Uni of Nottingham -Introduction to Geodesy -Dec2012

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Click to edit Master title styleNottinghamGeospatialInstitute

Introduction to Geodesy

Professor Terry Moore

Professor of Satellite Navigation

Nottingham Geospatial Institute

The University of Nottingham


Conventional CoordinateTerminology

• Coordinate Type or RepresentationLatitude, longitude & heightCartesian X, Y & ZMap projection north & east

• Coordinate (Reference) SystemDefinitions of origin, orientation, scaleFundamental constants, c, GM, etcAdoption of ellipsoid parameters

• Coordinate (Reference) FrameRealisation of a coordinate systemMeasurement of coordinates of points on the EarthRefinement & revision with time NG

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The Figure of the Earth

The solid earth

Approximation as a sphere

Approximation as an ellipsoid


The Shape of the EarthThe Geoid

• “The Equipotential of the Earth’s gravity field(including rotational forces) which most closelycorresponds to Mean Sea Level.”

• Geoid is only one of an infinite number ofequipotential surfaces

• Equipotential surfaces are not parallel

• The plumb line (vertical), perpendicular to theequipotential surfaces, is curved.

• Geoid can’t be used for coordinate calculation–(not a regular mathematical figure)

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Earth Gravity Model(EGM)96


The Figure of the Earth

The solid earth

Approximation as a sphere

Approximation as an ellipsoidNG

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Astronomical Coordinates

• Latitude fA, Longitude lA

• Equator–Plane perpendicular to Spin Axis, through mass centre

• Zero Longitude–Plane containing (or parallel to) Spin Axis (Greenwich Meridian)

A

Vertical

Solid Earth

Equator

Spin Axis

zero longitude

A


Astronomical Coordinates

• Spin Axis is not fixed–Polar motion, IERS Reference Pole

• Zero Meridian does not pass through Greenwich–IERS Reference Meridian

• Astronomical coordinates do not constitute a ‘true’coordinate system–Several points can have the same astronomical latitude fA

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• Latitude f, Longitude l

• Spherical model of Earth

• Latitude- Angle between equator and radius vector

• Longitude- Angle between zero meridian and meridian through point

Spherical GeographicalCoordinates

Greenwich


Geodetic EllipsoidalCoordinates

• Reference ellipsoid–semi major axis (a), flattening (f)

• Latitude fG

–Angle between ellipsoidal equator and normal

• Longitude lG

–Angle between zero meridian and planecontaining normal and minor axis of ellipsoid

Greenwich

G

normal

h

G

p

P

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Ellipsoidal (Geodetic)Coordinates

a = semi-major axisb = semi-minor axis

f = flattening

=

e2 = eccentricity

=

a - ba

a2 - b2

a2

G

b

a

normalp

P

E Q


Height

• Ellipsoidal height (h)–Length along the normal from the point to the ellipsoid

• Orthometric height (H)–Length along vertical from the point to the geoid

• Geoid–Gravitational surface closest to mean-sea-level

• Geoid - Ellipsoidal separation (N)

h = N + H

h

N

HMean Sea Level

Reference Ellipsoid NG

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Geodetic ReferenceEllipsoids

G

L

LocalEllipsoid

GeocentricEllipsoid

Normals

SolidEarth

G

L


Reference Ellipsoids

Name a (m) 1/f Usage

Everest (1830) 6377276 300 India

Airy (1830) 6376542 299 Great Britain

Clarke (1866) 6378206 295 North America

Clarke (1880) 6378249 293 France, Africa

International (1924) 6378388 297 Europe (ReTrig)

Krassovsky (1940) 6378245 298 Russia

WGS 72 6378135 298.26 DoD (Doppler)

GRS 80 6378137 298.257 IAG (Geo Ref Sys)

WGS 84 6378137 298.257 DoD (GPS)

Positioning NOT Size of Ellipsoid is Important

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Cartesian Coordinates

Solid Earth

Z

YY

X

Greenwich P

pp


Conversion Formulae

X = ( + h) cos G cos GY = ( + h) cos G sin G

Z = ( (1-e2) + h) sin G

=a

(1 - e sin )2 2G

tan G =Y

X

tan G =

Z + e sin

X + Y

G

2 2

2

h =X

cos cos

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CartesianCoordinates

X, Y, Z

GeodeticEllipsoidal

Coordinates

f, l, h

Conversion Formulae


Examples of Coordinates

• Cartesian X, Y and Z3 851 459 m -79 556 m 5 065 774 m

• Latitude , longitude, and height h52º 56’ 00” N1º 1’ 00” W 90 m

• National Grid, Easting E and Northing N354 885 m 337 673 m

• OS GB 36 datum, what about on WGS 843 851 834 m -79 667 m 5 066 205 m52º 56’ 01” N1º 1’ 06” W 137 m

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Terrestrial Coordinate ReferenceSystems and Frames






Definition of aGeodetic Datum

G

Ellipsoid Size (a & e2)

Ellipsoid Orientation (CIO)

Ellipsoid Position (3)

Zero Meridian (BIH, CZM)

Origin Pillar

MassGeocentre

Centre ofEllipsoid

CIO Axis

normal

Minor axis of Ellipsoidparallel to CIO Axis

P

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Positioning ofEllipsoid & Origin Pillar

Equip.

Geoid

Ellipsoid

vertical

normal

H

N

h

Formulae

= G- A

= (G - A) sin

h = N + H


At the Datum Point

Geoid

Ellipsoid

vertical

normal

In General

oG = o

A

oG = o

A

ho

= Ho

(No=0)

But Also

Arbitrary oG, o

G, No

(eg OSGB ‘70 & ED ‘50)

} ObservedO

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Basic TriangulationFigures

Chain of Triangles Centre-pointTriangle

BracedQuadrilaterals

Centre-pointed Polygon


Chain and NetworkTriangulation

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Ordnance Survey Datum

• Principal Triangulation started in 1784, adjusted bylog tables

• Astrogeodetic origin at Greenwich, Airy Ellipsoid

• Retriangulation 1935 - 1951 : OS GB 36

• Computed using log tables and mechanical calculators

• Implied origin, through 11 stations, at Greenwich

• Re-adjusted with EDM scale, using computersOrigin at HerstmonceuxOS GB 70 (SN) - Scientific Network

• Re-adjusted with Transit Doppler : OS (SN) 80

• All mapping still based on OS GB 36


Greenwich to ParisNetwork 1787

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Principal Triangulation

Jesse Ramsden’s36in Theodolite 1791


Measuring theLough Foyle Base

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• Principal Triangulation started in 1784, adjusted by logtables









Ordnance SurveyPrimary Triangulation

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• Principal Triangulation started in 1784, adjusted bylog tables









Differences betweenOSGB36 and OSSN80

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European Datum

• First computed in 1947 by US Army Map Services

• De-classification of ED50 - North Sea exploration

• IAG Sub-commission established1954–to re-compute triangulation of Europe (RETrig)

• ED 79 Terrestrial Network, only 25 years!

• ED87 Conclusion of RETrigTerrestrial network control by space geodesyInternational ellipsoid, origin near Munich

• EUREF IAG Sub-commission for unified EuropeanDatum consistent with GPS

• ETRF 89 Sub-set of ITRF 89 coords, at epoch 1989.0

• EUREF 89 Densification of ETRF 89 GPS (in 1989)

• ETRS 89 Coordinates consistent with the system


EUREF 89

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• Principal Triangulation 1784 - 1850

• Retriangulation 1935 - 1951 OS GB 36

• Readjusted with EDM scale OS GB 70 (SN)

• Readjusted with Transit Doppler OS (SN) 80

• European Reference Frame EUREF 89

• Scientific GPS Network SciNet 92

• National GPS Network OS (GPS) 93

• Definitive Network and Transformation OS TN 02

• National mapping and charting (still) OS GB 36


UK & Ireland EUREF& SciNet 92

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Geocentric Coordinate ReferenceSystems and Frames




The University of NottinghamNG

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Global Geocentric Systems

• Origin of axes close to the centre of mass of Earth

• Orientation of axes coincides with IERS system

• Ellipsoid (if defined) - best fit to Geoid for whole Earth

• Easy to define - difficult to realise

• Global systems are implicitly defined by theassignment of coordinates to a number of points onthe Earth’s surface (frame)

• In theory only 3 points required, usually many more.

• Unless based on high quality measurements errorsmay occur

• Progressively more accurate realisation of globalcoordinate systems as frames


World Geodetic SystemHistory

• Development started by US DOD in the late 1950s

–Need to relate local datums around the World

–Satellite Navigation

–Intercontinental Ballistic Missiles

• WGS 60 - only used satellite data for ellipsoidal shape

• WGS 66 & WGS 72 - large amount of optical satellitetracking data and Transit Doppler observations

• WGS 72 ellipsoid (equipotential) adopted consistentwith IUGG Geodetic Reference System 1967 (GRS 67)

• Datum transformations to convert to local systems

• WGS 72 Geoid and Geopotential modelNG

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World Geodetic System1984

• United States Department of Defense

• Fundamental constants and gravity field

• Coordinate system (origin, orientation and scale)–Defined by space geodetic methods (SLR and VLBI)

• Realisation by Transit Doppler–1591 precise ephemeris Doppler points

–NSWC - 9Z2 coordinates transformed to WGS 84 system

–Transit precise ephemeris coordinates - accurate to 1-2m

–Absolute accuracy of WGS 84 approx 1 to 2 m

DoD WGS 84 TR 8350.2, last update Jan 2000.Http://164.214.2.59/GandG/tr8350.2


WGS 84Original 1591 Stations

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Refinement of WGS 84

• WGS 84 (G730) - from 29 June 1994

• WGS 84 (G873) - from 29 January 1997

• WGS 84 (G1150) - from January 2002

• WGS 84 (G1674) – from 8 February 2012

• 6 USAF & 11 NGA sites re-coordinated

• IGS stations fixed to ITRF08 coordinates

• Accuracy of coordinates better than 1 cm

• Station coordinates and velocities at epoch 2005.0

• WGS 84 is closely coincident with ITRF08 (cm level)

• Gravity field (EGM96)

Recent Updates to the WGS84 Reference FrameR. Wong, C. Rollins, 2012.Proc ION GNSS 2012, Nashvile, Tenessee, USA, September 2012.


International TerrestrialReference Frame

• ITRF - International Terrestrial Reference Frame–Coordinates of space geodetic stations

–SLR, VLBI, LLR, GPS, Doris

• Published regularly

• Realisation of ITRS–International Terrestrial Reference System

–International Earth Rotation Service (IERS)

• ITRF 2000–Realisation of ITRS based on coordinates from 1970-2000

–With an epoch of 1997.0

–Station coordinates and velocities

• ITRF 2005

• ITRF 2008 (from May 2010) NG

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ITRF 2000 Stations


ITRF 2005 Stations

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ITRF 2005 Velocity Field


Implications ofITRF Revision

• National mapping/surveying organisations don’t wantto have to revise maps because of plate tectonics!

• EUREF, IAG Subcomm for the Euro Reference Frame

–National mapping/surveying organisations in Europe agreed to‘freeze’ their reference station coordinates, provided forcontrol surveys, and their maps to a common frame thatrepresents where the European plate was on 1 January 1989and is fixed in time

–Gradual divergence between ETRS89 and ITRF/WGS84(presently ~35cm)

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European TerrestrialReference System & Frame

• ETRS89

–The ‘system’ adopted by EUREF, which is coincident with theITRS at the epoch 1989.0 and fixed to the stable part of theEurasian Plate

• ETRFyy

–The realisation of ETRS89 as the European subset of stationsfor an ITRFyy expressed in ETRS89 at epoch 1989.0

–first realisation was ETRF89 and the latest was ETRF2000.

–The only reference stations that have ETRFyy coordinates arethose that were part of the realisation of the associatedITRFyy,eg Herstmonceux SLR and GPS in the UK


Realisation of theETRS

• ETRS89

–Somewhat confusingly used to define the ‘frame’ realisedfrom a network of active stations,

–Coordinates are computed in the ITRFyy at the epoch ofobservation (through a connection to stations that are partof the ITRFyy realisation)

–Then transformed into ETRS89 at epoch 1989.0

–The EUREF GB 2001 solution was used to define thecurrent coordinates of the active stations in Great Britain

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Coordinate Transformationsand Geoid Models






Transformation Methods

• Direct conversion of X, Y Z–Three shifts of origin X, Y, Z

• Helmert Transformation–Three shifts of the origin X, Y, Z

–Three rotations about X, Y, Z

–Scale

• Molodensky Formulae–Direct conversion of latitude, longitude, height

–Three shifts of origin X, Y, Z

–Modifications for scale and Z-rotation

• Multiple Regression Formulae–Equations of variations of X, Y, Z or , , h

• Chart Margin Notes, Contour Charts, Shift Tables–Simple correction of , or N, E NG

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Examples ofTransformations

• OS GB 36 to WGS 84 (38 stations)

X = 375 m ± 10 a = 573.640 mY = -111 m ± 5 f = 0.11960023 x 10-4

Z = 431 m ± 8

• ED 50 to WGS 84 (85 stations)

X = -87 m ± 3 a = -251mY = -98 m ± 8 f = -0.14192702 x 10-4

Z = -121 m ± 5


European Datums

ED50ED50

ED50

ED50

OSGB 36

Ireland 75

DHDN

NTF/ED50

ED50

BD72

NGO48

RT90 KKJ

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Origin Shift

Z1

Z2

Y1

X1

Y2

X2

Z

XYX2 = X1 + X

Y2 = Y1 + Y

Z2 = Z1 + Z


Rotation of Axes

Z1

Z2

Y2

Y1

X1

X2

y

z

x X2 = X1 + z Y1 - y Z1

Y2 = Y1 - z X1 + x Z1

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Scale Change

Z1

Y1

X1

P1

P2

X2 = X1 + X1

Y2 = Y1 + Y1

Z2 = Z1 + Z1


Z

Y

X

Z

Y

X

Z

Y

X

xy

xz

yz

1

1

1

2

2

2

1

1

1

Helmert Transformation

• Small rotations

• 7 parameter transformation

• Conversion from and to lat, lon, ht byconventional formulae

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Molodensky Transformation

• What do you do if you only know latitude & longitude?

• Often we have no knowledge of height

• So cannot convert from latitude & longitude tocartesian X, Y, Z

• Molodensky formulae allow direct conversion fromlat/long in one system to lat/long in another

Latitude and Longitude

System 1

Latitude and Longitude

System 2

Origin ShiftsDX, DY, DZ


Molodensky Transformation

(http://www.nima.mil/GandG/pubs.html)

DX DY DZ

Da Df

NAD 27 – WGS 84

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Longitude differences (m) Latitude differences (m)

Regional VariationsBetween OSGB36 and WGS 84


OSGB36Grid Look-Up Tables

East Shift (m)1400000 99 104 1071050000 93 99 106700000 85 97 108350000 89 96 105

y(m)

0 92 96 1020 350000 700000

x (m)

National Grid Eastings - OSGRS80 Grid x

North Shift (m)1400000 -44 -49 -521050000 -47 -52 -54700000 -58 -62 -62350000 -75 -75 -78

y(m)

0 -82 -80 -820 350000 700000

x (m)

National Grid Northings - OSGRS80 Grid yNG

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Ordnance SurveyDefinitive Transformation

• Active Network now includes ~100 permanent stations

• 1 second interval RINEX data available free of charge

• Passive stations - over 3500 coordinated points

• New transformation OSTN02 : ETRS89 to OSGB36

• Definitive transformation of National Grid

• New geoid model OSGM02 : ETRS89 to ODN

–Corrector Surface

• Access to data via website–www.gps.gov.uk–www.ordnancesurvey.co.uk/oswebsite/gps/


OS Grid InQuest

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Summary

• WGS 84 adopted as de facto standard

• Many different national and international datums

• Map, chart and coordinates still based on old datums

• Transformation possible, if:–Datum of historical coordinates is known

–Transformation parameters are known

–Source data is reliable and accurate

• Implementation of WGS 84–Civil aviation

–Marine navigation

–National mapping?


Contact Details


Director of the NGI

Nottingham Geospatial Building


Triumph Road

Nottingham

NG7 2TU

Telephone: +44 (0) 115 951 3886

Fax: +44 (0) 115 951 3881

Email: [email protected]

WWW: www.nottingham.ac.uk/ngiNG

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Uni of Nottingham -Introduction to Geodesy -Dec2012