Methodology and Parameters for Datum Transformation ...geotransform.napr.gov.ge/uploads/Methodology_and... · Methodology and Parameters for Datum Transformation between the New and

The European Union’s ENPI Programme for Georgia

Project Contract No.: 304 521 EU-Georgia E-Governance Facility

Methodology and Parameters for Datum Transformation between the New and Old Reference Systems

Project managed by the Delegation of the European Union to Georgia

Project Partner: Ministry of Justice, Georgia

This project is funded by the European Union

A project implemented by Consortium led by Diadikasia Business Consultants S.A.

Methodology and Parameters for Datum Transformation between the New and Old Reference Systems November 14 / 2013, Tbilisi, Georgia

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Contents Abbreviations ............................................................................................................. 4 Executive Summary ................................................................................................... 5 Introduction ................................................................................................................ 5

Transformation Parameters .................................................................................... 5 Transformation Models ........................................................................................... 5

Bursa-Wolf Model ................................................................................................ 6 Molodensky-Badekas Model ................................................................................ 6

Accuracy Assessment ............................................................................................. 6 Transformation Data Sets .......................................................................................... 7

Pulkovo 1942 Coordinates ...................................................................................... 8 WGS84 Coordinates ............................................................................................... 8 ITRF2008/IGS08 Coordinates ................................................................................. 8

Transformation Parameters between GGD and WGS84.......................................... 13 Application ............................................................................................................ 15

Transformation Parameters between GGD and Pulkovo 1942 ................................ 15 Application ............................................................................................................ 18 Improvement of Transformation Parameters......................................................... 18 Accuracy Testing .................................................................................................. 18 Local Transformations .......................................................................................... 20

Transformation Approach ......................................................................................... 20 Conversion of Pulkovo 1942 Gauss-Krüger to GGD Lambert Coordinates .......... 20 Conversion of WGS84 UTM to GGD Lambert Coordinates .................................. 20

Transformation Software .......................................................................................... 20 References ............................................................................................................... 23

Figures Figure 1. 3D Bursa-Wolf model. ................................................................................ 6 Figure 2. 3D Molodensky-Badekas model. ................................................................ 6 Figure 3. GPS data processing.. ............................................................................... 9 Figure 4. Transformation points between GGD and WGS84. ................................. 14 Figure 5. Transformation points between GGD and Pulkovo 1942. ........................ 15 Figure 6. Recommended location of transformation points. .................................... 19 Figure 7. Conversion of Pulkovo 1942 to GGD grid coordinates. ............................ 21 Figure 8. Conversion of UTM to GGD grid coordinates. .......................................... 22


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Tables Table 1. Observation data for computation of the ITRF2008/IGS08 positions. ......................... 8 Table 2. Measured coordinates in GGD. ................................................................................... 10 Table 3. Transformation coordinates in GGD. ........................................................................... 10 Table 4. Catalogue coordinates in Pulkovo 1942. ..................................................................... 11 Table 5. Transformation coordinates in Pulkovo 1942. ............................................................. 11 Table 6. Coordinates in WGS84 datum. .................................................................................... 12 Table 7. Parameters of Molodensky-Badekas transformation between GGD and WGS84. 13 Table 8. Parameters of Bursa-Wolf transformation between GGD and WGS84. .................. 14 Table 9. Transformation residuals from GGD to WGS84. ........................................................ 15 Table 10. Parameters of Molodensky-Badekas transformation between GGD and Pulkovo 1942. . 16 Table 11. Parameters of Bursa-Wolf transformation between GGD and Pulkovo 1942. ....... 17 Table 12. Transformation residuals from GGD to Pulkovo 1942. ............................................ 17


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Abbreviations 2D Two Dimensional 3D Three Dimensional GGD Georgia Geodetic Datum IGS International GNSS Service ITRF International Terrestrial Reference Frame ITRS International Terrestrial Reference System RTK Real Time Kinematic RMS Root Mean Square UTM Universal Transverse Mercator WGS84 World Geodetic System 1984


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Executive Summary Purpose. The purpose of this report is to present methodology and make recommendations for computation of transformation parameters between the old and new reference systems. Overview. Parameters and methodology for transformation from Pulkovo and WGS84 datums to the new Georgia Geodetic Datum (GGD) are developed. Instructions for data conversion and recommendations for relevant software are made.

Introduction To address the changing requirements for positional accuracy State government agencies responsible for maintaining the geodetic datum and reference frame continually assess their suitability and when necessary renovate and redefine outdated components. That was done in Georgia with the definition and realization of the new Georgia Geodetic Datum (GGD) which is based and aligned with the International Terrestrial Reference System (ITRS). The relationship between the new datum and the ITRS is realized through the ITRF2008/IGS08 coordinates for 12 zero-order CORS stations. In datum redefinition process, the need of many users to work in various datums and reference frames should be recognized. These users should be provided with transformation tools between historic and current datums and reference frames.

Transformation Parameters Transformation parameters are usually computed via common (or identical) points with known coordinates in both systems. These common points are then used to determine a transformation model for the other points in the survey network and the many derived spatial data sets that depend on the local datum but are not directly connected to the survey network. The known coordinates are obtained from a large number of observations that are adjusted together using a lot of assumptions. The observations in the old system are usually of lower quality and the assumptions are only approximately correct. The coordinates in the new system are also subject to error. Therefore only approximate models can ever exist to transform (convert) coordinates from one coordinate system to another. If the accuracy requirements are low then transforming is simple and easy. If the accuracy requirements are higher, a more involved transformation process will be required. The chosen common points should be a good sample of the true relationship between the datums. These sites should be chosen to represent the characteristics of the network, so where the survey network is consistent only a few would be required, but where it is inconsistent, many more would be required.

Transformation Models Various 2D and 3D transformation models are available. More advantages are offered by the 3D models.


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Figure 1. 3D Bursa-Wolf model.

Figure 2. 3D Molodensky-Badekas model.

Bursa-Wolf Model

The Bursa-Wolf model (Figure 1) assumes a similarity relationship between the datums. The identical points are used in a least squares process to solve for 7 parameters which represent the relationship between the two datums:

• origin shifts at the Earth's center of mass (ΔX, ΔY and ΔZ);

• rotations about each of the axes (a, b, q) at the origin of the Cartesian coordinate system of the destination system;

• scale change between the two systems (s).

Molodensky-Badekas Model

The Molodensky-Badekas model (Figure 2) is based on the same definition of translation and scale parameters, but assumes the rotation origin is the barycenter of the common points of the destination system which adds 3 additional parameters. The advantages of the Bursa-Wolf and Molodensky-Badekas models are that they maintain the accuracy of the original measurements and may be used over virtually any area as long as the local coordinates are accurate.

Accuracy Assessment The degree of error in a geodetic transformation depends on the patterns of errors present in the transformed terrestrial reference frames. Those patterns are characteristic of the methods used to establish the terrestrial reference frames, and also on how carefully the transformation has been designed to take account of those errors. For example, terrestrial reference frames established by triangulation generally contain significant errors in the overall size of the network and often, this


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scale error varies in different parts of the network. Therefore, a real transformation is likely to represent not only the difference between geodetic datums, but also the difference between the terrestrial reference frames that realize those datums due to errors in the original observations. The achievable accuracy of the datum transformation with common points is determined by the number, distribution and accuracy of these common points and the transformation technique adopted. It is necessary to obtain far more than the minimum number of common points. The redundant points will give an idea of the consistency of the survey network and the derived transformation parameters. A number of the redundant common points ("check points") should be reserved from the initial transformation modeling and later should be used as an independent check of the quality of the transformation process, by comparing actual and transformed positions. If the difference between the actual and transformed positions (residuals) is not acceptable, then:

• the derivation of the transformation process should be repeated using a different selection of common points, or

• more common points should be obtained, or

• a different transformation method should be used, or

• If the residuals show variable pattern in different regions then the transformed network should be subdivided into homogeneous regions and regional transformation models should be developed.

The RMS error is most often used as overall indicator for the suitability of the transformation method. That error may not be an ideal criterion because a transformation model with a large number of parameters will normally yield a smaller RMS error. Due to the high correlation between parameters, such models are highly sensitive to outliers and may incorrectly distort, stretch, or alter the system. High correlations are related to near singularity in matrix inversion, or to “ill-conditioned” problem in least squares adjustments. When an adjustment is ill conditioned, small changes in the data set can produce very different results. There may be a high correlation between the parameters of the Bursa-Wolf transformation when applied to areas which are not large enough. The reason is that the rotations and scale in that transformation are applied at the geocenter. Most correlations can be reduced if we use instead Molodensky-Badekas where the rotations and scale are applied at the barycenter (centroid) of the common points. A decision for selection of any particular transformation model should be taken on the basis of comparative analysis of the results with different models or set of parameters. The chosen model should produce minimal transformation errors and low correlations between the parameters.

Transformation Data Sets Three sets of coordinates have been provided for computation of transformation parameters.


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Pulkovo 1942 Coordinates The Pulkovo 1942 coordinates (Table 1) were obtained from different volumes of the Catalogue of Coordinates of Geodetic Stations (see References K1-K4). The relative horizontal positional accuracy is estimated to be 0.2 m.

WGS84 Coordinates The WGS84 coordinates were computed at the Massachusetts Institute of Technology in the frame of a geodynamic project for studying plate kinematics and dynamics in the eastern Mediterranean and Caucasus [Прилепин et al., 1997]. The coordinates are taken from an additional table to the cited paper. The accepted name of the datum “WGS84” is misleading because the reference frame in the MIT solutions for the eastern Mediterranean and Caucasus was defined by estimation of transformation parameters to a set of IGS core stations in the ITRF. By that reason the datum is rather ITRF93 than WGS84. The geocentric accuracy of the WGS84 coordinates is estimated at 3-5 mm. The coordinates for station INGU were received from the Head of the Topo-Geodetic Administration at the Department of Geodesy and Cartography of Georgia.

ITRF2008/IGS08 Coordinates The coordinates of stations ARMU, CHAC, FUND, ILMA, KIZI, NORI were computed through static baseline processing from the closest stations of the CORS network. Used observation data are summarized in Table 1. The coordinates of the new stations were obtained from a constrained least squares adjustment in which the coordinates of the CORS stations were fixed to their ITRF2008/IGS08 values.

The coordinates for stations GLDA, KODA are obtained by RTK measurements.

Table 1. Observation data for computation of the ITRF2008/IGS081 positions.

Station Start Date and Time End Date and Time Duration

CHAC 03/30/2012 09:51:50 03/30/2012 14:04:59 4h 13m 09s

FUND 06/05/2012 17:05:35 06/05/2012 21:17:45 4h 12m 10s

ILMA 10/17/2013 11:56:24 10/17/2013 15:56:52 4h 00m 28s

NORI 10/24/2013 11:08:54 10/24/2013 15:11:59 4h 03m 05s

KIZI 10/29/2013 12:27:16 10/29/2013 16:27:47 4h 00m 31s

ARMU 10/31/2013 08:02:24 10/31/2013 12:05:21 4h 02m 57s

CORS Station Start Date and Time End Date and Time Duration

ALGT 03/30/2012 01:59:45 03/31/2012 01:59:15 23h 59m 30s

DEDO 03/30/2012 01:59:45 03/31/2012 01:59:15 23h 59m 30s

1 Hereafter “GGD”.


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IORM 03/30/2012 01:59:45 03/31/2012 01:59:15 23h 59m 30s

TELV 03/30/2012 01:59:45 03/31/2012 01:59:15 23h 59m 30s

AKHA 06/05/2012 01:59:45 06/06/2012 01:59:15 23h 59m 30s

BATU 06/05/2012 01:59:45 06/06/2012 01:59:15 23h 59m 30s

GUDA 06/05/2012 01:59:45 06/06/2012 01:59:15 23h 59m 30s

TELV 10/17/2013 06:59:44 10/18/2013 00:59:14 17h 59m 30s

ALGT 10/17/2013 09:54:44 10/17/2013 18:24:14 8h 29m 30s

IORM 10/17/2013 09:54:44 10/17/2013 18:24:14 8h 29m 30s

TBIL 10/17/2013 09:54:44 10/17/2013 18:24:14 8h 29m 30s

KASP 10/24/2013 08:59:44 10/24/2013 16:59:14 7h 59m 30s

TBIL 10/24/2013 08:59:44 10/24/2013 16:59:14 7h 59m 30s

TELV 10/24/2013 08:59:44 10/24/2013 16:59:14 7h 59m 30s

TIAN 10/24/2013 08:59:44 10/24/2013 16:59:14 7h 59m 30s

AKHA 10/29/2013 07:59:44 10/29/2013 17:59:14 9h 59m 30s

KASP 10/29/2013 07:59:44 10/29/2013 17:59:14 9h 59m 30s

KAZR 10/29/2013 07:59:44 10/29/2013 17:59:14 9h 59m 30s

KAZR 10/31/2013 03:59:44 10/31/2013 13:59:14 9h 59m 30s

KASP 10/31/2013 03:59:44 10/31/2013 13:59:14 9h 59m 30s

AKHA 10/31/2013 03:59:44 10/31/2013 13:59:14 9h 59m 30s

ALGT 10/31/2013 03:59:44 10/31/2013 13:59:14 9h 59m 30s

Figure 3. GPS data processing..


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Table 2. Measured coordinates in GGD.

Station Measured Coordinates Map Sheet

1:200 000 Name Class Year Source X [m] Y [m] Z [m]

ARMU 3446418.4640 3339983.5498 4189323.0807 К-38-XXVII Армудлу 2 1959 [K6, 1084]

CHAC 3338791.9192 3453933.8266 4182047.5730 К-38-XXVII Чачуна 3 1978 [K7, 1982]

FUND 3490673.3338 3238264.9206 4232981.2575 К-38-XIX Фундук IV 1953 [K2, 1987]

GLDA 3377509.2890 3358357.8188 4228622.6271 К-38-XXI 347 3 1997 [O1, 1997]

ILMA 3385818.9286 3387473.2953 4198495.7483 К-38-XXII Илмазло 2 1959 [K5, 1984]

INGU 3484481.0943 3144325.1033 4305103.1740 К-38-VII Лекарде 4 1971 [K1, 1982]

KIZI 3443543.6706 3306899.5357 4217821.9946 К-38-XX Кизилкилиса 2 1958 [K3, 1987]

KODA 3391128.8952 3365339.2510 4212360.1736 К-38-XXI Кода 3 1959 [K4, 1988]

NORI 3372134.2888 3362261.8507 4230593.2821 К-38-XXI I-7098 3 1997 [O1, 1997] Table 3. Transformation coordinates in GGD.

Station Transformation Coordinates Geodetic Coordinates UTM Zone 38 Coordinates

X [m] Y [m] Z [m] Latitude Longitude Ell Height Northing [m] Easting [m]

ARMU 3445516.3359 3339109.2819 4188219.1028 41°18'30.57397"N 44°06'05.29962"E 1672.4076 4573392.9358 424785.4614

CHAC 3338630.2566 3453766.5889 4181843.7161 41°13'55.61716"N 45°58'16.01174"E 309.2911 4564979.2640 581385.5317

FUND 3489415.6435 3237098.1730 4231445.8386 41°49'43.34214"N 42°51'06.45090"E 2302.3024 4632988.7881 321609.4846

GLDA 3377208.6545 3358058.8889 4228243.6979 41°47'24.09779"N 44°50'13.54786"E 568.6190 4626476.4320 486464.4670

ILMA 3385641.3672 3387295.6472 4198274.0842 41°25'44.87237"N 45°00'50.37988"E 334.9953 4586396.5723 501169.2847

INGU 3484200.1998 3144071.6294 4304753.7877 42°43'14.32363"N 42°03'44.83447"E 514.9967 4733978.6827 259475.0859

KIZI 3442579.2331 3305973.3683 4216632.7450 41°38'59.89293"N 43°50'25.30709"E 1789.4805 4611563.4847 403436.3295

KODA 3390788.3632 3365001.3088 4211934.3244 41°35'36.17227"N 44°46'52.68479"E 641.4940 4604654.5000 481773.0430

NORI 3371555.6946 3361684.9504 4229862.5015 41°48'34.48070"N 44°54'57.62173"E 1096.1868 4628637.6461 493023.1189


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Table 4. Catalogue coordinates in Pulkovo 1942.

Station Pulkovo 1942 Zone 8 Coordinates

Map Sheet Map Sheet 1:200 000

Class Year Source Northing [m] Northing [m]

ARMU 4575309.060 8424856.090 К-38-XXVII К-38-XXVII Армудлу 2 1959

CHAC 4566892.470 8581519.310 К-38-XXVII К-38-XXVII Чачуна 3 1978

FUND 4634928.800 8321638.200 К-38-XIX К-38-XIX Фундук IV 1953

GLDA 4628414.090 8486559.660 К-38-XXI К-38-XXI 347 3 1997

ILMA 4588318.040 8501270.470 К-38-XXII К-38-XXII Илмазло 2 1959

INGU 4735959.680 8259478.370 К-38-VII К-38-VII Лекарде 4 1971

KIZI 4613494.950 8403498.390 К-38-XX К-38-XX Кизилкилиса 2 1958

KODA 4606583.240 8481866.370 К-38-XXI К-38-XXI Кода 3 1959

NORI 4630676.050 8493121.150 К-38-XXI К-38-XXI I-7098 3 1997 Table 5. Transformation coordinates in Pulkovo 1942.

Station Transformation Coordinates Geodetic Coordinates

X [m] Y [m] Z [m] Latitude Longitude ARMU 3445500.0727 3339235.4474 4188297.8676 41°18'30.77603"N 44°06'09.68096"E

CHAC 3338612.1316 3453891.5748 4181921.1900 41°13'55.76809"N 45°58'20.30128"E

FUND 3489400.6882 3237224.6679 4231525.7074 41°49'43.56137"N 42°51'10.91035"E

GLDA 3377191.7843 3358184.3013 4228322.0087 41°47'24.25156"N 44°50'17.91455"E

ILMA 3385624.3854 3387421.1013 4198352.1471 41°25'45.03695"N 45°00'54.71678"E

INGU 3484185.8789 3144197.8636 4304834.7429 42°43'14.53811"N 42°03'49.37507"E

KIZI 3442563.1242 3306099.6398 4216711.7723 41°39'00.08615"N 43°50'29.72512"E

KODA 3390771.6206 3365126.8642 4212012.5558 41°35'36.33434"N 44°46'57.04192"E

NORI 3371538.6740 3361810.5148 4229940.6537 41°48'34.62641"N 44°55'01.99444"E


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Table 6. Coordinates in WGS84 datum.

Station Cartesian Coordinates Geodetic Coordinates UTM Zone 38 Coordinates

X [m] Y [m] Z [m] Latitude Longitude Ell Height Northing [m] Easting [m]

INGU2 3484481.4163 3144324.9149 4305102.9848 42°43'14.31665"N 42°03'44.81885"E 514.9511 4733978.4796 259474.7229

khur 3419280.2574 3231380.5860 4293881.1802 42°34'41.80616"N 43°22'53.99520"E 1122.3982 4715254.3813 367192.1640

kudi 3312527.8978 3405762.7931 4241833.9146 41°57'02.30051"N 45°47'42.31187"E 457.8522 4644601.4215 565898.2766

nich 3393716.0853 3337967.4767 4232160.8065 41°49'50.36929"N 44°31'31.85181"E 829.7982 4631083.4755 460600.1661

sach 3430573.2323 3244133.8610 4274829.0300 42°20'55.18842"N 43°24'00.06421"E 777.0156 4689728.7839 368217.4751

shua 3539915.6401 3202260.0118 4216732.9870 41°38'51.80565"N 42°07'58.65321"E 431.3932 4614636.1543 261241.6069

2 See the map sheet 1:200 000 number in Table 4.


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Transformation Parameters between GGD and WGS84 Transformation parameters between GGD and WGS84 using Molodensky-Badekas model were first computed model by the Geodesy and Cartography Division in 2011. That computation is repeated here to check the transformation accuracy. Additionally an equivalent Bursa-Wolf transformation is computed to provide users with alternative parameters if the Molodensky-Badekas model is not supported by the application software. Table 7. Parameters of Molodensky-Badekas transformation between GGD and WGS84.

Molodensky-Badeks:

(1 )−

= + − + −

R S P P

R S P P

R S P P

X 1 -q b X X X XY s q 1 -a Y Y Y YZ -b a 1 Z Z Z Z

Δ+ Δ

Δ

where:

.∑ ∑ ∑i i i

n n n

P S P S P Si=1 i=1 i=1

X = X ,Y = Y , Z = Z

From GGD to WGS84 From WGS84 to GGD

ΔX [m] 0.3452 ±0.0152 -0.3452 ±0.0152

ΔY [m] -0.1805 ±0.0152 0.1805 0±.0152

ΔZ [m] -0.2060 ±0.0152 0.2060 ±0.0152

a [ " ] 0.05465 ±0.05465 -0.05465 ±0.06158

b [ " ] -0.06718 ±0.06362 0.06718 ±0.06362

q [ " ] 0.06143 ±0.02982 -0.06143 ±0.02982

s [ ppm ] 0.0181 ±0.1393 -0.0181 ±0.1393

PX [m] 3419202.2774 3419202.6226

PY [m] 3284301.1262 3284300.9457

PZ [m] 4251887.7897 4251887.5837

Points 5 5

Post Fit [m] 0.0340 0.0340


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Table 8. Parameters of Bursa-Wolf transformation between GGD and WGS84.

Bursa-Wolf:

(1 ) . = +

R S

R S

R S

X 1 -q b X XY s q 1 -a Y YZ -b a 1 Z Z

Δ+ Δ

Δ

From GGD to WGS84 From WGS84 to GGD

ΔX [m] -2.0796 ±1.4858 2.0796 ±1.4858

ΔY [m] -0.3484 ±1.4431 0.3484 ±1.4431

ΔZ [m] 1.7009 ±2.0078 -1.7009 ±2.0078

a [ " ] 0.05465 ±0.06158 -0.05465 ±0.06158

b [ " ] -0.06718 ±0.06362 0.06718 ±0.06362

q [ " ] 0.06143 ±0.02982 -0.06143 ±0.02982

s [ ppm ] 0.0181 ±0.1393 -0.0181 ±0.1393

Points 5 5

Post Fit [m] 0.0340 0.0340

Figure 4. Transformation points between GGD and WGS84.


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Table 9. Transformation residuals from GGD to WGS84.

Station ΔX [m] ΔY [m] ΔZ [m] ΔN [m] ΔE [m]

khur 0.0395 0.0122 -0.0294 -0.0468 -0.0183

kudi 0.0002 -0.0005 -0.0341 -0.0252 -0.0005

nich -0.0062 0.0041 0.0548 0.0419 0.0073

sach -0.0389 -0.0062 0.0236 0.0393 0.0223

shua 0.0054 -0.0097 -0.0150 -0.0095 -0.0108

Application The computed transformation parameters can be applied countrywide.

Transformation Parameters between GGD and Pulkovo 1942 The transformation between GGD and Pulkovo 1942 is performed on the ellipsoid using both Molodensky-Badekas and Bursa-Wolf models. That was done to account for the existence in the past of two separate classical datums in Georgia: a horizontal datum (Pulkovo 1942) which forms the basis for the computations of horizontal control surveys, and a vertical datum (Baltic Height System 1977) to which elevations are referred. That is, a survey monument that provided accurate horizontal coordinates was not normally connected to the vertical network, nor were vertical points related to the horizontal reference network. The Baltic heights of the horizontal monuments are often determined by trigonometric leveling to a sub-meter accuracy. That may introduce large post transformation residuals. To avoid that problem the ellipsoidal heights of the identical points in both GGD and Pulkovo 1942 are set to zero. The computed Molodensky-Badekas and Bursa-Wolf transformations are equivalent and can be used alternatively.

Figure 5. Transformation points between GGD and Pulkovo 1942.


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Table 10. Parameters of Molodensky-Badekas transformation between GGD and Pulkovo 1942.

Molodensky-Badeks:

(1 )−

= + − + −

R S P P

R S P P

R S P P


Δ+ Δ

Δ

where:

.∑ ∑ ∑i i i

n n n


X = X ,Y = Y , Z = Z

From GGD to Pulkovo 1942 From Pulkovo 1942 to GGD

ΔX [m] -16.3765 ±0.0449 16.3765 ±0.0449

ΔY [m] 125.7931 ±0.0449 -125.7931 ±0.0449

ΔZ [m] 78.7608 ±0.0449 -78.7608 ±0.0449

a [ " ] 1.30639 ±0.17501 -1.30637 ±0.17500

b [ " ] 1.43939 ±0.29061 -1.43940 ±0.29059

q [ " ] -2.64801 ±0.12960 2.64803 ±0.12959

s [ ppm ] 4.2753 ±0.4293 -4.2754 ±0.4292

PX [m] 3413948.4165 3413932.0400

PY [m] 3328006.6485 3328132.4417

PZ [m] 4221245.5331 4221324.2939

Points 9 9

Post Fit [m] 0.1347 0.1347


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Table 11. Parameters of Bursa-Wolf transformation between GGD and Pulkovo 1942.

Bursa-Wolf:

(1 ) . = +

R S

R S

R S


Δ+ Δ

Δ

From GGD to Pulkovo 1942 From Pulkovo 1942 to GGD

ΔX [m] 41.2107 ±7.6797 -41.2116 ±7.6793

ΔY [m] 41.0016 ±3.1915 -40.9999 ±3.1912

ΔZ [m] 57.9681 ±7.5187 -57.9676 ±7.5182

a [ " ] 1.30639 ±0.17501 -1.30637 ±0.17500

b [ " ] 1.43939 ±0.29061 -1.43940 ±0.29059

q [ " ] -2.64801 ±0.12960 2.64803 ±0.12959

s [ ppm ] 4.2753 ±0.4293 -4.2754 ±0.4292

Points 9 9

Post Fit [m] 0.1347 0.1347

Table 12. Transformation residuals from GGD to Pulkovo 1942.


ARMU 0.1097 -0.1288 0.0047 0.0125 -0.1687

CHAC 0.0869 0.1283 -0.2037 -0.2535 0.0295

FUND -0.0027 -0.0571 0.0381 0.0566 -0.0386

GLDA -0.0980 0.0820 0.0332 0.0323 0.1273

ILMA -0.1166 0.0837 0.0267 0.0354 0.1416

INGU 0.0234 0.2034 -0.1822 -0.2428 0.1271

KIZI 0.1699 -0.2342 0.0531 0.0699 -0.2857

KODA -0.1429 0.0396 0.0937 0.1185 0.1291

NORI -0.0297 -0.1170 0.1363 0.1708 -0.0617


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Application The computed transformation parameters can be applied countrywide.

The transformations should be applied to Cartesian coordinates ( , ,X Y Z ) computed from geodetic coordinates ( ,φ λ ) and ellipsoidal height is set to zero ( 0h = ). When necessary, heights should be set to their real values after the transformation.

Improvement of Transformation Parameters The degree of error in a geodetic transformation depends on the patterns of errors present in the transformed terrestrial reference frames. As most terrestrial reference frames established by triangulation, Pulkovo 1942 in Georgia contains significant errors in the overall size of the network and this scale error varies in different parts of the network. Therefore, a real transformation is likely to represent not only the difference between geodetic datums, but also the difference between the terrestrial reference frames that realize those datums due to errors in the original observations. Computed transformation is based on identical points in southern Georgia and might not valid for the rest of the territory. To compute better transformation parameters more historical triangulation points should be measured with GPS. To achieve good results, the points should be equally distributed at a density at least 1 point per 25-50 km2. The recommended location of the points is shown on Figure 6.

Accuracy Testing The transformation accuracy for any specific project should be tested by comparing actual and transformed positions of check points (see above). The actual positions should come from an independent source of higher accuracy e.g. GNSS measurements. The aerial extent of the check points should approximate that of the transformed dataset. The test should involve only horizontal accuracy. Once the coordinate values have been determined, the residual-distance for each check point should be computed using the formula:

,=ΔR ΔE + ΔN

where ΔE ΔNand are the residuals (actual minus transformed) in easting and northing. Then three values should be computed: (1) the sum of squared residual-distances, (2) the average of the sum by dividing the sum by the number of check points, and (3) the root mean square (RMS) error which is the square root of the average. The transformation is accepted if the root mean square error is less than 0.1 meters for WGS84 data and 0.5 m for Pulkovo 1942 data. These threshold values are based on the estimated transformation post-fit (Table 11 and Table 14). The data used for calculation of the root mean square error should be clean of outliers.

It the accuracy test is not passed the transformation model should be refined using transformation points within the region.


19

Figure 6. Recommended location of transformation points.

Technical Specifications for Establishment of a New Geodetic Reference System, November 14 / 2013, Tbilisi, Georgia

20

Local Transformations If a large number of common points are available in a small area and a more accurate approximation between GGD and Pulkovo 1942 is required, affine transformation can be applied. The affine model relates two 2D Cartesian coordinate systems through a rotation, a scale change in easting and northing direction, followed by translation. That method can compromise the accuracy of the GNSS coordinates because it squeezes or stretches them to fit the Pulkovo 1942 grid. The affine transformation should not be applied for regions larger than 15x15 km.

Transformation Approach The conversion of coordinates from one map projection to another when the source projection is based upon a different horizontal datum than the target projection should be combined with a datum transformation.

Conversion of Pulkovo 1942 Gauss-Krüger to GGD Lambert Coordinates The conversion should include Molodensky-Badekas (or Bursha-Wolf) datum transformation and re-projection of the 3D coordinates according to the flowchart in Figure 7.

Conversion of WGS84 UTM to GGD Lambert Coordinates The conversion should include Molodensky-Badekas (or Bursha-Wolf) datum transformation and re-projection of the 3D coordinates according to the flowchart in Figure 7.

Transformation Software Recommended software for computation of transformation parameters and data conversion is TransLT (http://www.topolt.com/en/products/translt.html) with the following capabilities:

• calculation of transformation parameters and conversion of coordinates using various 2D and 3D models;

• conversion between geodetic and Cartesian coordinates;

• conversion between geodetic and grid coordinates;

• support of a large number of map projections;

• transformations using own formula;

• user defined step by step transformations. The per-user cost of this software is approximately USD100. User manual and numerical examples for conversion of coordinates between the new and old reference system using TransLT are given in [Kotzev, 2013].

http://www.topolt.com/en/products/translt.html


21

Figure 7. Conversion of Pulkovo 1942 to GGD grid coordinates.


22

Figure 8. Conversion of UTM to GGD grid coordinates.


23

References IGN (2011): Georgia Continuously Operating Reference Stations Coordinates

Computation Report Version 1.0, Institut Géographique National, May 25, 2011.

K1 (1982): Каталог координат геодезических пунктов на лист карты масштаба 1:200 000 К-38-VII (Местиа), Военно-топографическое управление Генерального штаба, Москва.

K2 (1987): Каталог координат геодезических пунктов на лист карты масштаба 1:200 000 К-38-XIX (Ахалцихе), Военно-топографическое управление Генерального штаба, Москва.

K3 (1987): Каталог координат геодезических пунктов на лист карты масштаба 1:200 000 К-38-XX (Хашури), Военно-топографическое управление Генерального штаба, Москва.

K4 (1988): Каталог координат геодезических пунктов на лист карты масштаба 1:200 000 К-38-XXI (Тбилиси), Военно-топографическое управление Генерального штаба, Москва.

K5 (1984) Каталог координат геодезических пунктов на лист карты масштаба 1:200 000 К-38-XXII (Рустави), Военно-топографическое управление Генерального штаба, Москва.

K6 (1984) Каталог координат геодезических пунктов на лист карты масштаба 1:200 000 К-38-XXVII (Кировакан), Военно-топографическое управление Генерального штаба, Москва.

K7 (1982): Каталог координат геодезических пунктов на лист карты масштаба 1:200 000 К-38-XXVIII (Казах), Военно-топографическое управление Генерального штаба, Москва.

Kotzev, V. (2013): Manual for Datum transformation between the New and Old Reference Systems, EU-Georgia E-Governance Facility project document.

O1 (1997): Объeкт 04.01.04.1393 Астромомо-геодезический полигон, Грузинское аэрогеодезическое предприятие.

O2 (1989): Объeкт 04.03.0959 линия Гореловка-Квемо Орзомани, Грузинское аэрогеодезическое предприятие.

O3 (1980): Объект „Иорский“ 04.03.0040, Грузинское аэрогеодезическое предприятие.

S1 (1982): Сводный каталог высот пунктов нивелирования на лист карты масштаба 1:200 000 К-38-VII (Местиа), Предприятие № 4 Главного управления геодезии и картографии при Совете министров СССР, Тбилиси.

S2 (1987): Сводный каталог высот пунктов нивелирования на лист карты масштаба 1:200 000 К-38-XIX (Ахалцихе), Предприятие № 4 Главного управления геодезии и картографии при Совете министров СССР, Тбилиси.

S3 (1987): Сводный каталог высот пунктов нивелирования на лист карты масштаба 1:200 000 К-38-XX (Хашури), Предприятие № 4 Главного


24

управления геодезии и картографии при Совете министров СССР, Тбилиси.

S4 (1988): Сводный каталог высот пунктов нивелирования на лист карты масштаба 1:200 000 К-38-XXI (Тбилиси), Предприятие № 4 Главного управления геодезии и картографии при Совете министров СССР, Тбилиси.

S5 (1984): Сводный каталог высот пунктов нивелирования на лист карты масштаба 1:200 000 К-38-XXII (Рустави), Предприятие № 4 Главного управления геодезии и картографии при Совете министров СССР, Тбилиси.

S6 (1984): Сводный каталог высот пунктов нивелирования на лист карты масштаба 1:200 000 К-38-XXVII (Кировакан), Предприятие № 4 Главного управления геодезии и картографии при Совете министров СССР, Тбилиси.

S7 (1982): Сводный каталог высот пунктов нивелирования на лист карты масштаба 1:200 000 К-38-XXVIII (Казах), Предприятие № 4 Главного управления геодезии и картографии при Совете министров СССР, Тбилиси.

Прилепин, М.Т., С. Баласанян, С.М. Баранова, Т.В. Гусева, А.В. Мишин, М. Надария, Е.А. Рогожин, Н.К. Розенберг, Ю.П. Сковородкин, М. Хамбургер, Р. Кинг, Р. Рейлингер (1997): Изучение кинематики Кавказского региона с использованием GPS технологии, Физика Земли 6, 68–75.

The European Union’s ENPI Programme for Georgia

Project Contract No.: 304 521 EU-Georgia E-Governance Facility

Addendum to Methodology and Parameters for Datum Transformation between the New and Old Reference Systems

Project managed by the Delegation of the European Union to Georgia

Project Partner: Ministry of Justice, Georgia

This project is funded by the European Union

A project implemented by Consortium led by Diadikasia Business Consultants S.A.

Addendum to Methodology and Parameters for Datum Transformation between the New and Old Reference Systems – April 04 / 2014, Tbilisi, Georgia

2

Contents Abbreviations ............................................................................................................. 3

Executive Summary ................................................................................................... 4

Updated Transformation Parameters between GGD and Pulkovo 1942 .................... 4

Tables Table 1. Updated Parameters of Molodensky-Badekas transformation between GGD and Pulkovo 1942. ............................................................................................ 4 Table 2. Updated Parameters of Bursa-Wolf transformation between GGD and Pulkovo 1942. ............................................................................................................ 5 Table 3. Transformation residuals from GGD to Pulkovo 1942. ................................ 5


3

Abbreviations GGD Georgia Geodetic Datum


4

Executive Summary Purpose. The document contains updated parameters for transformation between GGD and Pulkovo 1942 computed from additional identical points measured since submission of the original report. Overview. The new parameters show insignificant differences with the original computed ones, better accuracy and slightly improved post transformation fit.

Updated Transformation Parameters between GGD and Pulkovo 1942 The new and originally computed Molodensky-Badekas and Bursa-Wolf transformations parameters are shown in Table 1 and Table 2. The residuals of the new solution аre given in Table 3. Table 1. Parameters of Molodensky-Badekas transformation from GGD to Pulkovo 1942.

Molodensky-Badeks:

(1 )−

= + − + −

R S P P

R S P P

R S P P


Δ+ Δ

Δ

where:

.∑ ∑ ∑i i i

n n n


X = X ,Y = Y , Z = Z

Originally Computed New Computed

ΔX [m] -16.3765 ±0.0449 -15.6260 ±0.0272

ΔY [m] 125.7931 ±0.0449 126.0343 ±0.0272

ΔZ [m] 78.7608 ±0.0449 79.3775 ±0.0272

a [ " ] 1.30639 ±0.17501 1.27530 ±0.13360

b [ " ] 1.43939 ±0.29061 1.42112 ±0.21582

q [ " ] -2.64801 ±0.12960 -2.69445 ±0.07631

s [ ppm ] 4.2753 ±0.4293 4.5284 ±0.2185

PX [m] 3413948.4165 3445619.6689

PY [m] 3328006.6485 3275369.7555

PZ [m] 4221245.5331 4236015.9558

Points 9 16

Post Fit [m] 0.1347 0.1089


5

Table 2. Parameters of Bursa-Wolf transformation between GGD and Pulkovo 1942.

Bursa-Wolf:

(1 ) . = +

R S

R S

R S


Δ+ Δ

Δ

Originally Computed New Computed

ΔX [m] 41.2107 ±7.6797 40.7436 ±5.4889

ΔY [m] 41.0016 ±3.1915 40.0018 ±2.0974

ΔZ [m] 57.9681 ±7.5187 56.7070 ±5.6937

a [ " ] 1.30639 ±0.17501 1.27530 ±

b [ " ] 1.43939 ±0.29061 1.42112 ±

q [ " ] -2.64801 ±0.12960 -2.69445 ±

s [ ppm ] 4.2753 ±0.4293 4.5284 ±

Points 9 16

Post Fit [m] 0.1347 0.1089

Table 3. Transformation residuals from GGD to Pulkovo 1942.


AKHL -0.0197 -0.0019 0.0101 0.0124 0.0178

ARMU 0.1330 -0.1388 0.0014 -0.1922 0.0038

CHAC 0.0572 0.1239 -0.1820 0.0475 -0.2213

CKHE 0.1254 -0.0853 -0.0345 -0.1490 -0.0446

FUND 0.0583 -0.0891 0.0263 -0.1042 0.0341

GLDA -0.0922 0.0547 0.0489 0.1039 0.0541

ILMA -0.1169 0.0699 0.0380 0.1321 0.0505

INGU 0.1110 0.1348 -0.1888 0.0168 -0.2568

KHET -0.0683 0.0136 0.0378 0.0578 0.0541

KHUN -0.0333 0.0159 0.0153 0.0348 0.0196

KIZI 0.2021 -0.2573 0.0523 -0.3247 0.0650

KODA -0.1366 0.0197 0.1051 0.1105 0.1335

MUKH -0.1515 0.1434 0.0050 0.2084 0.0076

NORI -0.0260 -0.1447 0.1535 -0.0839 0.1948

RION -0.0198 0.0160 -0.0040 0.0252 -0.0011

TAUR -0.0226 0.1251 -0.0844 0.1044 -0.1113

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