1. The Global Positioning System
The Global Positioning Sytem
4/21/2017
The Global Positioning System
M. Helper
GEO 420K, UT Austin
M. Helper, GEO 420k, UT Austin

2. 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
M. Helper
GEO 420K, UT Austin

3. 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.
M. Helper
GEO 420K, UT Austin

4. Ranging Techniques Two-way ranging: “Active”
Electronic Dist. Measuring devices (EDMs)
Radar, Sonar, Lidar
One-way ranging: “Passive”
GPS
M. Helper
GEO 420K, UT Austin

5. Ranging techniques Two-way ranging (EDM) Range Range = C x DTime/2
reflector
Light beam
Range = C x DTime/2
M. Helper
GEO 420K, UT Austin

6. Ranging techniques One-way ranging with GPS Range Range = C x DTime
“Sphere of position”
Range
Radio Signal
Range = C x DTime
1 microsecond error = ~ 300 meters 1 nanosecond error = ~ 1 foot
M. Helper
GEO 420K, UT Austin

7. Satellite Positioning
Observe DT
Orbit
Known
Determine
Geocenter
M. Helper
GEO 420K, UT Austin

8. 3-D (X, Y, Z) One-way Ranging
The Global Positioning Sytem
3-D (X, Y, Z) One-way Ranging
4/21/2017
“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
M. Helper
GEO 420K, UT Austin
M. Helper, GEO 420k, UT Austin

9. 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.
M. Helper
Figures from:
GEO 420K, UT Austin

10. 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
M. Helper
GEO 420K, UT Austin

11. 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
M. Helper
GEO 420K, UT Austin

12. Broadcast Signals - Codes
Coarse acquisition (C/A) code
Civilian access, least accurate; +1 -1
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
M. Helper
GEO 420K, UT Austin

13. Signal “Carrier” 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) l
M. Helper
GEO 420K, UT Austin

14. DT Code solutions
Compare offsets in satellite and receiver codes to arrive at DT +1 -1
Code generated by SV DT +1 -1
Code generated by receiver
Pseudorange = C x DT
M. Helper
GEO 420K, UT Austin

15. Tropospheric Delay (~ 0.5 m)
Sources of Error
Satellite Orbit Errors (~2.5 m)
SV clock error (~1.5 m) +/- Selective Availability (~30 m) L2 L1
50 km
Ionospheric Refraction (~ 5 m) (Can correct with L1 & L2 DTs)
200 km
Tropospheric Delay (~ 0.5 m)
Multipathing (~0.5 m)
+ GDOP (errors x 4-6)
(Geometric dilution of precision)
M. Helper
GEO 420K, UT Austin

16. Summary of Error Sources (m)
Source: Trimble Navigation.
Standard GPS
DGPS
SV Clocks
1.5
Orbit (Ephemeris)
2.5
Ionosphere
5.0
0.4
Troposphere
0.5
0.2
Receiver Noise
0.3
Multipath
0.6
S/A 30
3-D Accuracy 93
2.8
M. Helper
GEO 420K, UT Austin

17. 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)
M. Helper
GEO 420K, UT Austin

18. 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.
M. Helper
GEO 420K, UT Austin

19. 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 Guard WAAS
Commercial Services
Remote base station data combined with rover data during post-processing
CORS
M. Helper
GEO 420K, UT Austin

20. 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
M. Helper
GEO 420K, UT Austin

21. Signal “Carrier” 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) l
M. Helper
GEO 420K, UT Austin

22. 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
M. Helper
GEO 420K, UT Austin

23. 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
M. Helper
GEO 420K, UT Austin

24. Accuracy of Code vs. Phase Solutions
M. Helper
GEO 420K, UT Austin

25. GPS Equipment Hand-helds $100-$450 – Navigation instruments Garmin
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
M. Helper
GEO 420K, UT Austin

26. GPS Equipment Geodetic-quality Instruments Trimble Ashtech Sokkia
Others
Cm – mm in x, y and z
Stationary Antenna
Large memory for continuous data collection
M. Helper
GEO 420K, UT Austin

27. Recent Developments Hand-held equipment – Field GIS WAAS, LAAS NDGPS
European Union Galileo System
Glonass (presently 9 SVs; 24 by 2007)
Chinese Beidou System
M. Helper
GEO 420K, UT Austin

28. Recent Developments
Touch-screen GIS mapping tablets with integrated GPS
Hand-helds with touch screens
PDA GPS & GIS - ArcPad
M. Helper
GEO 420K, UT Austin

29. Recent Developments FAA WAAS and DGPS WAAS receivers
Commissioning of WAAS in December 2003
LAAS by late 2006?
M. Helper
GEO 420K, UT Austin

30. Geographic Datums & Coordinates
The Global Positioning Sytem
4/21/2017
Geographic Datums & Coordinates
What is the shape of the earth?
Why is it relevant?
M. Helper
GEO 420K, UT Austin
M. Helper, GEO 420k, UT Austin

31. 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
M. Helper
GEO 420K, UT Austin

32. 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
M. Helper
GEO 420K, UT Austin

33. Standard Earth Ellipsoids
Major Axis a (km)
Minor Axis b (km)
Flattening (1/f)
Clark (1886) 6, 6,
294.98
GRS 80 6, 6,
298.57
M. Helper
GEO 420K, UT Austin

34. The Global Positioning Sytem
4/21/2017
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
* Selection of a non-geocentric axis of rotation allows closer agreement between the geoid and ellipsoid – see notes below.
M. Helper
GEO 420K, UT Austin
M. Helper, GEO 420k, UT Austin

35. 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.
Scale 1: 42,000,000
Scale Factor
(for specific line(s))
Earth
Globe
Map
Peters Projection
Globe distance Earth distance
Map distance Globe distance
M. Helper
GEO 420K, UT Austin

36. 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
M. Helper
GEO 420K, UT Austin

37. 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.
M. Helper
GEO 420K, UT Austin

38. UTM Coordinate System
Cylinder is rotated about vertical axis in 6o increments to define 60 separate UTM “zones”.
(x)
(Y)
Rotate in 6o increments
UTM Zone is 6o wide
M. Helper
GEO 420K, UT Austin

39. 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
M. Helper
GEO 420K, UT Austin

40. UTM Coordinate System
(x)
(Y)
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 (max. distortion).
M. Helper
GEO 420K, UT Austin

41. UTM Coordinate System
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. y x
N. Hemisphere origin is (500,000m, 0)
S. Hemisphere origin is (500,000m, 10,000,000m)
M. Helper
GEO 420K, UT Austin

42. UTM Coordinate System UTM Coordinates for central Austin:
Central Meridian (X = 500,000 m) Y
Zone 14
Austin
99oW
Y = 3,000,000 mN
UTM Coordinates for central Austin:
Zone ,000 mE, 3,350,000 mN
M. Helper
GEO 420K, UT Austin

43. 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.
M. Helper
GEO 420K, UT Austin

44. Austin: Central Zone ~ 944,000mE ~ 3,077,000mN
Texas NAD83 SPCS
Austin: Central Zone ~ 944,000mE ~ 3,077,000mN
Zone Code
Stand. Parallels
Origin
F. Easting F. Northing
4201 North
200,000 1,000,000
4202 N. Cent.
600,000 2,000,000
4203 Central
700,000 3,000,000
4204 S. Cent.
600,000 4,000,000
4205 South
500,000 5,000,000 Y
Austin X
M. Helper
GEO 420K, UT Austin