Coordinate conversions and transformations.

Tomoiaga, Tiberius ; Alexei, Adrian ; Marinescu, Mirel 等

1. INTRODUCTION

The problem of coordinate conversions and transformations has continued to be one of the most important preoccupations of worldwide geodetic specialists.

In the past, the positioning specific problems were solved at regional or local level. This fact leaded to the existence of many coordinate and projection systems. Recent studies prove, from geodetic point of view, that the globalization phenomenon leaded to some discontinuities of geographic data at the boundary of certain countries.

While new GPS based data are geocentric referred (Fig. 1, left), local data are referred to local or regional datums (Fig. 1, right).

[FIGURE 1 OMITTED]

Nowadays, taking into account the huge complexity of the problems revealed after our country acceptance in NATO and European Union, we consider very important to be respected by Romanian specialists the existent standards elaborated by both National Geospatial-Intelligence Agency (NGA) from USA (DMA, 1987a,b; DMA, 1991) and EuroGeographics from Germany. In this way we could eliminate the matters mentioned above.

To work out all the problems revealed at coordinate conversion/transformation from/to coordinate systems and projections used in our country, the authors of this paper come to support military and civilian specialists by realizing software structured on two modules.

2. SOFTWARE DESCRIPTION

The software package was developed using Borland Delphi 7.0 programming language and several open source components for tables management, reporting and for geodetic network graphical representation.

By choosing this solution, the authors can have total control of the software, having the possibilities of modifying, updating, improving and adding new modules anytime found suitable or to derive new customized versions.

[FIGURE 2 OMITTED]

The first module realizes 2D and 3D transformation parameters computation (Fig. 3) between different datums in the following cases:

* 4 parameters (with/ without baricenter);

* 7 and 12 parameters (with/ without baricenter) in the following situations:

--without weights;

--with individual weights;

--with global weights.

[FIGURE 3 OMITTED]

The model used to compute the coordinate transformations with 4 parameters is given by the following relations (Moritz, 1980):

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)

The model used to compute the coordinate transformations with 7 parameters is described by the following relations (Moritz, 1980):

[[bar.X].sub.2] = (1 + k) R[[bar.X].sub.1] + [[bar.t].sub.x] (2)

In case of transformation without baricenter this is given by relation:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (3)

The difference between transformation with and without baricenter is given by rotation matrix conformation.

In case of transformation with baricenter the rotation matrix is expressed like a function of Hamilton normats quaternions (Grafarend & Richter, 1977):

R = ([I.sub.3] + S)[([I.sub.3] - S).sup.-1], (4)

where:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (5)

The second module is designed to coordinate conversion respectively transformation (Fig. 4 & 5):

[FIGURE 4 OMITTED]

[FIGURE 5 OMITTED]

This module allows realizing the following operations:

* coordinate conversion (Fig. 4) between:

--usual projections used in our country: UTM, Gauss-Kruger and Stereo70;

--geocentric coordinates;

* coordinate transformation (Fig. 5) between:

--S-42 and WGS84 datums using the projection mentioned above;

--ETRSYY and ETRS89.

This module offers the possibility of loading the parameters from a file generated with the first module or to be typed.

Both modules uses like reference surfaces the ellipsoid, the European Gravimetric (Quasi)geoid EGG97, the geoid computed from Global Geopotential Model EGM96 and the Romanian quasigeoid.

3. CONCLUSIONS

The described software is still under development. Upon request, the finished modules can be added with supplementary coordinate systems and projections.

Particularities of the current version, by modules, are:

* module 1:

--global and individual weighting;

* module 2:

--residual mean square error calculation for transformed points;

--transformation distortions (module and direction for error bias of transformed point).

Besides perfecting the already finished module, authors wishes to add some new ones. The final version of this software will allow the following operations:

--global transformation parameters determination between two coordinate systems, using S42, WGS84 and ETRS89 datums and Stereo70, Gauss-Kruger and UTM projections;

--computation and graphical representation of the vector of the horizontal and vertical errors;

--computation and graphical representation of Delaunay triangulation of the network;

--adding new points in a network by simulation;

--network scale variation determination.

Using the orientation and the module of the horizontal error vector and Thiessen proximity polygons different regions can be drawn for regional transformation parameters determination.

4. REFERENCES

DMA, (1987a). Supplement to Department of Defense World Geodetic System 1984 Technical Report: Part I--Methods, Techniques, and Data used in WGS84 development. DMA TR 8350.2-A, first edition, December 1.

DMA, (1987b). Supplement to Department of Defense World Geodetic System 1984 Technical Report: Part II--Parameters, Formulas, and Graphics for practical application of WGS84. DMA TR 8350.2-B, first edition, December 1.

DMA, (1991). Department of Defense World Geodetic System 1984: Its definition and Relationship with Local Geodetic Systems. DMA TR 8350.2, second edition, September 1.

Grafarend, E. and B. Richter, (1977). The generalized Laplace condition. Bulletin Geodesique, 51, 4, pp. 287-293.

Moritz, H, (1980). Geodetic reference system 1980. Bulletin Geodesique, Vol. 54, No. 3, pp. 395- 405.