# [Proj] ITRF to GDA94 transformation problems - bug in 7 parameters?

Mikael Rittri Mikael.Rittri at carmenta.com
Fri Aug 26 02:45:41 EST 2011

```Hello Mikhail,
you wrote

> I am trying to re-produce transformation described in this document:
>
> http://www.ga.gov.au/image_cache/GA3795.pdf
>
> appendix B, and I am getting errors about 0.11 m
> My
> +towgs84=-0.054100,-0.019100,0.009600,0.010833,0.010703,0.011403,0.006859,
> the same numbers as in the article.

You have made two subtle errors that nearly cancel each other, but not quite.

A) There are two sign conventions for the three rotations. The document
uses Coordinate Frame Rotation (according to sections 2 and 3), but cs2cs
uses the opposite Position Vector Transformation.  So with cs2cs you should
negate the rotations, and use

+towgs84=-0.054100,-0.019100,0.009600,-0.010833,-0.010703,-0.011403,0.006859

instead. (But wait, I am not done yet!)

B) In the document, transformation goes in the direction
from ITRF2000 to GDA94. With cs2cs, if you want to regard
ITRF2000 as equivalent to +datum=WGS84, then to model GDA94,
you need +towgs84 parameters that implement the opposite
direction: from GDA94 to ITRF2000. To do this, you negate
all parameters from A), and get

+towgs84=0.054100,0.019100,-0.009600,0.010833,0.010703,0.011403,-0.006859

With the parameters from B), I can reproduce the results of the document by doing

cs2cs +from -w4 +proj=latlong +datum=WGS84 +to +towgs84=0.054100,0.019100,-0.009600,0.010833,0.010703,0.011403,-0.006859 +proj=latlong

input:

133d53'7.8574"E  23d40'12.4314"S 603.287

output:

133d53'7.8478"E 23d40'12.4461"S 603.350

Best regards,

Mikael Rittri
Carmenta
Sweden
http://www.carmenta.com

-----Original Message-----
From: proj-bounces at lists.maptools.org [mailto:proj-bounces at lists.maptools.org] On Behalf Of Mikhail Tchernychev
Sent: den 25 augusti 2011 23:02
To: PROJ.4 and general Projections Discussions
Subject: [Proj] ITRF to GDA94 transformation problems - bug in 7 parameters?

Hello everyone,

I am trying to re-produce transformation described in this document:

http://www.ga.gov.au/image_cache/GA3795.pdf

appendix B, and I am getting errors about 0.11 m

My
+towgs84=-0.054100,-0.019100,0.009600,0.010833,0.010703,0.011403,0.00685
+9,
the same
numbers as in the article.

This is what I get if I use lat / lon -> lat/lon

cs2cs +from -w4  +proj=latlong +datum=WGS84 +to
+towgs84=-0.054100,-0.019100,0.009600,0.010833,0.010703,0.011403,0.00685
+9 +proj=latlong
<<EOF
133d53'7.8574"E  23d40'12.4314"S 603.287 EOF

Computed and Correct results:
133d53'7.8454"E    23d40'12.4468"S   603.261
133d53'7.8478"E    23d40'12.4461"S   603.350

I also tried to convert directly geocentric coordinates listed in the article. This is what I got:

cs2cs -f "%.3lf" +from  -w4 +proj=geocent +datum=WGS84 +to
+towgs84=-0.054100,-0.019100,0.009600,0.010833,0.010703,0.011403,0.00685
+9
+proj=geocent <<EOF
-4052052.048 4212836.105 -2545105.587
EOF

computed and correct result
-4052051.655    4212836.186   -2545106.011
-4052051.765    4212836.205   -2545106.027

I attached script with cs2cs calls, which exhibits the problem.

Help is greatly appreciated,

Thank you
Mikhail

```