Geodesy, Map Projections and Coordinate Systems Geodesy - the shape of the earth and definition of earth datums Map Projection - the transformation of a curved earth to a flat map Coordinate systems - (x,y,z) coordinate systems for map data Instructor: Dr. Ayse Kilic Civil Engineering and School of Natural Resources University of Nebraska *Some of the slide material is adapted from from Dr. David Maidment of the University of Texas and Dr. David Tarboton of Utah State University

Learning Objectives: By the end of this class you should be able to: Describe the role of geodesy as a basis for earth datums List the basic types of map projection Identify the properties of common map projections Properly use the terminology of common coordinate systems Use spatial references in arcmap so that geographic data are properly displayed Determine the spatial reference system associated with a feature class or data frame Use arcgis to convert between coordinate systems Calculate distances on a spherical earth and in a projected coordinate system

Memorial Stadium 40° 49’ 14.25” N 96° 42’ 20.34”W Z 47 E 306516.77 N 4521566.08 NE S E 2773253.915 N 432764.266 You are all familiar with memorial stadium. Focusing on the “N” in the center of memorial stadium, here are a bunch of numbers. Focusing on the “N” in the center of memorial stadium, here are a bunch of numbers. Survey question: What are these numbers?

Memorial Stadium Global Coordinate System (Latitude/Longitude) 40° 49’ 14.25” N 96° 42’ 20.34”W Z 47 E 306516.77 N 4521566.08 NE S E 2773253.915 N 432764.266 Universal Transverse Mercator (UTM) State Plane Coordinate System (SPCS) Nebraska South Here are three different coordinate systems. They all describe the location of the “N”. We are going to talk some about all three of these. Who has never heard latitude and longitude? Those are used to determine location. They are other systems for specifying the location. UTM is one of the most commonly used one/ Each set of numbers represent the location of the “N” in Memorial Stadium (Note that the SPCS NE South is not in use anymore. Now there is one zone for NE.) They are three separate, but related, coordinate systems They all point to the same place. But they have different references We’re going to talk about what those numbers mean and what they do for us They all point to the same place, but they have different references We’re going to talk about what those numbers mean and what they do for us

Readings: Introduction http://resources.arcgis.com/en/help/getting-started/articles/026n0000000s000000.htm Arc software has documentation that describe the coordinate system and georeferncing. I strongly encourage you to read these materials.

Readings: Further Detail http://resources.arcgis.com/en/help/main/10.2/index.html#//003r00000001000000 Note that this graphic gives us a preview of how we use gis to store many different layers of information.

History on maps Medieval Maps Ancient “Globe” Ptolemaic world 150 AD (1493 depiction) Ancient “Globe” Sun and stars rotating about “Island Earth” The oldest known maps are preserved on Babylonian Clay Tablets from about 600 B.C. Mercator’s Map-1569 AD Cylindrical projection – putting a round globe onto a piece of paper with meaningful accuracy In use for thousands of years, humans have wanted to have good maps for a long and long time. They speculated the shape and size of the Earth. Ancient concept of a representation of the Earth Sun and stars rotating about “Island Earth” Babylonian Clay Tablet form 600 BC – depicts Babylon and the cities around it Greek worldview in 300 BC 150 BC – Hipparchus of Rhodes invented the concept of Latitude and Longitude – Gridded circular measures Ptolemaic world in 150 AD – Roman citizen in Egypt – wrote in Greek – Used Lat/Long for his maps No map survived, but this 1493 depiction was based on his writings. Viking explorations in the North Atlantic gradually were incorporated into the world view beginning in the 12th century Mercator’s map – 1569 – Cylindrical projection – putting a round globe onto a piece of paper with meaningful accuracy So why do we care???? Navigation Real Estate Ownership Government Jurisdiction Zoning! Greek world view 300 BC 150 BC – Hipparchus of Rhodes invented the concept of Lat/Long

Revolution in Earth Measurement Some images and slides from Michael Dennis, National Geodetic Survey and Lewis Lapine, South Carolina Geodetic Survey Traditional surveying is at least 3000 years old Used by the ancient Egyptians to mark out fields after the annual Nile floods Refined by the ancient Greek and Romans Today our knowledge of shape of the earth is very advanced Uses benchmarks as reference points These benchmarks actually tie down the coordinates. Today our knowledge of shape of the earth is very advanced. The features of the earth are documented using benchmarks. These benchmarks actually tie down the coordinates. Benchmarks are buried in the rock (deep shaft in the soil), so they don’t move. Fixed location USGS has national responsibility for developing maps and survey benchmarks. Global Positioning uses fixed GPS receivers as reference points (Continuously Operating Reference System, CORS)

How accurate can we know a location? (and is it static?) If we really want to know the location very accurately, we have to appreciate every point on the earth is moving because of tectonic plates.

Tectonic Motions This has to take Tectonic Motions into account If we really want to know the location very accurately, we have to appreciate every point on the earth is moving because of tectonic plates. (These plates separate from each other and this is All the letters are names of major plates. For instance, Nu is Africa. The arrows show the direction that different continents are moving The length of arrow shows the speed of the plate/continent. You can see that North America is moving west. Australia is moving to North East. i.e. Earth is like a big egg shell with big cracks on it. You get the earthquake when you get two plates pushing against each other, and all of the sudden slipping. Pressure on a plate cause a buckle to create the mountains. When tectonic plates move, our benchmark locations change 30mm/yr equals 3 meters in 100 years From Sella et al., 2002

HORIZONTAL TECTONIC MOTIONS Motion in cm/year North American Plate North American plate is rotating and moving towards south west. Pacific plate is moving to the North West. They are colliding/sliding. A lot of California is moving to west 5 cm/years. Pacific Plate When is California not in North America … …. when its on the Pacific Plate!

This leads to adjustments in locations of the national network of survey benchmarks {Latitude (f), Longitude (l), Elevation (z)}

In 2011, US redefined its benchmark coordinates and used 79,000 stations. They used CORS (Continuously operating Receiving stations…) stations to make adjustments on passive benchmark stations. CORS is adjusted using GPS.

Types of Coordinate Systems (1) Global Cartesian coordinates (x,y,z) for the whole earth (2) Geographic coordinates Latitude (f), Longitude (l), Elevation (z) (3) Projected coordinates (x, y, z) on a local area of the earth’s surface The z-coordinate in (1) and (3) is defined geometrically; in (2) the z-coordinate is defined gravitationally

1. Global Cartesian Coordinates (x,y,z) Greenwich Meridian Equator • This is one way to describe your coordinate system, but it is convenient because the origin is in the middle of the earth. Cartesian system is a strict x, y, z system where the origin is at the center of the earth. The x, y plane is parallel to the equator. How far am I this way (x, y)?

Spatial Reference = Datum + Projection + Coordinate system For consistent analysis the spatial reference of data sets should be the same. ArcGIS does projection on the fly so it can display data with different spatial references properly if they are properly specified. (but it is “safest” if all layers are in the same projection) Earth datums define standard values of the ellipsoid and geoid Different datums use different estimates for the precise shape and size of the Earth (reference ellipsoids). ArcGIS terminology Define projection. Specify the projection for some data without changing the data. Project. Change the data from one projection to another. It would be good to take timeshare to define datum and projection.

2. Geographic Coordinates (f, l, z) Latitude (f) and Longitude (l) defined using an ellipsoid, an ellipse rotated about an axis Elevation (z) defined using geoid, a surface of constant gravitational potential Earth datums define standard values of the ellipsoid and geoid

GEOID Geoid is mean sea level at a particular point and varies with gravitational potential Geoid is where mean sea level would be if there was an ocean at that location Geoid elevation is usually below the land surface The geoid is the shape that the surface of the oceans would take under the influence of Earth's gravitation and rotation alone, in the absence of other influences such as winds and tides. All points on the geoid have the same gravitational potential. The force of gravity acts everywhere perpendicular to the geoid, meaning that plumb lines point perpendicular and water levels parallel to the geoid.

Shape of the Earth It is actually a spheroid, slightly larger in radius at the equator than at the poles We think of the earth as a sphere The shape of the Earth approximates an oblate spheroid, a sphere flattened along the axis from pole to pole such that there is a bulge around the equator.[57] This bulge results from the rotation of the Earth, and causes the diameter at the equator to be 43 km(kilometer) larger than the pole-to-pole diameter.[58] For this reason the furthest point on the surface from the Earth's center of mass is the Chimborazo volcano in Ecuador.[59] The average diameter of the reference spheroid is about 12742 km, which is approximately 40,000 km/π, as the meter was originally defined as 1/10,000,000 of the distance from the equator to the North Pole through Paris, France.[60] The earth is not round!

Ellipse Z b O a X  F1  F2 P An ellipse is defined by: Focal length =  Distance (F1, P, F2) is constant for all points on ellipse When  = 0, ellipse = circle Z b O a X F1   F2 For the earth: Major axis, a = 6378 km Minor axis, b = 6357 km Flattening ratio, f = (a-b)/a ~ 1/300 If a and b are the same, it will be a circle. When a not equal b, it is an ellipse. An ellipse is a 2 dimensional. A P

Ellipsoid or Spheroid Rotate an ellipse around an axis Z An Ellipse is 2 dimensional A Spheroid is 3 dimensional b O a a Y X 1. Origin of x,yz, is at the center of the earth. 2. So everyone agreed that z axis should exit the earth (go up through) at the North Pole 3. Because English were in control of navigation definitions at the time, they got to say where “zero” longitude is (Greenwich Meridian) 4. So by definition, the x axis exits the earth at Greenwich meridian. 5. Because y axis has to be perpendicular to x and z, then it also exits the earth at the equator as does x. The X, Y, and Z axes are at 90 degree angles to each other Rotational axis

Standard Ellipsoids Ref: Snyder, Map Projections, A working manual, USGS Professional Paper 1395, p.12

Geodetic Datums World Geodetic System (WGS) – is a global system for defining latitude (f) and longitude (l) on earth and does not change even with tectonic movement (military).Therefore, latitude and longitude coordinates of a point in Lincoln will change with time if Lincoln moves. North American Datum (NAD) – is a system defined for locating fixed objects on the earth’s surface and includes tectonic movement (civilian) (Everything is moving). Therefore, latitude and longitude coordinates of a point in Lincoln will not change with time if Lincoln moves. Lincoln (40.8106° N, 96.6803° W)

Horizontal Earth Datums An earth datum is defined by an ellipse and an axis of rotation NAD27 (North American Datum of 1927) uses the Clarke (1866) ellipsoid on a non geocentric axis of rotation NAD83 (NAD,1983) uses the GRS80 ellipsoid on a geocentric axis of rotation WGS84 (World Geodetic System of 1984) uses GRS80, almost the same as NAD83

Adjustments of the NAD83 Datum Slightly different (f, l) for benchmarks Continuously Operating Reference System Canadian Spatial Reference System National Spatial Reference System High Accuracy Reference Network

Representations of the Earth Mean Sea Level is a surface of constant gravitational potential called the Geoid Earth surface Ellipsoid Sea surface Geoid The earth is not a perfectly smooth ellipsoid. It has (mountains) and deep oceans, and bulges. Here are the

THE GEOID AND TWO ELLIPSOIDS CLARKE 1866 (NAD27) GRS80-WGS84 (NAD83) Earth Mass Center Approximately 236 meters GEOID

WGS 84 and NAD 83 North American Datum of 1983 (NAD 83) (Civilian Datum of US) International Terrestrial Reference Frame (ITRF) includes updates to WGS-84 (~ 2 cm) Earth Mass Center 2.2 m (3-D) dX,dY,dZ World Geodetic System of 1984 (WGS 84) is reference frame for Global Positioning Systems GEOID

Latitude (f) & Longitude (l)

Strict definition of Latitude, f m S p n O f q r (1) Take a point S on the surface of the ellipsoid and define there the tangent plane, mn (2) Define the line pq through S and normal to the tangent plane (3) Angle pqr which this line makes with the equatorial plane is the latitude f, of point S

Cutting Plane of a Meridian Equator plane Prime Meridian

Definition of Longitude, l l = the angle between a cutting plane on the prime meridian and the cutting plane on the meridian through the point, P 180°E, W -150° 150° -120° 120° 90°W (-90 °) 90°E (+90 °) -60° P l -60° -30° 30° 0°E, W

Latitude and Longitude on a Sphere Z Meridian of longitude Greenwich meridian N Parallel of latitude =0° P • =0-90°N  - Geographic longitude  - Geographic latitude  W O E • Y  R R - Mean earth radius • =0-180°W Equator =0° •  O - Geocenter =0-180°E X =0-90°S

Length on Meridians and Parallels (Lat, Long) = (f, l) Length on a Meridian: AB = Re Df (same for all latitudes) R Dl 30 N R D C Re Df B 0 N Re Length on a Parallel: CD = R Dl = Re Dl Cos f (varies with latitude) A Meridians converge as poles are approached

Example: What is the length of a 1º increment along on 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 radians 2p radians = 360 º, so 1º = 2p/360 = 2*3.1416/360 = 0.0175 radians For the meridian, DL = Re Df = 6370 * 0.0175 = 111 km For the parallel, DL = Re Dl Cos f = 6370 * 0.0175 * Cos 30 = 96.5 km Meridians converge as poles are approached

Curved Earth Distance (from A to B) Shortest distance is along a “Great Circle” A “Great Circle” is the intersection of a sphere with a plane going through its center. 1. Spherical coordinates converted to Cartesian coordinates. 2. Vector dot product used to calculate angle  from latitude and longitude 3. Great circle distance is R, where R=6378.137 km2 X Z Y •  A B Ref: Meyer, T.H. (2010), Introduction to Geometrical and Physical Geodesy, ESRI Press, Redlands, p. 108

Definition of Elevation Elevation Z P z = zp • z = 0 Land Surface Mean Sea level = Geoid Elevation is measured from the Geoid

Three systems for measuring elevation What reference system (datum) is used? Earth surface Ellipsoid Sea surface Geoid Geoid is mean sea level at a particular point and varies with gravitational potential. Effective seas surface at any particular location. It is a smooth surface. However, the earth surface Includes mountains and Ellipsoidal heights: You see a mountain ; how tall is the mountain? How tall is it relative to sea level, or relative to a smooth equation? 3000 ft above ellipsoidal Orthometric heights (land surveys, geoid) Ellipsoidal heights (lidar, GPS) Tidal heights (Sea water level) Geoid is mean sea level at a particular point and varies with gravitational potential

Three systems for measuring elevation Orthometric heights (land surveys, geoid) Ellipsoidal heights (lidar, GPS) Tidal heights (Sea water level) Conversion among these height systems has some uncertainty

Trends in Tide Levels (coastal flood risk is changing) Charleston, SC + 1.08 ft/century 1900 2000 Galveston, TX It is difficult to base elevation on sea level because sea level continuously changing at some places. + 2.13 ft/century - 4.16 ft/century 1900 2000 Juneau, AK 1900 2000

Gravity Anomaly Gravity Anomaly Earth surface Ellipsoid Ocean Geoid Gravity Anomaly Gravity anomaly is the elevation difference between a standard shape of the earth (ellipsoid) and a surface of constant gravitational potential (geoid)

Vertical Earth Datums A vertical datum defines elevation, z NGVD29 (National Geodetic Vertical Datum of 1929) NAVD88 (North American Vertical Datum of 1988) takes into account a map of gravity anomalies between the ellipsoid and the geoid

Converting Vertical Datums Corps program Corpscon (not in ArcInfo) http://crunch.tec.army.mil/software/corpscon/corpscon.html Point file attributed with the elevation difference between NGVD 29 and NAVD 88 NGVD 29 terrain + adjustment = NAVD 88 terrain elevation

Importance of geodetic datums NAVD88 – NGVD29 (cm) NGVD29 higher in East More than 1 meter difference NAVD88 higher in West Orthometric datum height shifts are significant relative to BFE accuracy, so standardization on NAVD88 is justified

Geodesy and Map Projections Geodesy - the shape of the earth and definition of earth datums Map Projection - the transformation of a curved earth to a flat map Coordinate systems - (x,y) coordinate systems for map data

Earth to Globe to Map Map Projection: Map Scale: Scale Factor To prepare a map, the earth is first reduced to a globe and then projected onto a flat surface Map Projection: Scale Factor at Central Meridian This is the ratio of map scale along the central meridian and the scale at a standard meridian, where scale distortion is zero. The scale factor at the central meridian is .9996 in each of the 60 UTM coordinate system zones, since each contains two standard lines 180 kilometers west and east of the central meridian. Scale distortion increases with distance from standard lines in all projected coordinate systems. Map Scale: Scale Factor Representative Fraction Globe distance Earth distance = Map distance Globe distance = (e.g. 0.9996) (e.g. 1:24,000)

Geographic and Projected Coordinates Map projection means how we go from the ‘true’ global (spheroid) system to a ‘flat’ X-Y system. There are many, many map projection systems. (f, l) (x, y) Map Projection Map projection is how we go from the ‘true’ global (spheroid) system to a ‘flat’ X-Y system. There are many, many map projection systems.

How do we make Maps? -- Types of Projections -- Conic (Albers Equal Area, Lambert Conformal Conic) - good for East-West land areas Cylindrical (Transverse Mercator) - good for North-South land areas Azimuthal (Lambert Azimuthal Equal Area) - good for global views These projection techniques are how we create the ‘flat’ map from the globe

Projections Preserve Some Earth Properties (but not all at once) Area - correct earth surface area (Albers Equal Area) important for mass balances Shape - local angles are shown correctly (Lambert Conformal Conic) Direction - all directions are shown correctly relative to the center (Lambert Azimuthal Equal Area) Distance - preserved along particular lines Some projections preserve two properties

Conic Projections (Albers Equal Area, Lambert Conformal Conic) In the Secant method, a Cone is placed over the globe but cuts through the surface. The cone and globe meet along two latitude lines. These are the standard parallels. The cone is cut along the line of longitude that is opposite the central meridian and flattened into a plane. Fits a cone over the sphere of the Earth and projects the surface conformally onto the cone The cone is unrolled, and the parallels that was touching the sphere is assigned unit scale That parallel is called the reference parallel or standard parallel.

Conic Projections A cone is placed over a globe. The cone and globe meet along a latitude line. This is the standard parallel. This is where the accuracy is highest (perfect). In other latitudes, the accuracy is less. The cone is cut along the line of longitude that is opposite the central meridian and flattened into a plane. A cone is placed over a globe but cuts through the surface. The cone and globe meet along two latitude lines. These are the standard parallels. The cone is cut along the line of longitude that is opposite the central meridian and flattened into a plane.

Cylindrical Projections (Transverse Mercator) Oblique  Projecting the sphere onto a cylinder tangent

Cylindrical Projections (Transverse Mercator) Wherever the cylinder touches the globe, the highest the accuracy. Other areas get some distortion.

Azimuthal (Lambert) A plane is placed over a globe. The plane can touch the globe at the pole (polar case), the equator (equatorial case), or another line (oblique case). All azimuthal projections preserve the azimuth (angle) from a reference point Presenting true direction (but not necessarily distance) to any other points. Also called planar since several of them are obtained straightforwardly by direct perspective projection to a plane surface. Taking a plane and pressing against the earth. Where it touches is called reference point. All other points are accurate for direction from reference point. However, distances may not be accurate. Use this method if accuracy in ‘direction’ is more important than accuracy in ‘distance.’

Albers Equal Area Conic Projection -- there are different styles of conic projections Albers Equal Area Conic Projection Conic projection that maintains accurate area measurements. It differs from the Lambert Conformal Conic projection in preserving area rather than shape and in representing both poles as arcs rather than one pole as a single point The meridians do not converge at the poles Uses two standard parallels, or secant lines Distances are most accurate in the middle latitudes.

Lambert Conformal Conic Projection Portrays shape more accurately than area The State Plane Coordinate System uses this projection for all zones that have a greater east–west extent Represents the poles as a single point

Universal Transverse Mercator Projection (more on UTM later) Universal Transverse Mercator Projection Uses a 2-dimensional Cartesian coordinate system to give locations on the surface of the Earth It is a horizontal position representation Divides the Earth into sixty zones, each a six-degree band of longitude, and uses a secant  in each zone This projection is conformal, so it preserves angles and approximates shape but distorts distance and area Each of the 60 zones uses a TM projection that can map a region of large north-south extent with low distortion UTM is a VERY important and widely used Projection

Lambert Azimuthal Equal Area Projection

Web Mercator Projection (used for ESRI Basemaps) Web Mercator is one of the most popular coordinate systems used in web applications because it fits the entire globe into a square area that can be covered by 256 by 256 pixel tiles. The spatial reference for the ArcGIS Online / Google Maps / Bing Maps tiling scheme is WGS 1984 Web Mercator (Auxiliary Sphere). Web Mercator Projection is also used by Google Maps

Web Mercator Parameters Central Meridian Standard Parallel (0,0) (20037, 19971 km) Distance from origin = earth rad * π 6378 km 6357 km Earth radius

Projection and Datum Two datasets can differ in both the projection and the datum, so it is important to know both for every dataset.

Geodesy and Map Projections Geodesy - the shape of the earth and definition of earth datums Map Projection - the transformation of a curved earth to a flat map Coordinate systems - (x,y) coordinate systems for map data

3. Coordinate Systems Universal Transverse Mercator (UTM) - a global system developed by the US Military Services State Plane Coordinate System - civilian system for defining legal boundaries

3. Coordinate System A planar coordinate system is defined by a pair of orthogonal (x,y) axes drawn through an origin Y X Origin (xo,yo) (fo,lo) The origin can be wherever the user wishes. However, there are standard locations.

Universal Transverse Mercator Uses the Transverse Mercator projection Each zone has a Central Meridian (lo), zones are 6° wide, and go from pole to pole 60 zones cover the earth from East to West Reference Latitude (fo), is the equator (Xshift, Yshift) = (xo,yo) = (500000, 0) in the Northern Hemisphere, units are meters

UTM Zone 14 -99° -102° -96° 6° Origin Equator -120° -90 ° -60 ° Zone 14 runs through Nebraska.

State Plane Coordinate System Defined for each State in the United States East-West States (e.g. Texas) use Lambert Conformal Conic, North-South States (e.g. California) use Transverse Mercator Nebraska has one zone, and Texas has five zones (North, North Central, Central, South Central, South) to give accurate representation Greatest accuracy for local measurements Note the different systems used by states to develop the coordinates!!!

ArcGIS Spatial Reference Frames Defined for a feature dataset in ArcCatalog XY Coordinate System Projected Geographic Z Coordinate system Domain, resolution and tolerance

Horizontal Coordinate Systems Geographic coordinates (decimal degrees) Projected coordinates (length units, ft or meters) There are many, many coordinate systems available in Arc!

Vertical Coordinate Systems None for 2D data Necessary for 3D data

ArcGIS .prj files The ‘prj’ file is used by Arc to hold information on the specific projection

Summary Concepts The spatial reference of a dataset comprises datum, projection and coordinate system. For consistent analysis the spatial reference of data sets should be the same. ArcGIS does projection on the fly so can display data with different spatial references properly if they are properly specified (but it is best to project layers to the same basis to check accuracy of overlapping). ArcGIS terminology Define projection. Specify the projection for some data without changing the data. Project. Change the data from one projection to another.

Summary Concepts (Cont.) Two basic locational systems: geometric or Cartesian (x, y, z) and geographic or gravitational (f, l, z) Mean sea level surface or geoid is approximated by an ellipsoid to define an earth datum which gives (f, l) and distance above geoid gives (z)

Summary Concepts (Cont.) To prepare a map, the earth is first reduced to a globe and then projected onto a flat surface Three basic types of map projections: conic, cylindrical and azimuthal A particular projection is defined by a datum, a projection type and a set of projection parameters

Summary Concepts (Cont.) Standard coordinate systems use particular projections over zones of the earth’s surface Types of standard coordinate systems: UTM, State Plane Web Mercator coordinate system (WGS84 datum) is standard for ArcGIS basemaps

Global Positioning Systems (Press and hold) You guys probably all have GPS these days. You probably have one in your car, one in your cell phone. Garmin GPSMAP 276C GPS Receiver Trimble GeoXHTM

GPS Satellites GLONASS NAVSTAR  Satellite-based navigation system originally developed for military purposes (NAVSTAR1 -1978). NAVSTAR Global Positioning System (GPS) Globally available since 1994 Maintained and controlled by the United States Department of Defense ( 50th Space Wing (50 SW)) There are two GPS systems: NAVSTAR - United State's system, and GLONASS - the Russian version GPS permits users to determine their three-dimensional position, velocity, and time. Landsat 90 minute orbit GLONASS A satellite navigation or sat nav system is a system of satellites that provide autonomous geo-spatial positioning with global coverage. It allows small electronic receivers to determine their location (longitude, latitude, and altitude) to high precision (within a few metres) using time signals transmitted along a line of sight by radio from satellites bits in less than 24 hours NAVSTAR

Constellation Arrangement GPS satellites fly in Medium Earth orbit (MEO) at an altitude of approximately 20,200 km (12,550 miles). Each satellite circles the Earth twice a day. 12 hour return interval for each satellite GPS uses radio transmissions. The satellites transmit timing information and satellite location information.  The United States is committed to maintaining the availability of at least 24 operational GPS satellites, 95% of the time. To ensure this commitment, the Air Force has been flying 31 operational GPS satellites for the past few years. Satellites are distributed among six offset orbital planes

How GPS works in five logical steps: The basis of GPS is triangulation from satellites GPS receiver measures distance from satellite using the travel time of radio signals To measure travel time, GPS needs very accurate timing Along with distance, you need to know exactly where the satellites are in space. Satellite location. High orbits and careful monitoring are the secret You must correct for any delays the signal experiences as it travels through the atmosphere Here's how GPS works in five logical steps: 1. The basis of GPS is "triangulation" from satellites. 2. To "triangulate," a GPS receiver measures distance using the travel time of radio signals. 3. To measure travel time, GPS needs very accurate timing which it achieves with some tricks. 4. Along with distance, you need to know exactly where the satellites are in space. High orbits and careful monitoring are the secret. 5. Finally you must correct for any delays the signal experiences as it travels through the atmosphere.

Distance from satellite Radio waves = speed of light Receivers have nanosecond accuracy (0.000000001 second) All satellites transmit same signal “string” at same time Difference in time from satellite to time received gives distance from satellite Speed of light - -approximate values kilometres per second 300,000 kilometres per hour 1,080 million miles per second 186,000 miles per hour 671 million Lets assume all satellite send a signal “Go Big Red” at the same time. Since each satellite is on a different location in the sky, we receive the signals at different times. In a sense, the whole thing boils down to those "velocity times travel time" math problems we did in high school. Remember the old: "If a car goes 60 miles per hour for two hours, how far does it travel?" Velocity (60 mph) x Time (2 hours) = Distance (120 miles) In the case of GPS we're measuring a radio signal so the velocity is going to be the speed of light or roughly 186,000 miles per second. The problem is measuring the travel time.

Triangulation Suppose we measure our distance from a satellite and find it to be 11,000 miles. Knowing that we're 11,000 miles from a particular satellite narrows down all the possible locations we could be in the whole universe to the surface of a sphere that is centered on this satellite and has a radius of 11,000 miles. Next, say we measure our distance to a second satellite and find out that it's 12,000 miles away. That tells us that we're not only on the first sphere but we're also on a sphere that's 12,000 miles from the second satellite. Or in other words, we're somewhere on the circle where these two spheres intersect.

Triangulation If we then make a measurement from a third satellite and find that we're 13,000 miles from that one, that narrows our position down even further, to the two points where the 13,000 mile sphere cuts through the circle that's the intersection of the first two spheres. So by ranging from three satellites we can narrow our position to just two points in space. To decide which one is our true location we could make a fourth measurement. But usually one of the two points is a ridiculous answer (either too far from Earth or moving at an impossible velocity) and can be rejected without a measurement. A fourth measurement does come in very handy for another reason however, but we'll tell you about that later

Differential GPS Differential GPS uses the time sequence of observed errors at fixed locations to adjust simultaneous measurements at mobile receivers A location measurement accurate to 1 cm horizontally and 2cm vertically is now possible in 3 minutes with a mobile receiver More accurate measurements if the instrument is left in place longer