Technical description of ivsd0001_dsnx:
=======================================
VLBI group of the Geodetic Institute of the University of Bonn
(Sarah Boeckmann, boeckmann@uni-bonn.de)
Januar 18, 2007
The ivsd0001_dsnx series is a combination product by accumulation of normal
equation matrices. The normal equation matrices in these files are
unconstrained (datum-free).
Input series are currently contributed by BKG, DGFI, GSFC, SHA and USNO.
Analysis center: | Software:
-----+-------------------------------------------------------------+-----------
BKG | Bundesamt fuer Kartographie und Geodaesie, Leipzig, Germany | CALC/SOLVE
DGFI | Deutsches Geodaetisches Forschungsinstitut, Munich, Germany | OCCAM
GSFC | Goddard Space Flight Center, Washington D.C., USA | CALC/SOLVE
SHA | Shanghai Astronomical Observatory, China | CALC/SOLVE
USNO | U.S. Naval Observatory, Washington D.C., USA | CALC/SOLVE
-----+-------------------------------------------------------------+-----------
Purpose of this solution:
=========================
The main objective of ivsd0001_dsnx is to provide IVS' contribution to the
Combination Pilot Project for the combination of different geodetic space
techniques and the rigorous determination of station positions and earth
orientation parameters.
Detailed description:
=====================
This approach of combining VLBI solutions is based on the principle of
addition of normal equation matrices and thus begins at an earlier step of
analysis. This approach is also known as "Adjustment of groups of observations".
This approach uses datum-free normal equation matrices of VLBI sessions which
are provided as SINEX files.
The combination is performed in the following way:
Apriori epochs:
---------------
Before accumulating the individual normal equation matrices the matrices are
transformed to the mean epoch of all contributions (they may differ by a few
minutes) by using the respective EOP rates.
Apriori values:
---------------
Furthermore the individual normal equation matrices have to be transformed to
a common set of apriori values. For station coordinates the ITRF2005 and for the
earth orientation parameters the apriori values of one particular analysis center
are used as apriori values for the normal equation matrices of all analysis centers.
These values are listed in the SOLUTION/APRIORI-block.
Weighting procedure:
--------------------
Weighting factors are used to weight the individual normal equation matrices
within the accumulation of normal equations.
(p = number of analysis centers,
k = iteration counter)
1 1
(SUM_{i=1}^{p} ------- * A_i'*P_i*A_i) * x = SUM_{i=1}^{p} ------ * A_i'*P_i*l_i
s_i^{2} s_i^{2}
1
The weights are definied as ------- , where s_i^{2} stands for sigma_i^{2} and
s_i^{2}
is determined within a variance component estimation.
The variance components are determined in an iterativ process with k iteration
steps as below
(k) (k)
(k+1) v_i' P_i v_i
sigma_i^{2} = ---------------- , with
(k)
r_i
(k) 1 1
r_i = n_i - ------- * tr((SUM_{j=1}^{p} ------ * A_j'*P_j*A_j)^{-1} * A_i'*P_i*A_i)
(k) (k)
s_i^{2} s_j^{2}
(k) (k) (k) (k) (k)
v_i' P_i v_i = x' * A_i' P_i A_i * x - 2 * x' A_i' P_i l_i + l_i' P_i l_i ,
(k)
where v_i' is the residual vector of the combined solution and the individual
solution.
After scaling and weighting the (singular) normal equations matrices they are
accumulated and a combined solution is being computed.
Generation of SINEX file for accumulated solution:
--------------------------------------------------
After applying scaling factors the normal equation matrices of the individual
solutions are accumulated. The resulting normal equation matrix is then written
into a new SINEX file (DATABASE_CODE_ivsd0001.snx).
Since the original normal equation matrices are datum-free or singular, the
accumulated normal equation matrices are still datum-free. So there is no
SOLUTION/ESTIMATE section in this file, since no datum information has been
imposed.
Estimated parameters:
=====================
Parameters combined are:
ALL station coordinates, x-pole, y-pole, UT1-TAI, x-pole-dot, y-pole-dot, LOD.
As mentioned before there are no estimated parameters at all since there is
no datum information imposed.
Software:
=========
- The processing of the individual matrices is done using a software from
the German Geodetic Research Institute (DGFI), Munich, called DOGS-CS.
- A software called combine_sinex has been developed at the Geodetic Institut
of the University of Bonn and is used to process the input SINEX files,
perform checks of the input data, to compute scaling factors and to visualize
results.
Contact:
========
Institute for Geodesy and Geoinformation of the University of Bonn
VLBI Group
Nussallee 17
D-53115 Bonn
Germany
eMail: boeckmann@uni-bonn.de