**FFI Associate Analysis Center :**

**Combination of VLBI, GPS and SLR data at the observation level**

**by**

**Per Helge Andersen**

**Introduction**

FFI has during the last 18 years developed a software package called
GEOSAT (Andersen, 1995) for the combined analysis of VLBI, GPS, SLR and
other types of satellite tracking data (DORIS, PRARE and altimetry). The
observations are combined at the observation level with a consistent
model and consistent analysis strategies. The data processing is
automized except for some manual editing of the SLR observations.

In the combined analysis of VLBI, GPS and SLR observations the data are
processed in arcs of 24 hours defined by the duration of the VLBI
session. The result of each analyzed arc is a state vector of estimated
parameter corrections and a Square Root Information Array (SRIF)
containing parameter variances and correlations. The individual arc
results are combined into a multi-year global solution using a Combined
Square Root Information Filter and Smoother program called CSRIFS
(Andersen, 2000). With the CSRIFS program any parameter can either be
treated as a constant or stochastic parameter between the arcs. The
estimation of multi-day stochastic parameters is possible and
extensively used in the analyses.

**Analysis strategy**

Presently, the most important stochastic parameters of the global level
state vector are the following: Geocenter coordinates (3d resolution),
Earth orientation parameters (1d), the C21 and S21 gravity coefficients
(6d), satellite independent SLR ranging biases (15d), Solar radiation
pressure scaling and empirical drag of the Lageos satellites (3d), and
GPS receiver antenna eccentricity vectors (station dependent time
resolution to account for instrumental changes). The reason for
including the two gravity coefficients is to account for the fact that
errors in the gravity field will map into the estimates of polar motion
derived from satellite tracking data. In order to be consistent with
VLBI, which is almost independent of gravity, these parameters must be
estimated. The arc length of the GPS and Lageos satellites is one day.

The main constant parameters of the global state vector are monument
coordinates and velocities, GPS and/or SLR eccentricity vectors relative
to the station monument if it's a colocated station, radio source
coordinates, relative zenith delay between VLBI and GPS at colocated
stations (to account for differences in antenna heights), VLBI antenna
axis offsets, and GPS satellite transmitter phase center z-coordinates
(relative to the satellite body-fixed reference frame). The latter is
important since the commonly adopted z-coordinates for the effective
phase center of the GPS transmitter antennas probably are wrong by 1-2
meters. Initial analyses indicate that the z-coordinate can be
determined to a formal precision of some centimeters (1 sigma). Using
the IGS z-coordinate values will result in a scale inconsistent with SLR
and VLBI by approximately 2 ppb.

The status of the analyses is that approximately 2300 daily SLR arcs
(with Lageos I & II data from 1993 to 1999) have been processed where
approximately 550 arcs are combinations with VLBI and approximately 150
arcs are combinations with VLBI and GPS. Typically, 60 GPS stations are
included in each arc. These 2300 arcs are currently being combined into
a global solution using the CSRIFS program. A new program called
CSRIFS-IERS reads the output of CSRIFS and estimates a time dependent
transformation from the internal terrestrial and celestial reference
frames to an ITRF reference frame (presently ITRF-2000) and an IERS
Celestial reference frame. Since the estimated Earth orientation
parameters in principle are 100 % consistent with the internal reference
frames the time dependent transformation parameters can be applied to
transform the EOP estimates to IERS for comparison with the IERS EOP
products. A possible inconsistency between the IERS reference frames and
the IERS EOP estimates should in principle be detectable. The
CSRIFS-IERS automatically generates SINEX files for the terrestrial and
celestial reference frames and the EOP's. These files can be directly
submitted to the IERS Product Centers.

During the last year a number of improvements have taken place in the
GEOSAT software. The most important are the following:

-   It is a problem that the VLBI observation time tags in many cases
    are not properly synchronized to UTC leading to errors in the UT1
    estimates. A procedure to reduce this problem to a minimum has been
    implemented.

-   Estimation of multi-day stochastic parameters.

-   A new nutation model has been included.

-   The strategy for atmospheric gradient estimation for VLBI and GPS
    has been improved.

-   The NMF mapping function is used for SLR instead of the
    Marini-Murray tropospheric model.

-   A tidal geocenter motion model has been implemented.

-   The number of GPS stations used in a combined VLBI, GPS and SLR arcs
    has been increased from 30 to 60 stations.

The combined global analyses are not completed yet and the plan is to
present results at the IAG-2001 meeting in Budapest and at the AGU-2001
fall meeting in San Francisco.

**References**

Andersen, P. H. High-precision station positioning and satellite orbit
determination. Ph.D. Thesis, NDRE/publication-95/01094. FFI/E, Box 25,
N-2007, Kjeller, Norway.

Andersen, P. H. Multi-level arc combination with stochastic parameters.

Journ. of Geod., 2000, Vol. 74, No. 7-8, pp. 531-551.