International Terrestrial Reference Frame (ITRF) Matlab Toolbox

Version 1.2 (26 May 2025).

Coordinate transformations between different ITRS and ETRS89 realizations.

Synopsis

Coordinate and velocity transformations between International and European Terrestrial Reference Frame (ITRF/ETRF) realizations, plate motion models (PMM) and analysis of velocity and coordinate changes between reference frames.

crdvelout=itrf2itrf(crdvelin,from,to,yearin,yearout)
crdout=itrf2itrf(crdin,from,to,yearin)

demoitrfmap

Functions

Main functions

itrf2itrf  - Transform coordinates/velocities between various ITRF's and ETRF2000, ETRF2014 and ETRF2020.  
pmmvel     - Get velocity from Plate Motion Model parameters.  
itrfmap    - Plot map of velocity and coordinate changes between ITRF/ETRF.  

Other functions

itrftp     - Get ITRF transformation parameters at a certain epoch  
itrftables - Print table with transformation parameters between ITRF's.    
itrf2etrf  - Transform coordinates/velocities between ITRFyy and ETRFyy.  

Support functions

itrftpdef  - Define ITRF transformation parameters   
etrftpdef  - Define ETRF transformation parameters   
pmmpar     - Define Plate Motion Model parameters.     
dijkstra   - Find shortest path in a graph using Dijkstra's algorithm  
trafo3d    - 3D similarity transformation with 7 or 14 parameters  

Demo/test scripts

demoitrfmap- Demo with itrfmap mapping velocity/coordinate changes  
liveitrfmap- Live editor (.mlx) itrfmap analysis tool  
testitrf   - Test itrf2itrf using actual ITRF coordinates  
testpmm    - Test Plate Model Motion (PMM) functions  

Notes

(1) itrf2itrf supports also transformations between ITRFyy and ETRF2000, ETRF2014 and ETRF2020.

(2) itrf2etrf only supports transformations between ITRFyy and ETRFyy, or vice versa, for the same year.

crdvelout=itrf2etrf(crdvelin,from,to,yearin,yearout)  
crdout=itrf2etrf(crdin,from,to,yearin)  

itrf2etrs is only useful for legacy ETRF. For operations involving ETRF2000, ETRF2014 and ETRF2020 you are better off with itrf2itrf.
To preform transformations between legacy ETRF split the transform in two steps, e.g.

        ITRFxx -> ETRFxx         itrf2etrf  
        ETRFxx -> ITRFxx         itrf2etrf  
        ITRFxx -> ETRFyy  :  
            ITRFxx -> ITRFyy     itrf2itrf  
            ITRFyy -> ETRFyy     itrf2etrf  
        ETRFxx -> ITRFyy  :  
            ETRFxx -> ITRFxx     itrf2etrf  
            ITRFxx -> ITRFyy     itrf2itrf  
        ETRFxx -> ETRFyy  :  
            ETRFxx -> ITRFxx     itrf2etrf  
            ITRFxx -> ITRFyy     itrf2itrf  
            ITRFyy -> ETRFyy     itrf2etrf  

(3) Dijkstra's algorithm to find the shortest path is used to construct all possible combinations of transformations.

Examples

crdvelout=itrf2itrf(  ...  
  [  3899225.258   396731.815  5015078.341    -.0130    .0158    .0092 ; ...  
     3812141.404   395731.729  4995987.219     .0004   -.0013    .0002 ],...   
  'ITRF2005','ITRF2000',2008.4,2000.0)  

crdout=itrf2itrf(  ...  
  [  3899225.258   396731.815  5015078.341  ; ...  
     3812141.404   395731.729  4995987.219  ],...   
  'ITRF2005','ITRF2000',2008.4)  

crdvelout=itrf2itrf(  ...  
  [3924687.552  301132.856  5001910.904 -.0150 .0164 .0070], ...  
  'ITRF2000','ETRF2000',1997.0,1989.0)  

License notice

The following notice applies to all Matlab functions and scripts in this repository.

Copyright 2012-2025 Hans van der Marel, Delft University of Technology.

Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 . Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License.