Datum Transformation: WGS-84 to Older
Ellipsoids and Horizontal Datums
By Joe Burnett
In many countries around the World (including the USA), most of their historical data are still
on horizontal datums, that are on older ellipsoids, and they require datum transformations
from a GPS's WGS-84 latitude and longitude positions, to the older, historical horizontal
datums.
In order to properly convert the WGS-84 positioning to the older horizontal datum, a datum
transformation with the proper parameters must be used. Within the HYPACK® GEODETIC
PARAMETERS program, we already have files for several countries, that make these
conversions to the older horizontal datum, in real-time, while the survey data is being
collected. However, we do not have these files for all locations around the world. Therefore,
some prior set up and calculations must be performed, in order to get the proper conversion
parameters. That's what this article is all about... What you must do to establish the needed
parameters, that provide you with the most accurate positioning in the older horizontal
datums, and the programs in HYPACK® that will help you accomplish this.
1.
Set up your HYPACK Project and establish the project geodesy. For this article, we
will use the Taiwan ( TWD67 ) Grid, which uses the GRS-1967 Ellipsoid (not WGS-84).
Here, we can see that the GEODETIC PARAMETERS defaulted with the following datum
transformation parameters:
Delta X
752.00
Delta Y
358.00
Delta Z
179.00
FIGURE 1. GEODETIC PARAMETERS
This is known as a 3-parameter shift, and will
convert your coordinates, accurately, for about a
5 Mile (10 km) area, before you will need to recalculate a new set of parameters.
Recently, one of our customers used these datum
transformation parameters and found that the
coordinates that were being calculated were off,
by 2.70 meters in the X direction, and 4.02 meters
in the Y direction, from the known values of their
control points in the project area. We asked this
user to provide us with the control point
information.
To calculate the correct 3-Parameter Shift
values, you will need a minimum of one control
point in the project area, that has the latitude and
longitude coordinates in both WGS-84 and the
historical horizontal datum (GRS-1967 in this
example).
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Note: If you are surveying a large area, numerous control points that cover the full reach of
your project area, will create parameter values that will generate lower residual errors
in the coordinate values that are calculated by the datum transformation conversion.
CONVERTING X, Y COORDINATES IN THE HISTORICAL DATUM
What ??!! You ONLY have XY Coordinates in the historical horizontal datum.... No Problem,
we can handle that too. But, you will need the WGS-84 latitude and longitude coordinates
for these control points.
Here is the information that we were provided:
Control
Point
TWD67
Northing
TWD67
Easting
GRS-1967
Latitude
GRS-1967
Longitude
WGS-84
Latitude
WGS-84
Longitude
KB01
2492699.328
179679.632
Unknown
Unknown
22.53083907
120.3244157
KB02
2493032.121
179418.225
Unknown
Unknown
22.53383375
120.3218599
KB03
2493388.591
179138.716
Unknown
Unknown
22.53704146
120.3191269
KB04
2493743.711
178860.376
Unknown
Unknown
22.54023698
120.3164053
KB05
2494106.37
178576.356
Unknown
Unknown
22.54350027
120.3136279
KB06
2494367.996
177433.037
Unknown
Unknown
Unknown
Unknown
KB07
2494542.529
177108.228
Unknown
Unknown
Unknown
Unknown
KB08
2494102.321
179437.555
Unknown
Unknown
Unknown
Unknown
KB09
2493649.055
179483.64
Unknown
Unknown
Unknown
Unknown
KB10
2493408.323
179695.439
Unknown
Unknown
22.53724247
120.3245382
Since we need the GRS-1967 latitude and longitude coordinates, we will need to convert the
TWD67 northings and eastings. To do this, we will use the GRID CONVERSION program:
1.
2
From the HYPACK Main Shell, select UTILITIESGEODESY-GRID CONVERSION.
FIGURE 2. Grid Conversion
Using the TWD67 northing and easting
coordinates (above):
Enter them in the appropriate 'XY to
Geographic' Easting and Northing
fields.
3. Select the 'Lat/Long Options for your
output.
4. Enter the 'Point Name'.
5. Click [Convert]. GRS-1967 Lat/Long (in
this example) is now displayed in the list
below.
Now that we have both the GRS-1967 and
WGS-84 Latitude and Longitude
coordinates, we can enter them into the
DATUM TRANSFORMATION program.
2.
THE DATUM TRANSFORMATION
Control
Point
TWD67
Northing
TWD67
Easting
GRS-1967
Latitude
GRS-1967
Longitude
WGS-84
Latitude
WGS-84
Longitude
KB01
2492699.328
179679.632
22.53261830
120.31637486
22.53083907
120.3244157
KB02
2493032.121
179418.225
22.53561280
120.31381886
22.53383375
120.3218599
KB03
2493388.591
179138.716
22.53882032
120.31108571
22.53704146
120.3191269
KB04
2493743.711
178860.376
22.54201565
120.30836386
22.54023698
120.3164053
KB05
2494106.37
178576.356
22.54527877
120.30558633
22.54350027
120.3136279
KB06
2494367.996
177433.037
Unknown
Unknown
Unknown
Unknown
KB07
2494542.529
177108.228
Unknown
Unknown
Unknown
Unknown
KB08
2494102.321
179437.555
Unknown
Unknown
Unknown
Unknown
KB09
2493649.055
179483.64
Unknown
Unknown
Unknown
Unknown
KB10
2493408.323
179695.439
22.53902160
120.31649701
22.53724247
120.3245382
1.
From the HYPACK® Main Shell, select UTILITIESGEODESY-DATUM TRANSFORMATION.
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FIGURE 3. DATUM TRANSFORMATION Program
Select the 'Transform Type' (3 Parameter recommended).
Select the 'Angle Format' (This is important because it will determine how you enter the
values in Step 4).
4. Verify the Ellipsoids you are Transforming 'From' and 'To'.
5. Enter the Lat/Long Coordinates for each Ellipsoid.
6. Click [Compute].
7. Confirm the calculated transformation parameters and click [Transfer]. This places
the transformation parameters in the corresponding boxes within the GEODETIC
PARAMETERS window.
[View Report] shows that the 'Residual' error is 0.000 for this particular control point.
2.
3.
FIGURE 4. Sample Transformation Report
However, when using these parameters for
shifting other points with the project area,
you will see that the residual errors will
increase as you move farther away from
this point.
Therefore, using several control points that
represent your full project area provides smaller and more uniform residual errors for all the
data points that are collected.
4
For example, using the six (6) control points in the DATUM TRANSFORMATION program
yields slightly different dX, dY, and dZ values:
FIGURE 5. Six Points in the DATUM TRANSFORMATIONS Program
It also yields low, overall residual error values for all the converted points. In this example, the
converted data points should be within 2.66 cm of the known value.
FIGURE 6. Residual Error Using Multiple Control
Points
Note: If you have datum transformation
parameters for your particular part of the
world, and would like to have HYPACK®
create a file that will automatically convert
WGS-84 Lat/Long data, in real-time, to
your horizontal datum, please provide this
data to us and we will gladly create it for
you. This is especially helpful if you are
transiting long reaches within or between
project areas.
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