Ticket #3176 (reopened enhancement)
Add TOWGS[] coefficients to Pulkovo 1942 (SK-42) coordinate system (EPSG 4284)
| Reported by: | dron | Owned by: | warmerdam |
|---|---|---|---|
| Priority: | normal | Milestone: | |
| Component: | OGR_SRS | Version: | 1.7.0 |
| Severity: | minor | Keywords: | datum shift, pulkovo |
| Cc: |
Description
There is no TOWGS transformation defined for "Pulkovo 1942" CS in EPSG tables. But this transformation is specified in appropriate Russian official documents. I am attaching such a document. It is a GOST (An Official State Standard) number "P 51794-2001". It is written in Russian, but the part interesting for us contains mostly math, so it is pretty readable. I will translate some parts of this document below.
Page 1:
GOST P 51794-2001 THE STATE STANDARD OF THE RUSSIAN FEDERATION Radionavigational equipment of global navigation satellite system and global positioning system. COORDINATE SYSTEMS. Methods of points coordinates transformations Introduced 2002/07/01 1. Scope of usage This document defines: coordinate systems included in the systems of geodesic parameters "Earth Parameters", "World Geodetic System" and coordinate system of the Russian Federation; methods of coordinate and coordinate increments transformations from system to another one, and usage of numerical values of coordinate system transformation parameters in geodesic, navigational, cartographic activities using radionavigational equipment of the GLONASS and GPS systems. 2. Terms and abbreviations ...skipped...
Page 4:
... skipped ... 4.2 Coordinate transformation Users of GLONASS and GPS navigation systems should perform the coordinate transformations from PZ coordinate system into WGS and back, as well as from PZ and WGS into reference ccoordinate system of the Russian Federation. These coordinate transformations should be performed using 7-parametric transformation. Parameters of the transformation between coordinate systems PZ and WGS are listed in Appendix B. Transformation from WGS system into the reference system of the Russian Federation is being performed by sequential transformation into PZ system and then into reference system coordinates. Transformation of the Cartesian coordinates performed using formula: |X| | 1 +RZ -RY | |X| |DX| |Y| = (1 + DS) * |-RZ 1 +RX |.|Y| + |DY| |Z| |+RY -RX 1 | |Z| |DZ| b a where DX, DY, DZ --- linear parameters of the transformation, m; RX, RY, RZ --- angular parameters of the transformation, radians; DS --- difference in scale parameters of the coordinate systems; a,b --- coordinate systems.
... and continues on page 5:
Reverse transformation of the cartesian coordinates performed using formula |X| | 1 -RZ +RY | |X| |DX| |Y| = (1 - DS) * |+RZ 1 -RX |.|Y| - |DY| |Z| |-RY +RX 1 | |Z| |DZ| a b ... the rest is skipped ...
Now lets look at the appendixes.
Page 9:
GOST P 51794-2001
APPENDIX A
(mandatory)
Parameters of transformation between coordinate system PZ ("Earth Parameters")
and national reference systems of Russia
Transformation from the reference Coordinate System 1942 into system PZ-90
DX = (+25 +/-2) m; RX = 0.00" +/-0.1";
DY = (-141 +/-2) m; RY = -0.35" +/-0.1;
DZ = (-80 +/-3) m; RZ = -0.66" +/-0,1";
DS = (0.00 +/-0.25) * 10^-6;
|X| | 1 -3.3*10^-6 +1.8*10^-6| |X| | 25 |
|Y| = |+3.3*10^-6 1 0 |.|Y| + |-141|
|Z| |-1.8*10^-6 0 1 | |Z| |-80 |
PZ-90 SK-42
Transformation from the PZ-90 coordinate system into the reference
Coordinate System 1942
|X| | 1 +3.3*10^-6 -1.8*10^-6| |X| | 25 |
|Y| = |-3.3*10^-6 1 0 |.|Y| - |-141|
|Z| |+1.8*10^-6 0 1 | |Z| |-80 |
SK-42 PZ-90
Transformation from the reference Coordinate System 1995 into system PZ-90
DX = +25.90 m;
DY = -130.94 m;
DZ = -81.76 m;
|X| |X| | 25.90 |
|Y| = |Y| + |-130.94|
|Z| |Z| |-81.76 |
PZ-90 SK-95
Transformation from the PZ-90 coordinate system into reference
Coordinate System 1995
|X| |X| | 25.90 |
|Y| = |Y| - |-130.94|
|Z| |Z| |-81.76 |
SK-95 PZ-90
Page 10
GOST P 51794-2001
APPENDIX B
(mandatory)
Parameters of transformation between coordinate system PZ ("Earth Parameters")
and WGS coordinate system
Transformation from the coordinate system PZ-90 into WGS-84
DX = (-1.08 +/-0.2) m; RX = 0;
DY = (-0.27 +/-0.2) m; RY = 0;
DZ = (-0.90 +/-0.3) m; RZ = -0.16" +/-0,01";
DS = (-0.12 +/-0.06) * 10^-6;
|X| | 1 -0.82*10^-6 0| |X| |-1.1|
|Y| = (1-0.12*10^-6) * |0.82*10^-6 1 0|.|Y| + |-0.3|
|Z| |0 0 1| |Z| |-0.9|
WGS-84 PZ-90
Transformation from the coordinate system WGS-84 into PZ-90
|X| | 1 0.82*10^-6 0| |X| |-1.1|
|Y| = (1+0.12*10^-6) * |-0.82*10^-6 1 0|.|Y| - |-0.3|
|Z| | 0 0 1| |Z| |-0.9|
PZ-90 WGS-84
The document states that in order to transform coordinates from the SK-42 into WGS-84 systems they should be transformed into PZ-90 first and afterward to WGS-84. After a trivial matrix math I've got the following formula for transformation from SK-42 to WGS-84:
|X| | 1 -4.12*10^-6 1.8*10^-6| |X| | 23.9 | |Y| = (1-0.12*10^-6) * | 4.12*10^-6 1 0 |.|Y| + |-141.3| |Z| |-1.8*10^-6 0 1 | |Z| |-80.9 | WGS-84 SK-42
After conversion to arc seconds we can get:
+towgs84=23.9,-141.3,-80.9,0,-0.37,-0.85,-0.12
Finally what I am suggesting to do is to apply the following patch
--- gcs.override.csv (revision 17777) +++ gcs.override.csv (working copy) @@ -25,4 +25,9 @@ # From Jan: http://bugzilla.remotesensing.org/show_bug.cgi?id=1336 # 4313,Belge 1972,6313,Reseau National Belge 1972,6313,9122,7022,8901,1,0,6422,9606,106.868628,-52.297783,103.723893,-0.336570,0.456955,-1.842183,1.0000012747 +# +# Seven-parameter transformation for Pulkovo 1942 +# as defined by the GOST P 51794-2001 +# +4284,Pulkovo 1942,6284,Pulkovo 1942,6284,9122,7024,8901,1,0,6422,9607,23.9,-141.3,-80.9,0,-0.37,-0.85,-0.12
and propagate this parameters in PROJ.4 data files.
Please, note that this issue is very important for Russia, because Pulkovo 1942 (SK-42) Coordinate System was used more than a half of the century in USSR and virtually every map produced here was made in that system. Also a very few people feel themselves confident with this datum conversion staff, so the chances that someone else will raise this issue are quite small.
Best regards, Andrey
Attachments
-
gost51794-2001.pdf
(505.4 KB) - added by dron
4 years ago.
- GOST P 51794-2001 (The Russian State Standard)
-
gost51794-2008.pdf
(0.7 MB) - added by dron
3 years ago.
- GOST P 51794-2008 (The Russian State Standard)
-
transform.mac
(2.0 KB) - added by dron
3 years ago.
- Maxima batch file to compute SK-42 to WGS-84 transformation parameters
