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## PowerPoint Slideshow about 'The Global Positioning System' - PamelaLan

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### The Global Positioning System

### Geographic Datums & Coordinates

GEO 420K, UT Austin

GPS Facts of Note

- DoD navigation system
- First launch on 22 Feb 1978
- 24 (+/-) Earth-orbiting satellites (SVs)
- 21 primary, 3 spares
- Altitude of 20,200 km
- In 6 orbital planes inclined 55o to equator, spaced 60o apart
- Orbital period of 12 hrs – not geostationary
- 5 to 8 SVs visible at all times anywhere in the world

GEO 420K, UT Austin

GPS Segments

- Space – Satellites (SVs).
- Control – Ground stations track SV orbits and monitor clocks, then update this info. (ephemeris, clock corrections) for each SV, to be broadcast to users (“almanac”). Control Facility at Schriever Air Force Base, CO.
- User – GPS receivers convert SV signals into position, velocity and time estimates.

GEO 420K, UT Austin

Ranging Techniques

- Two-way ranging: “Active”
- Electronic Dist. Measuring devices (EDMs)
- Radar, Sonar, Lidar
- One-way ranging: “Passive”
- GPS

GEO 420K, UT Austin

Ranging techniques

Range

- Two-way ranging (EDM)

reflector

Light beam

Range = C x DTime/2

GEO 420K, UT Austin

Ranging techniques

“Sphere of position”

Range

Radio Signal

- One-way ranging with GPS

Range = C x DTime

1 microsecond error = ~ 300 meters1 nanosecond error = ~ 1 foot

GEO 420K, UT Austin

3-D (X, Y, Z) One-way Ranging

- “Trilateration” (~Triangulation)
- Intersection of 2 spheres of position yields a circle of location
- Intersection of 3 spheres of position yields 2 points of location
- One point is position, other is either in space or within earth’s interior
- With earth ellipsoid (4th sphere)
- Get receiver clock synchronized and X & Y but no Z
- Intersection of 4 spheres of position yields XYZ location and clock synchronization

GEO 420K, UT Austin

3-D (X, Y, Z) One-way Ranging

- Intersection of 3 spheres of position yields 2 points of location; earth is 4th sphere, yielding 1 point.

Figures from: www.math.tamu.edu/~dallen/physics/gps/gps.htm

GEO 420K, UT Austin

Determine Position by:

1) Downloading almanac (ephemeris info., SV health, etc.)

2) Synchronize receiver clock/measure DT to 4 satellites = pseudorange

3) Account for error sources (see below) by modeling = range

4) Calculating intersection and compute X, Y, Z w.r.t. to center of selected reference ellipsoid

5) Converting to coordinates of interest

GEO 420K, UT Austin

How is DT measured?

- By using broadcast signals (“codes”)
- Code solutions
- Less precise, easiest to achieve

OR

- By using carrier cycles
- Carrier-phase solutions
- More precise, more difficult to achieve

GEO 420K, UT Austin

Broadcast Signals - Codes

+1

-1

- Coarse acquisition (C/A) code
- Civilian access, least accurate;

- Each SV broadcasts unique C/A code
- 1023 bits/millisecond, binary, pseudorandom
- Receiver generates same codes
- Precise or protected (P) code
- Authorized users only, more accurate (5-10 m absolute)
- Code requires algorithm “seed” that is classified
- P code for each satellite reset weekly
- Y code
- Military use only
- Code algorithm is encrypted
- Status message – satellite health, status and orbit info

GEO 420K, UT Austin

Signal “Carrier”

l

- Radio waves with following characteristics:
- L1: frequency = ~1575 MHz with l = 19 cm
- Carries C/A code and status message, modulated at 1 MHz
- Carries P code modulated at 10 MHz
- L2: frequency = ~1228 MHz with l = 24 cm
- Carries P code
- Fundamental precision in positioning limited by ability to determine phase of carrier (to ~ 0.01l = 1 or 2 mm)

GEO 420K, UT Austin

DT Code solutions

Code generated by SV

+1

-1

DT

+1

Code generated by receiver

-1

- Compare offsets in satellite and receiver codes to arrive at DT

Pseudorange = C x DT

GEO 420K, UT Austin

Sources of Error

Satellite Orbit Errors (~2.5 m)

SV clock error (~1.5 m)+/- Selective Availability (~30 m)

L2

50 km

L1

200 km

+ GDOP (errors x 4-6)

(Geometric dilution of precision)

Ionospheric Refraction (~ 5 m)(Can correct with L1 & L2 DTs)

Tropospheric Delay (~ 0.5 m)

Multipathing (~0.5 m)

GEO 420K, UT Austin

Summary of Error Sources (m)

GEO 420K, UT Austin

Differential GPS (DGPS)

- Requires two receivers
- One receiver (base) is established at known position
- Second receiver (rover) occupies unknown position(s)
- Common errors are eliminated by combining data from both receivers
- Most accurate results from use of carrier (L1, L2) phase DGPS (<cm)

GEO 420K, UT Austin

Differential GPS Positioning

Base: known position

Rover: unknown position

Base station pseudoranges compared to known position; differences are errors common to both receivers.

Base computes pseudorange corrections for rover.

Apply corrections and solve for position of rover.

GEO 420K, UT Austin

Base station DGPS data available from:

- On-site base station data combined with rover data
- Real-time, via telemetry
- Post-processing
- “Beacon” antenna to receive broadcast corrections in real-time
- US Coast GuardWAAS
- Commercial Services
- Remote base station data combined with rover data during post-processing
- CORS

GEO 420K, UT Austin

GPS & DGPS code solution precisions

- Selective availability on:
- Single receiver GPS precision ~ 100 meters
- DGPS precision with very short baseline ~ 1 – 4 meters
- Selective availability off (after May 02, 2000):
- Single receiver precision see here

GEO 420K, UT Austin

Signal “Carrier”

l

- Radio waves with following characteristics:
- L1: frequency = ~1575 MHz with l = 19 cm
- Carries C/A code and status message, modulated at 1 MHz
- Carries P code modulated at 10 MHz
- L2: frequency = ~1228 MHz with l = 24 cm
- Carries P code
- Fundamental precision in positioning limited by ability to determine phase of carrier (to ~ 0.01l = 1 or 2 mm)

GEO 420K, UT Austin

DGPS Carrier-Phase Solutions

- Use 19 cm wave as ruler to measure # of cycles (& phase of cycle) from each satellite
- Ruler is not labeled; track phase from several SVs and find intersection(s) of coincident phases.
- Know approx. position of antenna from code-phase DGPS; eliminates ambiguity.
- Passage of waves and motion of SVs need to be known
- Cycle Slips

Sub-centimeter precision possible

GEO 420K, UT Austin

Types of Carrier-phase solutions

- Static: “Rover” is stationary and collects data for several hours
- Rapid Static: Rover is stationary and collects for 5-20 minutes
- Kinematic: Rover collects on the move

GEO 420K, UT Austin

Accuracy of Code vs. Phase Solutions

GEO 420K, UT Austin

GPS Equipment

Hand-helds $100-$450 – Navigation instruments

For survey apps.:

Garmin

Magellan

GPS for PDAs

- Way Points collection
- Manual entry into GIS, no attribute info. stored
- “Differential ready” but no post-processing

+/- ~15 meters

+/- ~3 meters with WAAS

GEO 420K, UT Austin

GPS Equipment

Geodetic-quality Instruments

- Trimble
- Ashtech
- Sokkia
- Others

Cm – mm in x, y and z

Stationary Antenna

Large memory for continuous data collection

GEO 420K, UT Austin

Recent Developments

- Hand-held equipment – Field GIS
- WAAS, LAAS
- NDGPS
- European Union Galileo System
- Glonass (presently 9 SVs; 24 by 2007)
- Chinese Beidou System

GEO 420K, UT Austin

Recent Developments

- Touch-screen GIS mapping tablets with integrated GPS
- Hand-helds with touch screens
- PDA GPS & GIS - ArcPad

GEO 420K, UT Austin

Recent Developments

- FAA WAAS and DGPS WAAS receivers
- Commissioning of WAAS in December 2003
- LAAS by late 2006?

GEO 420K, UT Austin

What is the shape of the earth?

Why is it relevant?

GEO 420K, UT Austin

The “Figure” of the Earth

- Models
- Sphere with radius of ~6378 km
- Ellipsoid (or Spheroid) with equatorial radius (major axis) of ~6378 km and polar radius (minor axis) of ~6357 km
- Difference of ~21 km is usually expressed as the “flattening” (f) ratio of the ellipsoid:
- f = difference/major axis = ~1/300 for earth

GEO 420K, UT Austin

Ellipsoid / Spheroid

- Rotate an ellipse around an axis (c.f. Uniaxial indicatrix of optical mineralogy)

Rotation axis

a = Major axis

b = Minor axis

X, Y, Z = Reference frame

GEO 420K, UT Austin

Standard Earth Ellipsoids

GEO 420K, UT Austin

Horizontal Datums

Datum = ellipse and axis of rotation.

Common North American datums:

- NAD27 (1927 North American Datum)
- Clarke (1866) ellipsoid, non-geocentric axis of rotation*
- NAD83 (1983 North American Datum)
- GRS80 ellipsoid, non-geocentric axis of rotation
- WGS84 (1984 World Geodetic System)
- GRS80 ellipsoid, nearly identical to NAD83
- Other datums in use globally

GEO 420K, UT Austin

Laying the earth flat

- How?
- Projections – transformation of curved earth to a flat map; systematic rendering of the lat. & lon. graticule to rectangular coordinate system.

Scale1: 42,000,000

Scale Factor0.9996

(for specific line(s))

Earth

Globe

Map

Peters Projection

Globe distanceEarth distance

Map distanceGlobe distance

GEO 420K, UT Austin

Laying the earth flat

- Systematic rendering of Lat. (f) & Lon. (l) to rectangular (x, y) coordinates:

y

0, 0

x

Geographic Coordinates(f, l)

Projected Coordinates(x, y)

Map Projection

GEO 420K, UT Austin

Rectangular Coordinate Systems

- Universal Transverse Mercator (UTM)
- US military developed; Global cartesian reference system.
- State Plane Coordinate System (SPCS)
- Coordinates specific to states; used for property definitions.
- Public Land Survey System (PLS)
- National system once used for property description
- no common datum or axes, units in miles or fractional miles.

GEO 420K, UT Austin

UTM Coordinate System

(Y)

(x)

- Cylinder is rotated about vertical axis in 6o increments to define 60 separate UTM “zones”.

Rotate in 6o increments

UTM Zone is 6o wide

GEO 420K, UT Austin

UTM Coordinate System

- Zone boundaries are parallel to meridians.
- Zones numbered from 180o (begins zone 1) eastward and extend from 80o S to 84o N.

UTM Zones

20

9

10

19

11

12

18

13

14

15

16

17

GEO 420K, UT Austin

UTM Coordinate System

(Y)

(x)

- For each zone, the Central Meridian is the y-axis, the equator the x-axis
- Central meridian of each zone in US has a scale factor of 0.9996 (max. distortion).

GEO 420K, UT Austin

UTM Coordinate System

y

N. Hemisphereorigin is(500,000m, 0)

x

x

S. Hemisphereorigin is(500,000m, 10,000,000m)

y

- Locations are given in meters from central meridian (Easting) and equator (Northing).
- (-) Eastings avoided by giving X value of 500,000 m (“false easting”) to the Central Meridian
- In S. hemisphere, equator is given “false northing” of 10,000,000 m to avoid (-) Northings.

GEO 420K, UT Austin

UTM Coordinate System

Y

99oW

Zone 14

Austin

Y = 3,000,000 mN

Central Meridian(X = 500,000 m)

UTM Coordinates for central Austin:

Zone 14 621,000 mE, 3,350,000 mN

GEO 420K, UT Austin

State Plane Coordinate System (SPCS)

- Developed in 1930’s to provide states a reference system that was tied to national datum (NAD27); units in feet.
- Updated to NAD83, units in meters; some maps still show SPCS NAD27 coordinates.
- Larger states divided into several zones.
- X, Y coordinates are given relative to origin outside of zone; false eastings and northings different for each zone.

GEO 420K, UT Austin

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