Transcript Coordinate Transformations

Geodetic Surveying B
SVY3107
Coordinate
Transformations
Learning Objectives
After completing this lecture you will be
able to:
z Demonstrate the general process of 7
parameter datum transformations
z Explain why residual distortion grids are
needed for accurate transformations
Lecture Outline
z Background and Review of Terminology
z Coordinate Conversions
z Coordinate Transformations
y Block Shift
y Molodensky
y 7 Parameter
y Residual Distortions
z Conclusion
Coordinates Systems
Z
Semi-major
axis (a)
Semi-minor
axis (b)
X
-X
+Y
-Z
ECEF Cartesian
f
l
Y
h
Geodetic Coordinates
Geodetic Coordinates
Conversions
XYZ  flh
z YES!!!
z You guessed it!
z We have a spreadsheet that will do these
calculations for us!
Ellipsoids and Geoids
Geocentric Datum
(best fit globally)
The Geoid
(Mean Sea Level)
Local Datum
AGD84
(best fits Australia)
AGD - The Old Datum
z Terrestrial
Observations
z Systematic Errors
z Constrained by
Doppler (transformed)
z Distribution
z Homogeneity
z Location of Marks
GDA
z
z
z
z
z
z
GPS Observations
Small Random Errors
Constrained by GPS
Distribution
Homogeneity
Marks are Accessible
GDA and the ITRF
Link to ITRF by GPS observations
at IGS sites and the Australian
National Network (500km).
GDA’s link to ITRF makes it
compatible with WGS84
Universal Transverse
Mercator Projections
144o
147o
150o
Scale
Factor
0.9996
ZONE 54
ZONE 55
6o wide zones
ZONE 56
UTM Coordinates
NMGA
NAMG
EAMG
EMGA
Australian Terminology
GDA Datum
AGD Datum
GDA94 Latitudes, Longitudes & heights AGD84
GRS80
?
ANS
Coordinate Transformations
z Block Shift
z Molodensky’s formulae
z 7 Parameter transformation
z Distortion Modeling (Surface
interpolation)
z Height is not critical!
Block shift Transformation
GDA94
Accuracy
AGD66
~ 10 m
AGD84
Molodensky’s Formulae
GDA94
Accuracy
AGD66
~5m
AGD84
Molodensky’s Formulae
z National AGD66 &
AGD84 parameters
z No coordinate
conversion required
z Simple formulae
z Accuracy ~ 5 m
z Assumes no rotations
(4 parameter)
General Form of
Datum Transformation
z 3 Directional Translation
z
z
z
z
z
(dX, dY, and dZ)
3 Rotations (about X, Y and
Z axes)
3 Scale Errors (X, Y and Z
directions)
3 Shear Distortions
Total of 12 parameters
Ignore Shear and use
“similarity” transformation
= 7 parameters
Z
Rz
Y
Ry
Dz
Dx
Dy
Rx
X
7 Parameter
Transformation
z 7 Parameters : 3
Origin Shifts, 3
Rotations and 1 Scale



3D Transformation
between AGD84 and
GDA94
Use published
parameters
2-3 metre accuracy
Z
RZ
Y
RY
DX
DY
RX
X
DZ
AGD84 to GDA94
7 Parameter Transformation
ANS/AGD
ECEF - XYZ
GRS80/GDA
Bowring’s or Bomford’s
Formula, or similar
AGD84
ANS
Latitudes, Longitudes & heights
?
GDA94
GRS80
7 Parameter Transformation
GDA94
Accuracy
AGD66
~ 2-3 m
AGD84
7 Parameter Transformation
z National AGD84 parameters
z Accuracy ~ 2-3 m
z Also some regional AGD66
parameters
(NSW, ACT & Tasmania)
Spreadsheets for
Calculations
2. Change
Datums
1. Reverse sign for
reverse calculations
7 Parameter Transformation
ANS
XYZ
GRS80
Bowring’s or Bomford’s
Formula, or similar
AGD84
ANS
Latitudes,
Longitudes & h
GDA94
Redfearn’s Formula
GRS 80
UTM
UTM
AMG84
Eastings, Northings
& Zone (maybe RL)
MGA94
Calculating the 7 Parameters
Not recommended!
Distortions between Transformed
AGD84 and GDA94
Western Qld
Central Coast
Summary of Accuracy
abt. 5cm
2-3 metres
Shift determined from
7 Parameter Transformation
(most of 200m shift)
True GDA
Shift determined from
Distortion Modelling
(Most of what’s left)
abt.190 metres
True AGD
abt. 110 m
Distortion Grid
Component in
E-W Direction
Component in
N-S Direction
Differences between
GDA94 derived from AGD84
and TRUE GDA94
Distortion Modelling
(Surface Interpolation)
z Accuracy ~ 5 cm
z Based on State/Territory subsidiary positions
z Can include distortion modeling
z Complex calculations
z For simple interpolation, a standard, national
grid of accurate shifts is available - GDAy
NTv2 Grid Format
z In use by
G rid 1
many some software
packages
(e.g. ArcInfo)
z Variable grid density
z Can be extended as required
G rid 2
G rid 4
G rid 3
GDAy
Practical Problem
AGD Base
AGD Rover
Reverse
Dodgy
Dodgy
GPS Baseline
DX DY DZ
WGS84 Base
True WGS84/GDA94
Base
WGS84 Rover
True WGS84/GDA94
Rover
Conclusion
You can now:
z Demonstrate the general process of 7
parameter datum transformations
z Explain why residual distortion grids are
needed for accurate transformations
Self Study
z Read relevant module in Study Book
Review Questions