment for the VSH
estimation is carried out using a weight matrix $P$, where
$P=P_{cat1}+P_{cat2}$ and the $P_{cat}$ contains correlation between
$\alpha^{*}$ and $\delta$ for the respective source as reported in the
catalog. The elements of $P_{cat}$ for one source $i$ are computed as:

$\displaystyle
P_{i\alpha^{*},i\alpha^{*}}=(\sigma_{\alpha}\cdot\cos\delta)^{-2},$ (5)
$\displaystyle P_{i\delta,i\delta}=(\sigma_{\delta})^{-2},$ $\displaystyle
P_{i\alpha^{*},i\delta}=P_{i\delta,i\alpha^{*}}=(cr\cdot\sigma_{\alpha}\cdot\cos\delta\cdot\sigma_{\delta})^{-1},$

where $cr$ stands for the correlation coefficient. In the first two columns of
Table 9, we show the weighted VSH computed between VIE2022b-sx and ICRF3, and
between VIE2022b-sx and USNO-2022July03666
https://crf.usno.navy.mil/quarterly-vlbi-
solutionhttps://crf.usno.navy.mil/quarterly-vlbi-solution. USNO-2022July03 is
a CRF solution computed in the same manner as the ICRF3 by the USNO where the
time span of processed VLBI experiments is similar to VIE2022b-sx. For both
CRF catalogs, ICRF3 and USNO-2022July03, the difference to VIE2022b-sx is
described with similar VSH estimates where each of them is below the noise
floor of 30 µas of the catalogs. The maximum rotation parameter is 13 µas for
$R_{3}$ between VIE2022b-sx and ICRF3. The two largest VSH parameters are the
$D_{3}$ and the quadrupole term $a_{2,0}^{e}$ which reach $-25\pm
2\leavevmode\nobreak\ $µas and $20\pm 3\leavevmode\nobreak\ $µas for
VIE2022b-sx w.r.t. ICRF3, and $-18\pm 1\leavevmode\nobreak\ $µas and $11\pm
2\leavevmode\nobreak\ $µas for VIE2022b-sx w.r.t. USNO-2022July03. The
connection of these two parameters to the modeling of tropospheric gradients
in the VLBI analysis and their constraints applied in the adjustment was
shown, e.g., by Mayer & Böhm (2020). Additionally, we computed the VSH between
VIE2022b-sx and USNO-2022July03 without the weight matrix $P$. In the last
column of Table 9 one sees a slight decrease of the $D_{3}$ and $a_{2,0}^{e}$
parameters. One possible explanation lies in the larger declination formal
errors of sources located around $-40^{\circ}$ declination as discussed in Fig
10. Taking their formal errors as weights into account in the VSH computation
can lead to the larger distortion in the north-south direction described by
the $a_{2,0}^{e}$ term.

Table 9: VSH parameters up to degree two for VIE2022b-sx minus ICRF3, and VIE2022b-sx minus USNO-2022July03 after eliminating outliers. The parameter ”weights” denotes the weight matrix applied in the VSH least squares adjustment. Units are µas. | VIE2022b-sx versus
---|---
| ICRF3 | USNO-2022July03
weights | yes | yes | no
$R_{1}$ | $+9\pm 2$ | $+11\pm 1$ | $+3\pm 6$
$R_{2}$ | $-9\pm 2$ | $+4\pm 1$ | $-11\pm 6$
$R_{3}$ | $-13\pm 2$ | $-7\pm 1$ | $-10\pm 6$
$D_{1}$ | $+1\pm 2$ | $-2\pm 1$ | $-14\pm 6$
$D_{2}$ | $-6\pm 2$ | $-7\pm 1$ | $-7\pm 6$
$D_{3}$ | $-25\pm 2$ | $-18\pm 1$ | $-14\pm 6$
$a_{2,0}^{e}$ | $+20\pm 3$ | $+11\pm 2$ | $-8\pm 7$
$a_{2,0}^{m}$ | $+6\pm 2$ | $-1\pm 1$ | $-10\pm 7$
$a_{2,1}^{e,Re}$ | $-3\pm 3$ | $-2\pm 2$ | $-10\pm 8$
$a_{2,1}^{e,Im}$ | $+1\pm 3$ | $-0\pm 2$ | $-2\pm 8$
$a_{2,1}^{m,Re}$ | $-2\pm 3$ | $-0\pm 2$ | $+4\pm 8$
$a_{2,1}^{m,Im}$ | $+3\pm 3$ | $+5\pm 2$ | $-6\pm 8$
$a_{2,2}^{e,Re}$ | $-0\pm 1$ | $+1\pm 1$ | $-5\pm 4$
$a_{2,2}^{e,Im}$ | $-4\pm 1$ | $-3\pm 1$ | $+3\pm 4$
$a_{2,2}^{m,Re}$ | $+4\pm 1$ | $-0\pm 1$ | $+0\pm 4$
$a_{2,2}^{m,Im}$ | $+1\pm 1$ | $-0\pm 1$ | $-4\pm 4$
Table 10: List of sources with angular separation between ICRF3 and VIE2022b-sx larger than 10 mas. IERS | IVS | $\Delta\alpha^{*}$ | $\Delta\delta$ | angular separation | first obs. | last obs. | no. of | no. of
---|---|---|---|---|---|---|---|---
name | name | [mas] | [mas] | [mas] | [mjd] | [mjd] | sessions | obs.
0106-391 | - | $-3.51\pm 4.80$ | $-23.60\pm 18.08$ | $23.86\pm 17.89$ | 58203.3 | 59460.3 | 6 | 64
0134+329 | 3C48 | $1.25\pm 0.05$ | $-56.85\pm 0.08$ | $56.87\pm 0.08$ | 48193.8 | 59378.0 | 49 | 1736
0201-440 | - | $1.34\pm 17.40$ | $-99.25\pm 55.92$ | $99.26\pm 55.92$ | 58143.4 | 59508.8 | 4 | 15
0316+162 | CTA21 | $2.10\pm 0.06$ | $-10.22\pm 0.12$ | $10.44\pm 0.12$ | 50084.5 | 59378.0 | 17 | 1299
0328-060 | - | $29.73\pm 4.54$ | $-16.02\pm 6.97$ | $33.77\pm 5.19$ | 56874.5 | 59440.3 | 8 | 54
0350+177 | - | $-6.78\pm 0.84$ | $63.43\pm 1.33$ | $63.79\pm 1.33$ | 57924.7 | 59405.2 | 6 | 116
0512-129 | - | $-3.68\pm 1.74$ | $9.31\pm 4.41$ | $10.01\pm 4.15$ | 58143.4 | 59522.9 | 5 | 69
0709+008 | - | $7.36\pm 2.74$ | $7.27\pm 3.12$ | $10.35\pm 2.94$ | 52939.7 | 58631.3 | 7 | 82
0748-378 | - | $-9.33\pm 10.52$ | $48.22\pm 25.45$ | $49.12\pm 25.07$ | 57011.1 | 59508.8 | 8 | 40
0753-425 | - | $1.46\pm 0.73$ | $12.36\pm 2.24$ | $12.45\pm 2.22$ | 55370.8 | 59522.9 | 7 | 123
0903-392 | - | $1.93\pm 4.72$ | $-15.35\pm 14.04$ | $15.47\pm 13.94$ | 57046.0 | 58981.5 | 7 | 32
0932-281 | - | $6.54\pm 1.79$ | $7.87\pm 4.55$ | $10.23\pm 3.68$ | 50687.3 | 59508.8 | 6 | 99
0951+699 | - | $12.00\pm 35.25$ | $-4.94\pm 34.56$ | $12.98\pm 35.15$ | 58203.3 | 58592.8 | 3 | 12
1015-314 | - | $3.58\pm 2.21$ | $-17.51\pm 5.26$ | $17.87\pm 5.17$ | 52305.8 | 59560.6 | 8 | 77
1117-248 | - | $-12.40\pm 2.21$ | $11.22\pm 3.09$ | $16.72\pm 2.64$ | 50631.3 | 59463.5 | 12 | 71
1306+660 | - | $-15.08\pm 3.58$ | $-33.07\pm 4.77$ | $36.35\pm 4.59$ | 57011.1 | 59405.2 | 8 | 65
1305-241 | - | $6.90\pm 8.14$ | $14.74\pm 9.89$ | $16.27\pm 9.60$ | 58158.9 | 59440.3 | 5 | 44
1328+254 | - | $8.48\pm 0.57$ | $17.13\pm 0.89$ | $19.11\pm 0.83$ | 52408.7 | 58644.9 | 6 | 164
1422+268 | - | $-2.98\pm 4.87$ | $-12.57\pm 4.64$ | $12.91\pm 4.66$ | 58136.6 | 58981.5 | 4 | 46
1507-246 | - | $70.00\pm 1.80$ | $-128.92\pm 3.36$ | $146.70\pm 3.08$ | 57924.7 | 59611.7 | 8 | 68
1539-093 | - | $-29.52\pm 12.78$ | $13.61\pm 10.61$ | $32.50\pm 12.43$ | 50575.3 | 58981.5 | 9 | 36
1612+797 | - | $7.06\pm 0.64$ | $-7.36\pm 0.74$ | $10.20\pm 0.70$ | 53780.1 | 58510.3 | 6 | 237
1657-298 | - | $346.60\pm 5.03$ | $-687.18\pm 8.32$ | $769.64\pm 7.76$ | 57973.7 | 59611.7 | 7 | 40
1706-223 | - | $-3.66\pm 0.64$ | $-14.04\pm 1.73$ | $14.51\pm 1.68$ | 57011.1 | 58746.6 | 5 | 123
1711-251 | - | $213.09\pm 188.33$ | $-466.99\pm 364.28$ | $513.31\pm 340.50$ | 57596.8 | 58981.5 | 7 | 16
1755+626 | - | $-21.04\pm 2.94$ | $-41.25\pm 2.63$ | $46.31\pm 2.70$ | 55370.8 | 59522.9 | 9 | 105
1829-106 | - | $21.41\pm 4.07$ | $-35.84\pm 3.56$ | $41.74\pm 3.70$ | 51731.8 | 59560.6 | 10 | 17
1858-143 | - | $-2.82\pm 12.25$ | $28.09\pm 16.33$ | $28.23\pm 16.29$ | 58203.3 | 58981.5 | 4 | 23
1934-638 | - | $-22.59\pm 0.88$ | $2.69\pm 0.72$ | $22.75\pm 0.88$ | 48765.9 | 59065.7 | 8 | 36
2028-204 | - | $494.59\pm 15.25$ | $-1021.10\pm 32.61$ | $1134.58\pm 30.10$ | 58203.3 | 59460.3 | 5 | 19
2105-212 | - | $9.91\pm 1.25$ | $-4.23\pm 2.42$ | $10.77\pm 1.49$ | 57011.1 | 59535.8 | 8 | 83
2216-007 | - | $73.13\pm 2.36$ | $-85.80\pm 3.11$ | $112.73\pm 2.82$ | 56266.8 | 58644.9 | 6 | 80
2219-340 | - | $13.60\pm 6.72$ | $10.41\pm 18.62$ | $17.13\pm 12.51$ | 57098.3 | 58981.5 | 7 | 36
2318-195 | - | $10.27\pm 0.73$ | $20.12\pm 1.80$ | $22.59\pm 1.64$ | 58143.4 | 59460.3 | 6 | 101
2346+750 | - | $-1.74\pm 0.47$ | $10.99\pm 0.63$ | $11.12\pm 0.62$ | 57808.9 | 59560.6 | 7 | 134

##  5 Summary

We presented high-quality celestial and terrestrial reference frames as
provided by the IVS Special Analysis Center VIE. We compared our recent
solution which includes IVS sessions until June 2022 with the current
international reference frames, i.e., ICRF3 and ITRF2020, and highlighted the
differences coming from the additional VLBI observations after the data
deadlines for the international frames, i.e., spring 2018 and December 2020,
respectively. The consistent Vienna celestial and terrestrial reference frames
were estimated in a common global least squares adjustment and are publicly
available together with the corresponding Earth orientation parameters at
https://www.vlbi.at/index.php/productshttps://www.vlbi.at. In this paper, we
provided a detailed description of the underlying a priori models and the
selected parametrization for the global least squares solution.

###### Acknowledgements.

The authors acknowledge the International VLBI Service for Geodesy and
Astrometry (IVS) and all its components for providing VLBI data. J.B. and F.J.
would like to thank the Austrian Science Fund (FWF) for supporting their work
with project VGOS-Squared (P 31625).

## References

  * Altamimi et al. (2022) Altamimi, Z., Rebischung, P., Collilieux, X., Métivier, L., & Chanard, K. 2022, EGU General Assembly 2022, 3958
  * Altamimi et al. (2016) Altamimi, Z., Rebischung, P., Métivier, L., & Collilieux, X. 2016, J Geophys Res: Solid Earth, 121, 6109
  * Artz et al. (2014) Artz, T., Springer, A., & Nothnagel, A. 2014, J Geodesy, 88, 1145
  * Beasley et al. (2002) Beasley, A., Gordon, D., Peck, A., et al. 2002, Astrophys J Suppl Ser, 141, 13
  * Böhm et al. (2018) Böhm, J., Böhm, S., Boisits, J., et al. 2018, Publ Astron Soc Pac, 130, 044503
  * Böhm et al. (2006) Böhm, J., Werl, B., & Schuh, H. 2006, J Geophys Res: Solid Earth, 111
  * Capitaine et al. (2003) Capitaine, N., Wallace, P. T., & Chapront, J. 2003, Astron Astrophys, 412, 567
  * Charlot et al. (2020) Charlot, P., Jacobs, C. S., Gordon, D., et al. 2020, Astron Astrophys, 644, A159
  * de Witt et al. (2021) de Witt, A., Basu, S., Charlot, P., et al. 2021, in EVGA WM Proceedings, ed. R. Haas, 85–89
  * de Witt et al. (2022) de Witt, A., Charlot, P., Gordon, D., & Jacobs, C. S. 2022, Universe, 8
  * de Witt et al. (2019) de Witt, A., Le Bail, K., Jacobs, C., et al. 2019, in IVS GM Proceedings”, ed. K. L. Armstrong, K. D. Baver, & D. Behrend (NASA), 189–193
  * Desai & Sibois (2016) Desai, S. D. & Sibois, A. E. 2016, J Geophys Res: Solid Earth, 121, 5237
  * Egbert & Erofeeva (2002) Egbert, G. D. & Erofeeva, S. Y. 2002, J Atmos Ocean Tech, 19, 183
  * Fey et al. (2015) Fey, A. L., Gordon, D., Jacobs, C. S., et al. 2015, Astron J, 150, 58
  * Fomalont et al. (2003) Fomalont, E., Petrov, L., D.S., M., Gordon, D., & Ma, C. 2003, Astron J, 126, 2562
  * Frey & Titov (2021) Frey, S. & Titov, O. 2021, Research Notes of the AAS, 5, 60
  * Gipson et al. (2008) Gipson, J., MacMillan, D., & Petrov, L. 2008, in IVS GM Proceedings, ed. A. Finkelstein & D. Behrend, 157–162
  * Gordon et al. (2016) Gordon, D., Jacobs, C., Beasley, A., et al. 2016, Astron J, 151, 154
  * Hellmers et al. (2022) Hellmers, H., Modiri, S., Bachmann, S., et al. 2022, in International Association of Geodesy Symposia (Springer Berlin Heidelberg), 1–11
  * Jacobs et al. (2010) Jacobs, C., Heflin, M., Lanyi, G., Sovers, O., & Steppe, J. 2010, in IVS GM Proceedings, ed. D. Behrend & K. D. Baver (NASA), 305–309
  * Kovalev et al. (2007) Kovalev, Y., Petrov, L., Fomalont, E., & Gordon, D. 2007, Astron J, 133, 1236
  * Krásná et al. (2021) Krásná, H., Jaron, F., Gruber, J., Böhm, J., & Nothnagel, A. 2021, J Geodesy, 95, 126
  * Krásná et al. (2015) Krásná, H., Malkin, Z., & Böhm, J. 2015, J Geodesy, 89, 1019
  * Landskron & Böhm (2018) Landskron, D. & Böhm, J. 2018, J Geodesy, 92(4), 349
  * MacMillan & Ma (1997) MacMillan, D. S. & Ma, C. 1997, Geophys Res Lett, 24, 453
  * Mathews et al. (2002) Mathews, P. M., Herring, T. A., & Buffett, B. A. 2002, J Geophys Res: Solid Earth, 107, ETG 3
  * Mayer & Böhm (2020) Mayer, D. & Böhm, J. 2020, in Beyond 100: The Next Century in Geodesy, ed. J. T. Freymueller & L. Sánchez (Cham: Springer International Publishing), 21–28
  * McCallum et al. (2022) McCallum, L., Chin Chuan, L., Krásná, H., et al. 2022, J Geodesy, 96, 1
  * McCallum et al. (2019) McCallum, L., Wakasugi, T., & Shu, F. 2019, in IVS GM Proceedings, ed. K. L. Armstrong, K. D. Baver, & D. Behrend (NASA/CP-2019-219039), 131–134
  * Mignard, F. & Klioner, S. (2012) Mignard, F. & Klioner, S. 2012, Astron Astrophys, 547, A59
  * Nothnagel (2009) Nothnagel, A. 2009, J Geodesy, 83(3), 787
  * Nothnagel et al. (2017) Nothnagel, A., Artz, T., Behrend, D., & Malkin, Z. 2017, J Geodesy, 91(7), 711
  * Petit & Luzum (2010) Petit, G. & Luzum, B., eds. 2010, IERS Conventions 2010 ((IERS Technical Note No. 36) Frankfurt am Main: Verlag des Bundesamts für Kartographie und Geodäsie), 179
  * Petrachenko et al. (2009) Petrachenko, B., Niell, A., Behrend, D., et al. 2009, Design Aspects of the VLBI2010 System. Progress Report of the VLBI2010 Committee, Technical Memorandum NASA/TM-2009-214180
  * Petrov et al. (2005) Petrov, L., Kovalev, Y., Fomalont, E., & Gordon, D. 2005, Astron J, 129, 1163
  * Petrov et al. (2006) Petrov, L., Kovalev, Y., Fomalont, E., & Gordon, D. 2006, Astron J, 131, 1872
  * Petrov et al. (2008) Petrov, L., Kovalev, Y., Fomalont, E., & Gordon, D. 2008, Astron J, 136, 580
  * Saastamoinen (1972) Saastamoinen, J. 1972, Bull. Geodesique, 106, 383–397
  * Tesmer et al. (2009) Tesmer, V., Steigenberger, P., Rothacher, M., Böhm, J., & Meisel, B. 2009, J Geodesy, 83, 973
  * Titov et al. (2022) Titov, O., Frey, S., Melnikov, A., et al. 2022, Mon Not R Astron Soc, 512, 874
  * Titov, O. & Lambert, S. (2013) Titov, O. & Lambert, S. 2013, Astron Astrophys, 559, A95
  * Wijaya et al. (2013) Wijaya, D. D., Böhm, J., Karbon, M., Krásná, H., & Schuh, H. 2013, Atmospheric Effects in Space Geodesy, ed. J. Böhm & H. Schuh (Springer Berlin Heidelberg), 137–157
  * Zensus et al. (1995) Zensus, J., Diamond, P., & Napier, P., eds. 1995, Very Long Baseline Interferometry and the VLBA, ASPC Series, Vol. 82 (Astronomical Society of the Pacific)