Technical description of solution rfc_2021b
Purpose of solution: get the best positions of all sources with
two or more good observations
Short narrative description of solution:
1) Data set:
All dual-band X/S Mark-3, Mark-4, Mark-5, S2, K3, K4, K5, VLBA, VERA,
LBA observations under geodesy and astrometry programs, and K-band only
VLBA sessions. This includes 897 absolute astromery experiments from
59 dedicated astrometric pgrograms and 6779 IVS geodetic VLBI experiments.
In total, 7381 VLBI experiments from 1980.04.11 through 2021.03.11,
19,908,564 estimates of group delay were used in solutions.
The dataset was split into seven parts: VLBA X/S experiments,
VLBA X/C experiments, VLBA X-band experiments, VLBA K-band experiments,
VLBA C-band experiments, VERA experiments, and selected astrometric
experiment and all other observing sessions. These parts were processed
with slightly different procedures for outlier elimination and
re-weighting. Positions of sources with declination above -40 deg are
almost entirely derived from VLBA data. Non-VLBA data
contributed to positions of southern sources and only marginally
contributed to positions of sources with declination > -40 deg.
All absolte astromery exeriments at the VLBA, LBA, and EVN were
reprocessed anew using measured interferometric visibilites that can be
found in raw correlator output using advanced fringe fitting software PIMA.
PIMA improves detection limit with respect to AIPS processing by sqrt(N_IF),
where N_IF is the number of intermediate frequencies (IF) per band,
either 4 or 8 in most VLBA experiment, thus improving sensitivity by the
factor of 2-3. Reprocessing allowed to detect many sources previously
undetected, and increase the number of points for other weak sources.
X-band, S-band, C-band, K-band, and dual-band (X/C plus X/S) data were
processed separately: outliers eliminated, group delay ambiguities were
resolved once again, and additive contributions to apriori weights were
re-evaluated. The sequence: group delay ambiguity resolution, outlier
elimination, re-weighting, astrometric solutions, apriori position
update was repeated several times.
For IVS data, outliers were eliminated and reweighting parameters
were recomputed.
2) Theoretical path delay was computed using VTD package with the state of the
art model:
-- including computation of the troposphere slant path delay by
integration of a system of non-linear differential equations of
radio wave propagation using the field of refractivity index
computed from results of the 4D numerical weather model MERRA2.
-- including ocean loading, atmospheric pressure loading, atmospheric tides;
-- including solid Earth tides according to the Mathews anelastic model
MDG97AN
-- using empirical harmonic Earth orientation variations model heo_20210317
-- using computation of the ionosphere delay using GPS TEC maps after
April 1998 (only for single-band experiments).
3) Parameterization:
3.1) Clock for each station except the one taken as a reference was modeled
with a sum of the 2nd degree polynomial over the experiment duration
and the B-spline of the first degree with time span of 60 minutes.
The clock rate was constrained to zero with reciprocal weights
2.D-14 s/s. Clock breaks and clock rate breaks at some stations were
estimated for a limited number of experiments.
3.2) Atmosphere path delay in zenith direction for each station was
modeled with the B-spline of the first degree with time span of
20 minutes. The atmosphere path delay rate in zenith direction
was constrained to zero with reciprocal weights 40 ps/s.
3.3) The direction of the axis symmetry of the local atmospheric path
delay for each station, except those defined in the exception list,
was modeled with the B-spline of the first degree with time span of
6 hours.
3.4) The baseline-dependent clocks were estimated for each linear
independent triangle for each experiment separately.
3.5) The polar motion and UT1 as well as their rates of change were
estimated for each experiment separately.
3.6) Daily offsets to nutation were estimated for each experiment
separately.
3.7) Position of stations was modeled with a sum of four components
using all available data:
a) position at reference epoch, 2000.01.01
b) linear velocity
c) Sum of harmonic model at four frequencies:
alpha) diurnal
beta) semi-diurnal
gamma) annual
delta) semi-annual
d) B-spline for the following stations:
AIRA
CHICH10
DSS15
DSS65
EFLSBERG
FORTORDS
GGAO7108
GILCREEK
HOBART26
HRAS_085
KASHIM11
KASHIM34
KOGANEI
MEDICINA
MK-VLBA
MIURA
MOJAVE12
PIETOWN
PRESIDIO
SINTOTU3
SOURDOGH
TATEYAMA
TIGOCONC
TSUKIB32
VERAMZSW
WHTHORSE
YAKATAGA
The B-spline model accounts for non-linear motion and
discontinuities caused by seismic and post-seismic motion,
as well displacement of the antenna reference point caused
by rail repairs.
3.8) Coordinates of all sources with 2 or more good observations
were estimated using all available data.
3.9) Antenna axis offsets lengths for 66 stations were estimated
using all available data.
4) Constraints:
4.1) Net translation and net rotation constraints were imposed
on positions of 48 stations in such a manner, that the resulting
position of these stations have no net translation and net rotation
with respect to the positions in the ITRF2000 catalogues.
4.2) Net translation and net rotation constraints were imposed
on velocities of 44 stations in such a manner, that the resulting
velocities of these stations have no net translation and net rotation
with respect to the velocities in the ITRF2000 catalogues.
4.3) Net rotation constraints were imposed on coordinates of 212 sources
in such a manner, that the resulting coordinates of these sources
have no net rotation with respect to the coordinates of these
sources in the ICRF catalogue marked as "defining".
4.4) Velocities of 38 stations with insufficiently long history were
constrained to the apriori values with reciprocal weights
0.1 mm/yr for the vertical component and 3 mm/year for horizontal
components.
4.5) Weak constraints with reciprocal weights of 1.D-4 rad were imposed
on portions of all sources.
Comment: constraints 4.1, 4.2, and 4.3 are necessary for solving for
coordinates and their first time derivatives. Coordinates and their time
derivatives cannot be determined solely from observations. The observations
allows to determine the family of solutions. Since equations of photon
propagation are differential equations, the solution of differential
equations depends on boundary conditions. The constraints 4.1, 4.2, and 4.3
provide the set of boundary condition that allows to pick up an element
from the family of solution determined by observations.
5) Solutions.
Fice solutions were produced, each in a single least square run:
a) X/S and X/C ionosphere free combinations of group delays;
b) X-band only group delays;
c) K-band only group delays;
d) C-band only group delays;
e) S-band only group delays.
For single-band observation after 1998 ionosphere contribution
from GPS Bernese solution was computed and applied.
Four separate sets of source coordinates were produced. Sources with
less than 3 detections at any band were discarded. If a source had
more than 8 pairs of X/S or X/C band observables, the X/S band positions
were used in the final catalogue. For sources with less than 8 pairs of
X/S or X/C observables, positions from the diual-bandm, X-band only,
K-band only, C-band, and S-band only solutions were compared. If X-band
only, K-band-only, C-band-only, or S-band only positions were significantly
better then X/S band solutions, because more single band data were
collected than X/S pairs, or there were no X/S ionosphere free data
for that source, single band positions replaced X/S band positions
for that sources in the final catalogue.
The a priori uncertainties were re-scale by
E = dsqrt ( E_A^2 + E_B(B)^2 + e*M(E1)^2 + e*M(E2)^2 )
where
E_A is the a priori uncertainties of the group delay or the
ionosphere free combination of group delays computed
by the fringe fitting algorithm
E_B(B) is the baseline dependent correction to weight computed
for each experiment, each baseline separately in such
a manner that the ration of the weighted sum of
postfit residuals for a given baseline to its
mathematical expectation is close to zero.
M(e) mapping function, i.e. the ratio of the slanted
path delay in neutral atmosphere at given direction
to the path delay at zenith direction.
Ei elevation angle of a source at the i-th station
e scaling coefficient of propagation of remaining
errors in atmospheric path delay. Value of 0.02
was used in this solution.
The reported errors in the output catalogue were produced from
formal uncertainties by applying the reweighting:
err = sqrt ( ( a(delta)*unc)**2 + b(delta)**2 ) where
unc is formal uncertainty of estimates from the LSQ solutions
and a(alpha), b(delta) are elevation dependent parameters of the empirical
error model.