m. helper 3-8-06 geo 420k, ut austin 5-1 the global positioning system

M. Helper 3-8-06

GEO 420K, UT Austin 5-1

The Global Positioning System

M. Helper 3-8-06


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


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


Ranging Techniques

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

• One-way ranging: “Passive”• GPS

M. Helper 3-8-06


Ranging techniques

• Two-way ranging (EDM)

Light beam

Range

Range = C x Time/2

reflector

M. Helper 3-8-06


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


Satellite Positioning

Geocenter

Known

OrbitObserve T

Determine

M. Helper 3-8-06


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


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


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


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


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


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


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


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


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


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


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


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

http://www.navcen.uscg.gov/dgps/coverage/GulfCoast.htm

http://gps.faa.gov/programs/index.htm

http://www.omnistar.com/howitworks.html

http://www.ngs.noaa.gov/CORS/cors-data.html

M. Helper 3-8-06


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

http://www.ngs.noaa.gov/FGCS/info/sans_SA/

http://www.ngs.noaa.gov/FGCS/info/sans_SA/

M. Helper 3-8-06


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


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


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


Accuracy of Code vs. Phase Solutions

M. Helper 3-8-06


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


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


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


Recent Developments

• Touch-screen GIS mapping tablets with integrated GPS

• Hand-helds with touch screens• PDA GPS & GIS - ArcPad

http://www.xploretech.com/products.html

http://www.trimble.com/geoxt.html

http://www.trimble.com/geoxt.html

http://www.esri.com/software/arcpad/index.html

M. Helper 3-8-06


Recent Developments

• FAA WAAS and DGPS WAAS receivers• Commissioning of WAAS in December

2003

• LAAS by late 2006?

http://gps.faa.gov/programs/waas/howitworks.htm

M. Helper 3-8-06


Geographic Datums & Coordinates

•What is the shape of the earth?•Why is it relevant?

M. Helper 3-8-06


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


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


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


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

http://www.colorado.edu/geography/gcraft/notes/datum/edlist.html



M. Helper 3-8-06


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


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


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


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



• 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



• 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



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



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


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


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

m. helper 3-8-06 geo 420k, ut austin 5-1 the global positioning system

Documents

ut austin

world slide

passive gps slide

foot sphere of position

clock synchronization

z oneway ranging intersection

lidar oneway ranging

c x time2 reflector