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# shape of the earth and GPS

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shape of the earth , datum , time zones , projections , gps , ...... for students

shape of the earth , datum , time zones , projections , gps , ...... for students

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• 1. An idea about Geodesy -GPSPvvss Dileep A and Srinivas R Nmotherindia.energy@gmail.comSchool of Gravity, Gravity Observatory-NGRI, India
• 2. Shape of the earth ZAn ellipse is defined by: Focal length = Distance (F1, P, F2) is constant for all points on ellipseWhen  = 0, ellipse = circle bFor the earth: aMajor axis, a = 6378 km O XMinor axis, b = 6357 km F1   F2Flattening ratio, f = (a-b)/a ~ 1/300Computed Solid Earth fromSatellite observations P View of Atmospheric Ear Z b a a O Y X
• 3. Earth shape …………Spheroid means original shape of solid earth surface……(general statement )Ellipsoid means geocentric rotational ,mathematical fit,equi-radial surface tothe original shape andGeoid means computed equi-gravitational surface extrapolation withgravity at mean sea level P…may coincide at coast z = zp • Land Surface z=0 Mean Sea level = Geoid Earth surface EllipsoidOcean Gravity Anomaly or Undulation Geoid
• 4. GeoidMean Sea Level is approximated as Geoid.But there is variation between Mean Sea Level and Geoid.It is called Sea Surface Topography (SST).MSL  Geoid  SST ( 1 to 2 metres)
• 5. Representation of a point: Ellipsoid (Horizontal),Geoid (Vertical) Sea surface Ellipsoid Datum(Horizontal Earth Datum) is defined by an ellipse and an axis of rotation Earth surface NAD27 (North American Datum of 1927) uses the Clarke (1866) ellipsoid on a non Geoid geocentric axis of rotation INDIA NAD83 (NAD,1983) uses the GRS80 ellipsoid on a geocentric axis of rotation CG WGS84 (World Geodetic System of 1984) uses GRS80, almost the same as NAD83Geoid Best Fitting Local ellipsoid and Geocentric Ellipsoid
• 6. Geocentric and Local Fits of Ellipsoid Zw P(X,Y,Z) (,,h) GeoidGlobally Fitting Ellipsoid Yw CGLocally BestFitting Ellipsoid Translations - x, y, z Xw Rotations - x, y, z Xe Scale - s
• 7. GLOBALLY ACCEPTED DATUMThe system which is truly universal is satellite based, as Global PositioningSystem (GPS) - Geo-centric Ellipsoid.LOCALLY ACCEPTED DATUMEverest is a Locally best fitting non geocentric ellipsoid. In India the horizco-ordinates are computed on the Everest Spheroid.Semi-major axis is having an error of 1 km. Origin of the co-ordinates hasbeen taken as Kalianpur.GPS use becomes easier as its co-ordinates are referred to in WGS -84 and updation ofmaps using Satellite Imageries like that from IRS, IKONOS, Quick Bird etc. becomeseasier as the satellite parameters are also referred to in geocentric reference frame.Open Series maps being published by SOI are based on WGS-84 ellipsoid on UTM projection.observations using satellite missions like Galileo, Glonass can also be made use of.all the guided missile systems, latest state-of-the-art weaponry are based on geocentricco-ordinate system, it becomes mandatory for us also to switch over to similarco-ordinate system.
• 8. METHODS TO REALISE GEOCENTRICCO-ORDINATESUsing Transformation ParametersRedefining and Transforming Horizontal DatumRe-observing in Entirely New co-ordinate System (ITRF)Using Transformation ParametersAlready available co-ordinates in Everest Spheroid can be transformed to WGS-84 byusing transformation parameters, already determined.These transformed co-ordinates will be suitable only for Mapping on small scale like1:25,000 or 1: 50,000 scales.Using this technique switching over to WGS-84 co-ordinate system can be completedby mid of year 2007.
• 9. Open Series Maps:Polyconic / Everest  UTM / WGS84Defence Series Maps:Polyconic / Everest  LCC / WGS84Types of Coordinate Systems:(1) Global Cartesian coordinates (x,y,z) for the whole earth(2) Geographic coordinates (f, l, z)(3) Projected coordinates (x, y, z) on a local area of the earth’s surfaceThe z-coordinate in (1) and (3) is defined geometrically; in (2) the z- coordinate is defined gravitationally
• 10. Global Cartesian Coordinates (x,y,z):Geographic Coordinates (, , z):Latitude () and Longitude () defined using an ellipsoid, an ellipse rotatedabout an axis ,elevation (z) defined using geoid, a surface of constantgravitational potential earth datums define standard values of the ellipsoidand geoid
• 11. Longitude , = the angle Latitude,  = the anglebetween a cutting plane on the between normal at a point S onprime meridian and the cutting the tangent plane of ellipsoidplane on the meridian through surface to the equatorial planethe point, PLength on a Meridian: Length on a Parallel:AB = Re  CD = R  = Re  Cos (same for all latitudes) (varies with latitude)
• 12. Example: What is the length of a 1º increment alongon a meridian and on a parallel at 30N, 90W?Radius of the earth = 6370 km.Solution:• A 1º angle has first to be converted to radiansp radians = 180 º, so 1º = p/180 = 3.1416/180 = 0.0175 radians• For the meridian, L = Re  = 6370 * 0.0175 = 111 km• For the parallel, L = Re  Cos  = 6370 * 0.0175 * Cos 30 = 96.5 km• Parallels converge as poles are approached
• 13. Projected Coordinates :Transformation of Three Dimensional Space onto a two dimensional mapA systematic arrangement of intersecting lines on a plane that represent and have a one to one correspondence to the meridians and parallels on the datum surface Projections Preserve Some Earth Classification: Properties: (Based on Extrinsic property) Area - correct earth surface area (Albers Nature: Equal Area) important for mass balances Plane, Cone, Cylinder Shape - local angles are shown correctly Coincidence: (Lambert Conformal Conic) Tangent, Secant, Polysuperficial Direction - all directions are shown correctly relative to the center (Lambert Position: Azimuthal Equal Area) Normal, Transverse, Oblique Distance - preserved along particular (Based on Intrinsic Property) lines Property of Projection: Some projections preserve two properties Equidistant Conformal or Orthomorphic Equivalent or Equal area Generation: Geometric, Semi Geometric, Mathematical
• 14. LCC PROJECTIONGNOMONIC PROJECTION REGULAR CYLINDRICAL PROJECTION: THE MERCATOR
• 15. For a conic projection, the projection surface is cone shaped Locations are projected onto the surface of the cone which is then unwrappedand laid flatLambert Conformal Conic Projection(LCC):Conical, Conformal ,Parallels are concentric arcsMeridians are straight lines cutting parallels at right angles.Scale is true along two standard parallels, normally, or along just one.It projects a great circle as a straight line – much better than MercatorUsed for maps of countries and regions with predominant east west expanseUsed for plane coordinate system (SPCS) in USAPoly conic projection (Pc):Three partial equidistant conic maps, eachbased on a different standard parallel, thereforewrapped on a different tangent cone (shown onthe right with a quarter removed plus tangencyparallels). When the number of cones increasesto infinity, each strip infinitesimally narrow, theresult is a continuous polyconic projection
• 16. Poly conic Projection(Pc):In this projection all parallels are projected without any distortionScale is exact along each parallel and central meridian.Parallels are arcs of circles but are not concentric.It is neither conformal nor equal area.Central meridian and equator are straight lines; all other meridians are curves.Central Meridian cuts all parallels at 90 degreesFree of distortion only along the central meridian.It has rolling fit with adjacent sheets in EW direction.Used in India for all topographical mapping on 1:250,000 and larger scales.
• 17. For an azimuthal,or planar projection, locations are projected forward onto a flat plane.The normal aspect for these projections is the North or South Pole.Universal Polar Stereographic (UPS):Defined above 84 degrees north latitude and 80 degree southConformal Meridians are straight linesParallels are circlesScale increases from center pointUsed in conformal mapping of polar regions
• 18. Cylindrical map projections are made by projecting from the globe onto the surface ofan enclosing cylinder, and then unwrapping the cylinder to make a flat surface. Mercator Transverse Mercator Cassini-SoldnerMercator Projection:Cylindrical, ConformalMeridians are equally spaced straight linesParallels are unequally spaced straight linesScale is true along the equatorGreat distortion of area in polar regionUsed for navigationTransverse Mercator Projection:Cylindrical (Transverse)ConformalCentral meridian and equator are straight linesOther meridians and parallels are complex curvesUsed extensively for quadrangle maps at scales from 1:24,000 to 1:250,000For areas with larger north-south extent than east- west extent
• 19. Cassini- Soldener Projection:Cylindrical, Tangent, Transverse EquidistantCylinder is tangent along the meridian centrally locatedScale deteriorates away from central meridianNormally used in 70 km belt from the central meridian, as linear distortion factor at 70 km is 1.00006Used for old cadastral surveys in India.False Northing and False Easting:Calculating coordinates is easier if negative number aren’t involved.State Plane and Universal transverse Mercator coordinatesExpressed in coordinate units, not degrees.
• 20. Universal Transverse Mercator:Particular case of Transverse Mercator Projection.The earth between latitudes 84 N and 80 S, is divided into 60, 6 wide;Latitude origin – the equatorAssumed (false) northing (y): 0 metres for northern hemisphere; 10,000,000 metres for southern hemisphereAssumed (false) easting (x): 500,000 metres; scale factor at the central meridian: 0.9996
• 21. State Plane Coordinates:Lambert Conformal Conic Projections are used for rectangular zones with a larger east-west than north south extent.Transverse Mercator projections are used to define zones with a larger north- south extent.One State Plane zone in Alaska uses an oblique Mercator projection.Projection Parameters:To define the coordinate system completely, it is not sufficient simply to name the kind of projection used, it is also necessary to specify the projection parameters.The set of parameters required depends on the kind of projection.The central meridian of the projection for cylindrical, where it touches the ellipsoid surface.The standard parallel(s) for conic projections.The false easting and false northingThe unitsReference ellipsoid
• 22. Choosing a map Projection:The choice of map projection is made to give the most accurate possible representation of the geographic information, given that some distortion is inevitable.The choice depends on:The locationShapeSize of the region to be mappedThe theme or purpose of the map
• 23. minimum four satellites are required to compute four unknown values –(Xo, Yo, Zo) and To (X2, Y2, Z2) (X3, Y3, Z3) Satellite in Space (X1, Y1, Z1) (X4, Y4, Z4) (,, h) (X0, Y0, Z0) Z P Earth’s Surface h rid ch Me e n w i ian Q Z e Spiral Helix Antennas Gr O X   Y GPS Antennas YX Choke Ring Antenna
• 24. GPS Accuracies & ConsiderationsGrades of Accuracy (Type-III)Recreational / Mapping grade 5-15 meter (1-5 meter with differential correction) (Type-II)Sub-meter Mapping grade 10 cm – 1 meter (Type-I)Survey grade 1 cm
• 25. Types of GPS instrumentsPrice of unit largely dependent upon grade Most Expensive \$20,000 - \$45,000 Mid-level Cheapest \$5,000-\$14,000 \$100- \$1000+ Recreational / Navigational Ex. Hiking, boating, automobiles Mapping Surveying (Type –III GPS receivers) Ex. GIS data Ex. Surveying, Collection, Cadastral, Mine Agriculture Surveying (Type-II GPS (Type-I GPS Receivers) receivers)
• 26. Factors Influencing GPS Accuracy : Ionospheric and atmospheric delays Satellite and Receiver Clock Errors Multipath Dilution of Precision Selective Availability (S/A) Anti Spoofing (A-S)
• 27. What is meant by a DOP ?DOP means Dilution of PrecisionIt is a number which indicates the satellite geometry at a particular epoch at a particular place whether good or bad.Lesser the DOP value better the accuracy Types of DOP’s GDOP – Geometric Dilution of Precision PDOP – Positional DOP HDOP – Horizontal DOP Poor PDOP – Satellites more closely assembled.
• 28. DOP without ObstructionDOP with Obstruction 11-09-2012 N.Srinivasa Rao 33
• 29. Field Observation Procedure & Planning: Techniques: Pre-field survey planning – MissionAbsolute Positioning or planning – Sky plot Single point Positioning technique Select time of observation when GDOP/PDOP is lessRelative positioning techniques Site selection – Free from obstructions- at least 15 degree clearance Construction of monuments (ifRelative positioning techniques required)Select starting and closing stations – GeodeticStatic positioning techniqueFast static or Rapid staticStop-and-go techniqueDifferential GPS techniqueRTKM (Real time Kinematic technique)Computations:Computation is based on – What type of coordinates are required by the usersWGS-84 – can be obtained directly after processing Local (Everest co-ordinates for India)–require transformation parameters orcomputation workLocal Grid or UTM Gird – can be obtained from the above two using mathematicalformulae / software package
• 30. Important applications of GPS:Navigation – aircraft, spacecraft, ship, vehicleControl surveysCadastral surveyingGeodynamicsMonitoring and Engineering ProblemsPrecise NavigationPhotogrammetry and Remote SensingMarine and Glacial Geology and many moreOther applications of GPS:Creation and maintenance of spatial data inventory ie. Provision of ground controlpoints (GCP’s) for subsequent ground / air survey / remote sensing methodUtilities, public facilities and other infrastructureEmergency Management , Dispatch, Road side assistance, search and rescueFleet (Transport) Management, Recourse ManagementWetland, Forests, waste land , Town Planning, Precision farming, Location basedservices
• 31. Military,Civil,Transportation,Aviation,Automobile,Maritime,Rail Control, Public ServicesTiming & FrequencySurveying,SurveillanceOther
• 32. Thank U