## ITRF96

### Input data

$$\global\def\fig#1{\scriptsize\textcolor{E83E8C}{fig.#1}}$$ $$\global\def\tab#1{\scriptsize\textcolor{E83E8C}{tab.#1}}$$

The current strategy adopted for the ITRF96 solution is twofold :

• a simultaneous combination of positions and velocities using full variance/covariance matrices
• a rigorous weighting scheme based on the analysis and estimation of the variance components using Helmert method.

The ITRF96 solution is based on a combination of :

• a selected sets of individual solutions submitted to the IERS Central Bureau in 1997
• some past data provided in SINEX format
• recent submissions from GPS and DORIS specifically asked to improve ITRF by supplying new stations or recent positions to upgrade velocities.
The individual solutions selected for the ITRF96 analysis are 4 VLBI , 2 SLR , 8 GPS and 3 DORIS solutions, summarized in $\tab1$.

On the other hand, as a first step in the improvement of the use of the local ties, all the available vector eccentricities of colocated sites were converted into a complete set of positions for each site expressed in SINEX format.

Solution Technique Ref. Epoch Data Span
SSC(GSFC) 97 R 01 VLBI 93:001 79-97
SSC(GIUB) 97 R 01 VLBI 93:001 84-96
SSC(NOAA) 95 R 01 VLBI 93:001 79-94
SSC(JPL) 97 R 01 VLBI(DSN) 93:001 91-96
SSC(CSR) 96 L 01 SLR Lageos 93:001 76-96
SSC(GSFC) 97 L 01 SLR Lageos 86:182 80-96
SSC(EMR) 97 P 01 GPS IGS 96:001 95-97
SSC(GFZ) 97 P 02 GPS IGS 94:365 93-96
SSC(CODE) 97 P 02 GPS IGS 95:076 93-97
SSC(EUR) 97 P 04 GPS EUREF 96:090 95-96
SSC(EUR) 97 P 03 GPS EUREF 96:339 96-97
SSC(MIT) 97 P 01 GPS IGS GNAAC 97:151 94-97
SSC(NCL) 97 P 01 GPS IGS GNAAC 96:001 95-97
SSC(JPL) 97 P 02 GPS IGS GNAAC 96:001 91-96
SSC(GRGS) 97 D 01 DORIS 93:001 93-96
SSC(CSR) 96 D 01 DORIS 93:001 93-96
SSC(IGN) 97 D 04 DORIS 93:001 90-97

$\tab1$: Selected Solutions for the ITRF96 analysis

### Data analysis

The data analysis was performed in three steps :

• Each individual solution was compared to the ITRF94 in order in one hand to estimate the transformation parameters of the system attached to the solution with respect to ITRF94 and, on the other hand, the level of agreement with the ITRF94 values.
• In order to assess the relative quality of the individual solutions, and their behaviour with respect to each other independently from the influence of local ties, a combination within each technique was also performed.
• A global combination was finally performed. Matrix Scaling Factors have been rigorously estimated during this combined adjustment which was iterated.

The ITRF96 global combination is achieved with the following properties :

• It includes the 17 selected space geodetic solutions provided by the IERS analysis centers and 70 constructed SINEX files containing positions and covariances, derived from local ties
• The reference frame definition (origin, scale, orientation and time evolution) of the combination is achieved in such a way that ITRF96 is in the same system as the ITRF94
• Velocities are constrained to be the same for all points within each site.

### Result Analysis

$$\global\def\fig#1{\scriptsize\textcolor{E83E8C}{fig.#1}}$$ $$\global\def\tab#1{\scriptsize\textcolor{E83E8C}{tab.#1}}$$

The ITRF96 adjusted coordinates at epoch 1996.0 and velocities were split into several tables and SINEX files. The subsets are :

Moreover, compressed ITRF96 SINEX files for the following networks are also available via FTP :

A file ITRF96.TSG contains the adjusted transformation parameters at the epoch of each individual solution as well as the corresponding rates. The transformation parameters are from each individual solution to the ITRF96 and should be used with the equation ($\fig1$). The rates have to be considered as annual variations to the transformation parameters. So for a given transformation parameter T provided at an epoch ts, its value at an epoch t in years could be obtained by equation ($\fig2$).

$$\begin{pmatrix}X_s \\ Y_s \\ Z_s\end{pmatrix} = \begin{pmatrix}X \\ Y \\ Z\end{pmatrix} + \begin{pmatrix}T1 \\ T2 \\ T3\end{pmatrix} + \begin{pmatrix} D & -R3 & R2 \\ R3 & D & -R1 \\ -R2 & R1 & D \end{pmatrix}\begin{pmatrix}X \\ Y \\ Z\end{pmatrix} ~~~~~~~~~~~~~~~ \fig1$$

With, $X,Y,Z$ are the coordinates in the ITRF96, and $Xs,Ys,Zs$ are the coordinates in the individual system.

$$T(t) = T(t_k) + \dot{T} \times (t-t_k) ~~~~~~~~~~~~~~~ \fig2$$

The quality analysis of the ITRF96 results is based more specifically on global residuals per solution ($\tab2$) as well as per site. All residuals on a site-by-site basis resulting from the combination are available in the file ITRF96.RESIDUALS.

Solution id

Number
of points
RMS Position
in mm
Epoch

RMS Velocity
in mm/y
SSC(GSFC) 97 R 01 120 5.80 93:001 1.90
SSC(GIUB) 97 R 01 43 13.60 93:001 0.50
SSC(NOAA) 95 R 01 111 14.70 93:001 1.90
SSC(JPL) 97 R 01 8 20.70 93:001
SSC(CSR) 96 L 01 89 11.10 93:001 3.80
SSC(GSFC) 97 L 01 38 10.90 86:182 1.70
SSC(EMR) 97 P 01 36 10.00 96:001 3.50
SSC(GFZ) 97 P 02 66 16.80 94:365 3.30
SSC(CODE) 97 P 02 100 7.10 95:076 1.90
SSC(EUR) 97 P 04 39 2.40 96:090 0.30
SSC(EUR) 97 P 03 58 2.90 96:339 0.30
SSC(MIT) 97 P 01 132 8.50 97:151 9.20
SSC(NCL) 97 P 01 114 5.40 96:001 6.30
SSC(JPL) 97 P 02 113 9.40 96:001 3.80
SSC(GRGS) 7 D 01 48 26.90 93:001 8.00
SSC(CSR) 96 D 01 54 26.10 93:001 10.60
SSC(IGN) 97 D 04 62 28.30 95:100 12.80