m. helper 3-8-06 geo 420k, ut austin 5-1 the global positioning system
TRANSCRIPT
M. Helper 3-8-06
GEO 420K, UT Austin 5-1
The Global Positioning System
M. Helper 3-8-06
GEO 420K, UT Austin 5-2
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 3-8-06
GEO 420K, UT Austin 5-3
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 3-8-06
GEO 420K, UT Austin 5-4
Ranging Techniques
• Two-way ranging: “Active”• Electronic Dist. Measuring devices (EDMs)• Radar, Sonar, Lidar
• One-way ranging: “Passive”• GPS
M. Helper 3-8-06
GEO 420K, UT Austin 5-5
Ranging techniques
• Two-way ranging (EDM)
Light beam
Range
Range = C x Time/2
reflector
M. Helper 3-8-06
GEO 420K, UT Austin 5-6
Ranging techniques
• One-way ranging with GPS
Range
Radio Signal
Range = C x Time
1 microsecond error = ~ 300 meters1 nanosecond error = ~ 1 foot
“Sphere of position”
M. Helper 3-8-06
GEO 420K, UT Austin 5-7
Satellite Positioning
Geocenter
Known
OrbitObserve T
Determine
M. Helper 3-8-06
GEO 420K, UT Austin 5-8
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
M. Helper 3-8-06
GEO 420K, UT Austin 5-9
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.
Figures from: www.math.tamu.edu/~dallen/physics/gps/gps.htm
M. Helper 3-8-06
GEO 420K, UT Austin 5-10
Determine Position by:
1) Downloading almanac (ephemeris info., SV health, etc.)
2) Synchronize receiver clock/measure T 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 3-8-06
GEO 420K, UT Austin 5-11
How is T 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 3-8-06
GEO 420K, UT Austin 5-12
Broadcast Signals - Codes
• 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
+1-1
Coarse acquisition (C/A) code Civilian access, least accurate;
M. Helper 3-8-06
GEO 420K, UT Austin 5-13
Signal “Carrier”
• Radio waves with following characteristics:• L1: frequency = ~1575 MHz with = 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 = 24 cm• Carries P code
• Fundamental precision in positioning limited by ability to determine phase of carrier (to ~ 0.011 or 2 mm)
M. Helper 3-8-06
GEO 420K, UT Austin 5-14
T Code solutions
• Compare offsets in satellite and receiver codes to arrive at T
T
Pseudorange = C x T
+1
-1
Code generated by SV
+1
-1Code generated by receiver
M. Helper 3-8-06
GEO 420K, UT Austin 5-15
200 km
50 km
Sources of Error
SV clock error (~1.5 m)+/- Selective Availability (~30 m)
Ionospheric Refraction (~ 5 m)(Can correct with L1 & L2 Ts)
Tropospheric Delay (~ 0.5 m)
Multipathing (~0.5 m)
+ GDOP (errors x 4-6)(Geometric dilution of precision)
L2L1
Satellite Orbit Errors (~2.5 m)
M. Helper 3-8-06
GEO 420K, UT Austin 5-16
Summary of Error Sources (m)
Source: Trimble Navigation. Standard GPS DGPSSV Clocks 1.5 0Orbit (Ephemeris) 2.5 0Ionosphere 5.0 0.4Troposphere 0.5 0.2Receiver Noise 0.3 0.3Multipath 0.6 0.6S/A 30 0
3-D Accuracy 93 2.8
M. Helper 3-8-06
GEO 420K, UT Austin 5-17
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 3-8-06
GEO 420K, UT Austin 5-18
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 3-8-06
GEO 420K, UT Austin 5-19
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 3-8-06
GEO 420K, UT Austin 5-20
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 3-8-06
GEO 420K, UT Austin 5-21
Signal “Carrier”
• Radio waves with following characteristics:• L1: frequency = ~1575 MHz with = 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 = 24 cm• Carries P code
• Fundamental precision in positioning limited by ability to determine phase of carrier (to ~ 0.011 or 2 mm)
M. Helper 3-8-06
GEO 420K, UT Austin 5-22
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 3-8-06
GEO 420K, UT Austin 5-23
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 3-8-06
GEO 420K, UT Austin 5-24
Accuracy of Code vs. Phase Solutions
M. Helper 3-8-06
GEO 420K, UT Austin 5-25
GPS Equipment
Hand-helds $100-$450 – Navigation instruments
GarminMagella
n GPS for
PDAs
• Way Points collection
• Manual entry into GIS, no attribute info. stored
• “Differential ready” but no post-processing
For survey apps.:
+/- ~15 meters
+/- ~3 meters with WAAS
M. Helper 3-8-06
GEO 420K, UT Austin 5-26
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 3-8-06
GEO 420K, UT Austin 5-27
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 3-8-06
GEO 420K, UT Austin 5-28
Recent Developments
• Touch-screen GIS mapping tablets with integrated GPS
• Hand-helds with touch screens• PDA GPS & GIS - ArcPad
M. Helper 3-8-06
GEO 420K, UT Austin 5-29
Recent Developments
• FAA WAAS and DGPS WAAS receivers• Commissioning of WAAS in December
2003
• LAAS by late 2006?
M. Helper 3-8-06
GEO 420K, UT Austin 5-30
Geographic Datums & Coordinates
•What is the shape of the earth?•Why is it relevant?
M. Helper 3-8-06
GEO 420K, UT Austin 5-31
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 3-8-06
GEO 420K, UT Austin 5-32
Ellipsoid / Spheroid
• Rotate an ellipse around an axis (c.f. Uniaxial indicatrix of optical mineralogy)
a = Major axis
b = Minor axis
X, Y, Z = Reference frame
Rotation axis
M. Helper 3-8-06
GEO 420K, UT Austin 5-33
Standard Earth Ellipsoids
Ellipsoid
Major Axisa (km)
Minor Axisb (km)
Flattening (1/f)
Clark (1886)
6,378.206 6,356.584 294.98
GRS 80 6,378.137 6,356.752 298.57
M. Helper 3-8-06
GEO 420K, UT Austin 5-34
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
M. Helper 3-8-06
GEO 420K, UT Austin 5-35
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.
Map distanceGlobe distance
Globe distanceEarth distance
Scale1: 42,000,000
Scale Factor0.9996
(for specific line(s))
Peters Projection
Earth Globe Map
M. Helper 3-8-06
GEO 420K, UT Austin 5-36
Laying the earth flat
• Systematic rendering of Lat. () & Lon. () to rectangular (x, y) coordinates:
Geographic Coordinates()
Projected Coordinates(x, y)
0, 0x
y
Map Projection
M. Helper 3-8-06
GEO 420K, UT Austin 5-37
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 3-8-06
GEO 420K, UT Austin 5-38
UTM Coordinate System
• Cylinder is rotated about vertical axis in 6o increments to define 60 separate UTM “zones”.
UTM Zone is 6o wide
Rotate in 6o increments
(x)
(Y)
M. Helper 3-8-06
GEO 420K, UT Austin 5-39
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.
10 1
1 12 1
314
15
16
17
18
19
UTM Zones
920
M. Helper 3-8-06
GEO 420K, UT Austin 5-40
UTM Coordinate System
• 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).
(x)
(Y)
M. Helper 3-8-06
GEO 420K, UT Austin 5-41
UTM Coordinate System
y
x
N. Hemisphereorigin is
(500,000m, 0)
x
y
S. Hemisphereorigin is
(500,000m, 10,000,000m)
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.
M. Helper 3-8-06
GEO 420K, UT Austin 5-42
UTM Coordinate System
UTM Coordinates for central Austin:
Zone 14 621,000 mE,
3,350,000 mNCentral Meridian(X = 500,000 m)
Y
Zone 14
Austin
99oW
Y = 3,000,000 mN
M. Helper 3-8-06
GEO 420K, UT Austin 5-43
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 3-8-06
GEO 420K, UT Austin 5-44
Texas NAD83 SPCS
Zone Code
Stand. Parallels
Origin F. EastingF. Northing
4201North
34.65036.183
-101.50
34.00
200,0001,000,000
4202N. Cent.
32.13333.967
-98.5031.67
600,0002,000,000
4203Central
30.11731.883
-100.33
29.67
700,0003,000,000
4204S. Cent.
28.38330.283
-99.0027.83
600,0004,000,000
4205South
26.167 27.833
-98.5025.67
500,0005,000,000
Austin
Austin:Central Zone ~ 944,000mE
~ 3,077,000mN
X
Y