Maintaining High Accuracy
in Modern Geospatial Data
Patrick Cunningham
President
[email protected]
www.bluemarblegeo.com
+1 (207) 582 6747
Copyright 2010 Blue Marble Geographics
Concepts
Geodesy - Geomatics
Geoid – Ellipsoid
Semi-major axis
(a)
Flattening (f)
Name
International
1924
6378388 m
WGS84
6378137 m
1/297.0
1/298.25722356
3
Semi-Major Axis/Semi Minor Axis
a2- b2
Datum
e2 =
b2
Prime Meridian
Datum Shift
C6H12O6
-a
A
2 CH3CH2OH + 21 CO2
z
Geocentric Translation / Position Vector
Frame Rotation
R=
Projection
Universal Transverse Mercator/Robinson
Coordinate Reference System
y
A
1
-az
-ay
Ax
1
=a/ (1-e2sin2 )0.5
E = FE + [A-TA3/6-(8-T+8C)TA5/120]
NAD83/Texas North Central (USft)
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kAB=(kAB+4kM+kB)
2
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Coordinate System ???
Coordinate “Reference” System
A reference system used to measure horizontal
and/or vertical distances and angles on a map.
Defined by:
Ellipsoid
Datum
Map Projection
Units
Origin
E.D.P.U.O.
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Mind the Gap
Between the
World and Map!
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Image Courtesy of Merrick & Co., Inc.
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Geodetic Coordinate Ref. Systems
Geodetic Coordinate Systems
The Earth is not round, but rather a lumpy pseudosphere. Despite this, globes are the most accurate
map of Earth we have.
Globes – good earth model, without too
much distortion
Ellipsoid turned into a datum with an
origin, all angles
All geodetic systems use Latitude and Longitude
to define the positions on the Earth. These are
angular measurements, not linear.
The two main reference lines from which all
distances and locations are calculated are the
Equator and the Prime Meridian.
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Units – The Overlooked Step Child
What are Coordinates?
A set of numbers used to represent points in space
Relative to the Origin and Axes
Depending on the coordinate system, coordinates can be
displayed in various formats of various units.
Units
Angular
In Geodetic Coordinate Systems, coordinates
are given in angular units, the most common
being Degrees.
Angular units can be displayed in a number of
formats
Linear
Cartesian and Projected coordinate systems
use linear measures
Unit format is mostly limited to decimal
precision.
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Types of Coordinate Ref. Systems
• Geographic (2d +1)
• Projected (2d +1)
• Geocentric or Earth
Centered, Earth
Fixed (3d)
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Datum Transformations - Examples
• When coordinates exist on one datum, and the need exists to plot or display
them based on another, a datum transformation is required.
3 Parameter shift (Molodensky, Geocentric):
• When performing a 3 parameter datum transformation, a linear shift
is applied to the x, y, and z axes at the geocenter.
•Accuracy can be +/- 1 to 50 meters.
•Does not model network distortions well.
•But, they are easy to calculate!
7 Parameter Shift (Bursa-Wolfe, Helmert):
• The same x,y,z shift found in the Molodensky method, but with 3
additional parameters of rotations of the axes and a scale.
•If applied properly can allow for more accurate mapping of +/- 1m over
large areas.
•Rotation sense is critical
Other Transformation Methods (High Accuracy):
•Molodensky-Badekas 10 parameter (10-15cm)
•NADCON, HARN, NTv2, OSTN02, etc: (7-15cm)
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Transformations – Example
NAD 27 to NAD 83
– NADCON (15cm)
– DMA Multiple Regression Eq.
(1m)
– Canadian NTv2 (3m)
– 3 Parameter
• Eastern US (13m)
• Continental US (14.5m)
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Early Binding vrs Late Binding
World Geodetic System of 1984 is a standard ellipsoid definition that is widely
used all over the world.
Earth-centered, a “best fit” for the whole earth
Originally created as Geodetic Reference System of 1980 by the US
Defense Mapping Agency
Used as the basis worldwide for the GPS satellite network
It serves as a common ellipsoid/datum through which we convert most
other datums
NAD27
Timbalai
ED50
AGD66
Minna
WGS84
M’poraloka
?
Beijing 54
PSAD56
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Vertical Datums
• Horizontal Datum
– Defines the Earth’s curvature over a region or the entire planet
– Oversimplifies the shape
• Vertical Datum
– Adds the lumps back in
– Models of Mean Sea Level
• Both types give us a “zero” surface to base elevations on
– Surface is irrelevant to ECEF
Normal to Ellipsoid
Normal to Geoid
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Ellipsoid
Geoid
Terrain
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Geoids and Mean Sea Level
• NOT equal!
– Vertical models are
approximations of Mean Sea
Level
• MSL is a moving target
– For highest accuracy, local vertical
deflections must be taken into account
– The models are not all the same!
Image Courtesy of Seacoos.org
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< 1 Meter
• Working at high precision levels
requires care and persistence
• The work isn’t done when the data
has been collected
• There are:
– Assumptions (to question)
– Data Manipulations (to understand)
– Limitations (to acknowledge)
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+/- 1 Meter - Assumptions
EPSG Database states that:
WGS84 Transit, WGS84 (G730), WGS84 (G873),
WGS84 (G1150), NAD83 (1986), NAD83(NSRS2007),
NAD83 (CSRS), ITRF (all epochs), GDA94, RGF95,
JGD2000, IRENET95, ETRS89…
…About 60 datums in all, worldwide are
coincident at the +/- 1 meter level
Because of this, many applications are set
up with that assumption.
Because of this, a lot of people are too.
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Where When is your data?
If WGS 84 were a person, it would now be old
enough to get cheap car insurance.
In the 28 years it’s been around,
the Earth hasn’t stopped changing.
Your coordinates aren’t where you
left them.
Image courtesy of NGS
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Time Dependant Shifts
• Horizontal Time Dependant Positioning
(HTDP) for North America
• AUSPOS for Australia
• 14 parameter transformations for other
parts of the world
– These can be implemented in current
software as fixed epoch transforms
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In Sum
•
•
•
•
•
•
•
•
CRS
Transform not convert
Types of CRS’
Types of Datum Transformations
Geoids
WGS 84 – early & late / age
HTDP
Processes/Assumptions
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Solutions
• Metadata
– Vague descriptions lead to assumptions!
• Education
– GIS is science, there’s a lot to learn!
• Training
– Software tools are not always as simple
as we would like; you have to know how
to use them!
Mind the Gap Between the World and Map
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Thank You!
Questions?
Patrick Cunningham
President
[email protected]
www.bluemarblegeo.com
+1 (207) 582 6747
Copyright 2010 Blue Marble Geographics