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УДК 528.47:004.9
DOI 10.33764/2618-981X-2022-1-3-12
Вопросы обработки топографических карт среднего масштаба Монголии
П. Эрдэнэчимэг1 *, Д. Оюунцэцэг1 1 Монгольский государственный университет науки и технологии, г. Улаанбаатар, Монголия, * e-mail: erdenechimeg.must@gmail.com, erdenechimeg.geo@must.edu.mn
Аннотация. В статье рассмотрен вопрос, связанный с исправлением ошибок топографических карт среднего масштаба при переобразовании из системы координат СК-42 в систему WGS-84. Необходимость переобразования системы обусловлена постановлением правительства Монголии № 25 от 28 января 2009 года. Постановление предусматривает использование всемирной геодезической системы WGS-84, Балтийской системы высот и картографической проекции UTM для проведения геодезических съемочных работ и равития геодезических сетей на территории Монголии.
Ключевые слова: система координат, расчет проекции, способ Хельмерта, проекция, трансформирование
Research of processing for the medium scale topographic maps
of Mongolia
P. Erdenechimeg1 *, D. Oyuntsetseg1
1 Mongolian University of Science and Technology, Ulaanbaatar, Mongolia, *e-mail: erdenechimeg.must@gmail.com, erdenechimeg.geo@must.edu.mn
Abstract. Article Resolution #25 of the Government of Mongolia dated as of January 28, 2009 provides that the international geodesy coordinates of WGS-84 shall be used for geodesy measurement and processing, the Baltic sea structure shall be used for height network and the UTM reflex of the world horizontal merkater shall be used for large and medium scale topographic mapping respectively based on Articles 5.2.1 of the Geodesy and Mapping Law of Mongolia. There is a research rationale to adjust distortion generated from transferring procedure from TM projection of CS-42 (coordinate system 1942) reference system into UTM projection of WGS-84, an Earth-fixed terrestrial reference system.
Keywords: coordinate system, projection calculation, Helmert method, projection, transformation
Introduction
In order to create the topographic map that meets the resolution requirements, it is significant to choose a proper map projection fits for geographic features of Mongolia. Therefore, the research purpose is to develop a medium-scale topographic map meeting standard requirements. To reach this goal, the calculation and creation of the topographic base grid, and defining parameters used for translating elements on the grid are in need to be fulfilled.
In Mongolia, the work of translating parameters between coordinate systems has been carried out. But there is not an adequate performance in identifying parameters to translate medium-scale topographic mapping. In this circumstance, there is ongoing
research to identify errors during translation of 1:200 000 scale topographic mapping and coordinate system into other scale maps. Conformal cylinder coordinate system is extensively used, but there is remote error when producing topographic map grid and calculating coordinate conversions [5].
The territory of Mongolia consists of 323 sheets of 1:200 000 scale. Calculation is executed using Microsoft Office Excel 2010 and production has completed by AutoCAD 2018, AutoCAD Land 2019, and ArcGIS 10.6.1 and ENVI 4.7.
WGS-84 system calculates the difference in rectangular coordinates that resulted from the UTM and TM projections. With this difference, graphs of length and area deflections are plotted [13] (Fig. 1, 2).
As length scales along the meridian line (m) and parallel line (n) of the conformal cylindrical projection is equal (m = n):
P 2
m = n = —; p = m2; © = 0, (1)
r
Projection deflections are defined as follows:
m = n = 1,332; p = m2 = 1,774 .
The deflection charts have been created with the assistance of m, n (m = n) and p.
1:200 000 scale topographic mapping grids on the TM and UTM projections for Mongolian geographic features, and defining distortions within the framework of confidence level 95%, the length and area distortions are 0.9997 and 0.994 respectively so that 0<P<1 is approved.
There is a distortion 1.8-2.3 km along the X axis and -0.09-0.08 km along the Y axis after overlaying 8832 points of calculated grids and printed map grids.
From this point on, each country needs to use the grid taken out from the result of computation of projection suitable for their own countries.
M projection of the rectangle in a 1: 200 000 scale L-46-II topographic map was performed:
- using Formula (3), 10-point geodetic coordinates on a map sheet L-46-II to be determined (Table 2).
- in geodetic coordinates, the rectangular coordinates X, Y in the UTM projection estimated by formula (5) (Table 3).
The results of converted by formulas 3 and 5 from the geodetic coordinates of the WGS-84 coordinate system to the rectangular coordinates of the plane of the UTM projection are shown in Table 3.
line
p - Area deflection line m - Length scale along the meridian
^ - Latitude
2,5
1,5
o
LO
(N
m oo
,2
o
,5 m"
m oo
o
,5 ,5
r-v m
oo
id ID"
o
,5
pv"
00
m oo oo
o
,5
pv m
oo
o" o" 55
M 111111
O pv
5
Mean Standard Error
Median Mode Standard viation
Sample iriance Kurtosis Skewness Range Minimum Maximum Sum Count Confidence Level (95.0%
Fig. 1. Area deflection chart
2.158573447
0.971362544 2.131002577 #N/A
0.251999902
0.06350395 1.108523591 0.275183925 0.858392111 1.78277183 2.641163941 138.1487006 64
0.99428214
3
2
1.462204286 0.985577265 1.455311864 #N/A
0.084618121
0.007160226 0.203514089 0.287352322 1.331798096 1.619150418 93.58107432 64
0.997136978
Fig. 2. Length deflection chart
1,5
11111111111
11111111111111111111111111111
opvmopvmopvmopvmopvmop--
LO *—I 00 LO *—I 00 LO *—I 00 LO *—I 00 LO *—I 00 LO *—I fN fN m" "tf" "tf" LO ID" ID" pv" 00 00 o" o" fN
Mean
Standard Error Median Mode Standard Deviation
Sample Variance
Skewness Range Minimum Maximum Sum Count Confidence Level (95.0%
2
1
The test task of translating the geodetic coordinates of the 1942 system to the UT
Table 2
Conversions from the CS-42 system to the WGS-84 system
№ CS-42 system, Geodetic coordinates WGS-84 system, Geodetic coordinates
B L B L
1 47°20'00 91°00'00 47°20'01.691 90°59'59.422
2 48°00'00 91°00'00 48°00'01.749 90°59'59.400
3 48°00'00 91°15'00 48°00'01.753 91°14'59.429
4 48°00'00 91°30'00 48°00'01.757 91°29'59.459
5 48°00'00 91°45'00 48°00'01.761 91°44'59.489
6 48°00'00 92°00'00 48°00'01.764 91°59'59.519
7 47°20'00 92°00'00 47°20'01.706 91°59'59.540
8 47°20'00 91°45'00 47°20'01.702 91°44'59.510
9 47°20'00 91°30'00 47°20'01.699 91°29'59.481
10 47°20'00 91°15'00 47°20'01.695 91°14'59.451
Table 3
The results of conversion of Geodetic coordinates to rectangular coordinates
№ WGS-84 system, Geodetic coordinates WGS-84 system, Rectangular coordinates
B L X Y
1 47°20'01.690 90°59'59.422 5244199.393 348888.759
2 48°00'01.749 90°59'59.400 5318289.961 350801.097
3 48°00'01.753 91°14'59.429 5317836.356 369449.383
4 48°00'01.757 91°29'59.459 5317443.272 388097.930
5 48°00'01.753 91°14'59.429 5317836.356 369449.385
6 48°00'01.764 91°59'59.519 5316838.616 425395.644
7 47°20'01.706 91°59'59.540 5242744.935 424439.877
8 47°20'01.702 91°44'59.510 5243017.597 405551.853
9 47°20'01.699 91°29'59.481 5243350.886 386663.972
10 47°20'01.695 91°14'59.451 5243744.813 367776.264
By above method, on grid 238 map sheet with a scale of 1: 200 000, the grid was determined and the grid rectangles were identified in the UTM projection of the WGS-84 system (Fig. 3).
When implementing a linear referencing out of five types of georeferencing it shows the result that RMSx = 44.3 m and RMSj; = 40 m cannot meet the requirements of accuracy (Fig. 4). The reason of this distortion is that the result of calculation is 0.25
mm and 0.2 mm along the X and Y axis respectively because the mathematical accuracy of topographic mapping must be less than 0.1 mm.
— — — — rr:
rffl m
_ _
n
Ml 3
Ml
j-
j
—
Fig.4. The polynomial conversion at 4th degree
Therefore, the polynomial and affine referencing were experimented and the result was RMSx = 43.3 m and RMS^ = 40.0 m after the affine conversion, RMSx = 12 m and RMSy = 20 m after the polynomial conversion at 4th degree, RMSx = 12 m, RMSy=16 m at 5th degree and RMS* = RMSj, = 0 at 10th degree respectively (Fig. 5).
From this perspective, it is obvious that using the conversion at 4th degree is appropriate because the deviation is minimum if the degree of polynomial reference is lower.
Also, the conversion of polynomy has higher resolution than the conversion of affin. RMS equals 0 at the points of the state geodesy network according to the references of linear and "nonlinear rubber paper". When evaluating the results of nonlinear referencing the distortion scale was identified as 20 m at the corners and 0m at the center of the map board. The following conclusions can be derived from the
matrix of deviation. It is determined that polynomial referencing called "nonlinear rubber paper" has the least distortion at the spatial referencing for the medium scale topographic map of Mongolia.
Fig. 5. The polynomial conversion at 10th degree
Topographic mapping system of Mongolia and the conversion of projection
The task of transforming the geodetic coordinates of the 1942 system to the UTM projection of the plane rectangle in a 1:200 000 scale L-46-II topographic map was performed:
- 10-point geodetic coordinate on the L-46-II map sheet tablet to be determined;
- The rectangular coordinates X, Y in the UTM projection by the geodetic coordinates to be found.
UTM and TM projections are types of transverse cylindrical projections on marketers. In the UTM projection the scale on the average will be m = 0.9996 and the further away from the average the magnification will be m = 1.
Reverse conversion is performed in the following sequence including:
- B— = -—) find first approximate value;
a
- s = a[A'B - B' sin 4B - D' sin 6B + sin 8B];
- B2 = —^ + B1;
a
- -4e'4 cos4 B' - 9 • tg2B' • e'2 cos2 B' ;
- in case of (X- S) << 0.001 B'n result will be determined by M, N. Next you find the latitude and longitude value;
- in case of (X - S)) < 0.001 repeat the description back to B. After determine B' conversion shall be use following formula.
By above method, in grid 323 map sheet with a scale of 1: 200 000 the grid was identified by the rectangular coordinates of UTM projection in the WGS-84 system.
Conversion of geodetic data of the large and medium scale topographic maps is one of the very important issues. The rectangular coordinates of 25 points of the base
network of 1:200 000 scale topographic map, which was geo-referenced, was determined (Fig. 6).
Fig. 6. Location of GNSS/GPS points on base network in Mongolia
These defined coordinates were compared with the points on base network catalogue issued from Agency for Land Administration and Management, Geodesy and Cartography then, it met the accuracy requirements so that the coordinates of 63 points were decided to be used for specifying the converion parameters [1] .
The conversion of geodetic network points from the old system to the new system was performed using Helmert's method and SEVEN PAR 7.0 conversion software [3]:
f X ^
X WGS-84 YWGS-84 V ZWGS-84 J
y
V z J
+ ^ ■ R
f X ^
XCS-42 YCS-42 V ZCS-42 J
(2)
r 1 -W z W. ^
where r = W z 1 -W x
-W y W x 1
V y x y
^ = 1 + m
XWGS -84 = xcs - -42 +AX + W yzcs
- WYs-42 + mXCS-42 YWGS-84 = YCS-42 +AY - ®*ZCS-42 + WzXcS-42 + mYCS-42 ZWGS-84 = ZCS-42 +AZ + WxYcs-42 - WyXCS-42 + mZCS-42
(AX, AY, AZ, ro>>, and m) = Helmert's parameter for converting from one system to another (Fig. 7)
AX, AY, AZ = second system starting point coordinates, angular parameters <x, <<y, < a ZOY and ZOX vertical X, equals to the angle of rotation of the axis counterclockwise. The conversion error is not less than 1-2 mm [18].
ZcK-42
Xwgs-84
Fig. 8. Graphic shows coordination reversed axle
For this case the conversion error is not less than 1-2 mm.
When defining seven parameters for the conversion within geo-reference of Mongolia, the parameters are showed up as Ax = 30.5 m, Ay = -118.4 m, Az = -132.6 m, < = -1.43", <y = -1.21", <z = -1.89" and m = 0.00001098 with the help of software SEVENPAR 7.02.
After examining and measuring the points, transferred with the help of seven parameters, in the static mode of GPS network [10], RINEX file was calculated in the service of ONLINE AUSPOS (International calculation of GPS measurement outcome) and met the accuracy requirements of the medium-scale topographic map [2, 19] (Table 4).
Table 4
The results of field measurements
Vector 95%
Vector Identifier Length Error Components Error SV PDOP QA
Solution
Fixed UB01 - 0177 6898.233 0.033 X 6616.161 0.014 18 1.1
16/10/23 10:54:00.00 Y 1952.430 0.014
+21:05:45.00 Z 6.789 0.014
Fixed UB01 - 4153 4894.155 0.024 X -4778.995 0.010 18 1.1
16/10/23 08:09:15.00 Y -960.886 0.010
+23:50:30.00 Z -436.639 0.010
Fixed 4153 - 0177 11770.028 0.057 X 11395.152 0.023 18 1.1
16/10/23 10:54:00.00 Y 2913.318
+21:33:30.00 Z 443.428 0.023
Conclusions
This research aims to enhance the error accuracy when creating a topographic mapping grid through the mathematical basis-calculation of projection after converting the medium scale topographic maps of Mongolia from CS-42 into WGS-84. While the process of converting and calculating, the following results arose.
There are possibilities to enhance the baseline error accuracy of the previous topographic maps during the conversion to the digital formation thanks to the study of the projection of the medium-scale topographic map of Mongolia and the development of the methodology for the calculation of mapping grids. 1:200 000 scale topographic mapping grids on the TM and UTM projections for Mongolian geographic features, and defining distortions within the framework of confidence level 95%, the length and area distortions are 0.9997 and 0.994 respectively so that 0<P<1 is approved. Parameters of geo-referencing of Mongolia generated as Ax = 30.5 m; Ay =
-118.4 m; Az = 132.6 m; < =-1.43"; < = -1.21"; < = -1.89"; and m = 0.00001098 with the help of SEVENPAR 7.02 and the methodology of Helmert. This shows the accuracy of requirements of topographic mapping projection was met by measuring the points of GPS network at static mode.
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© n. Эрдэнэнимэг, ff. O^yn^s^sz, 2022
