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© 2007, EMH&T, Inc. GPS: A Primer GPS: A Primer presented by Jim Pugh, GISP GIS Project Manager presented by Jim Pugh, GISP GIS Project Manager
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GPS: A Primer - MITweb.mit.edu/ncfmtc/pubs/Pugh_GPSPrimer.pdf© 2007, EMH&T, Inc. GPS: A Primer •GPS = G lobal Positioning System • 24 Satellites in Orbit around Earth • Each

Jul 20, 2020

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Page 1: GPS: A Primer - MITweb.mit.edu/ncfmtc/pubs/Pugh_GPSPrimer.pdf© 2007, EMH&T, Inc. GPS: A Primer •GPS = G lobal Positioning System • 24 Satellites in Orbit around Earth • Each

© 2007, EMH&T, Inc.

GPS: A PrimerGPS: A Primerpresented by

Jim Pugh, GISPGIS Project Manager

presented by

Jim Pugh, GISPGIS Project Manager

Page 2: GPS: A Primer - MITweb.mit.edu/ncfmtc/pubs/Pugh_GPSPrimer.pdf© 2007, EMH&T, Inc. GPS: A Primer •GPS = G lobal Positioning System • 24 Satellites in Orbit around Earth • Each

© 2007, EMH&T, Inc.

GPS: A PrimerGPS: A Primer• GPS = Global

Positioning System• 24 Satellites in Orbit

around Earth• Each Broadcasts

precise time and known location

• Receivers triangulate position

• GPS = Global Positioning System

• 24 Satellites in Orbit around Earth

• Each Broadcasts precise time and known location

• Receivers triangulate position

Page 3: GPS: A Primer - MITweb.mit.edu/ncfmtc/pubs/Pugh_GPSPrimer.pdf© 2007, EMH&T, Inc. GPS: A Primer •GPS = G lobal Positioning System • 24 Satellites in Orbit around Earth • Each

© 2007, EMH&T, Inc.

By the way…By the way…

• “GPS” is an American system

• “GLONASS” is Russian

• “Galileo” is EU

• “GPS” is an American system

• “GLONASS” is Russian

• “Galileo” is EU

Page 4: GPS: A Primer - MITweb.mit.edu/ncfmtc/pubs/Pugh_GPSPrimer.pdf© 2007, EMH&T, Inc. GPS: A Primer •GPS = G lobal Positioning System • 24 Satellites in Orbit around Earth • Each

© 2007, EMH&T, Inc.

GPS OrbitGPS Orbit

• About 12,000 miles above Earth

• 6 Circular Orbital Planes– Global Coverage

• Equipped with very precise atomic clocks

• About 12,000 miles above Earth

• 6 Circular Orbital Planes– Global Coverage

• Equipped with very precise atomic clocks

Page 5: GPS: A Primer - MITweb.mit.edu/ncfmtc/pubs/Pugh_GPSPrimer.pdf© 2007, EMH&T, Inc. GPS: A Primer •GPS = G lobal Positioning System • 24 Satellites in Orbit around Earth • Each

© 2007, EMH&T, Inc.

It’s about time…It’s about time…

• Distance = Velocity x Time

• Velocity is fixed at the Speed of Light

• Calculate signal travel time and distance is solved

• Location is somewhere within a sphere

• Distance = Velocity x Time

• Velocity is fixed at the Speed of Light

• Calculate signal travel time and distance is solved

• Location is somewhere within a sphere

Page 6: GPS: A Primer - MITweb.mit.edu/ncfmtc/pubs/Pugh_GPSPrimer.pdf© 2007, EMH&T, Inc. GPS: A Primer •GPS = G lobal Positioning System • 24 Satellites in Orbit around Earth • Each

© 2007, EMH&T, Inc.

It’s about time…It’s about time…

• A second distance can calculate an area…• A second distance can calculate an area…

Page 7: GPS: A Primer - MITweb.mit.edu/ncfmtc/pubs/Pugh_GPSPrimer.pdf© 2007, EMH&T, Inc. GPS: A Primer •GPS = G lobal Positioning System • 24 Satellites in Orbit around Earth • Each

© 2007, EMH&T, Inc.

It’s about time…It’s about time…

• The third distance can calculate a point…• The third distance can calculate a point…

Page 8: GPS: A Primer - MITweb.mit.edu/ncfmtc/pubs/Pugh_GPSPrimer.pdf© 2007, EMH&T, Inc. GPS: A Primer •GPS = G lobal Positioning System • 24 Satellites in Orbit around Earth • Each

© 2007, EMH&T, Inc.

If it were a perfect World…If it were a perfect World…

• Extremely precise clocks required– Average time from

Satellite <0.06 sec– 1ns error = 1 ft

• Speed of Light– Not a constant

• Orbits change

• Extremely precise clocks required– Average time from

Satellite <0.06 sec– 1ns error = 1 ft

• Speed of Light– Not a constant

• Orbits change

Page 9: GPS: A Primer - MITweb.mit.edu/ncfmtc/pubs/Pugh_GPSPrimer.pdf© 2007, EMH&T, Inc. GPS: A Primer •GPS = G lobal Positioning System • 24 Satellites in Orbit around Earth • Each

© 2007, EMH&T, Inc.

If it were a perfect World…If it were a perfect World…

• Each reading is slightly different

• Due to changing– Satellite location– Satellite DOP’s &

combinations– Varied clock errors

• Points are averaged

• Each reading is slightly different

• Due to changing– Satellite location– Satellite DOP’s &

combinations– Varied clock errors

• Points are averaged

Page 10: GPS: A Primer - MITweb.mit.edu/ncfmtc/pubs/Pugh_GPSPrimer.pdf© 2007, EMH&T, Inc. GPS: A Primer •GPS = G lobal Positioning System • 24 Satellites in Orbit around Earth • Each

© 2007, EMH&T, Inc.

GPS ErrorGPS Error

• Satellite Clocks• Selective Availability

(SA)• Orbital Errors

(Ephemeris)• Atmospheric

– Delays & Signal Strength

• Multipath• Receiver Clock

• Satellite Clocks• Selective Availability

(SA)• Orbital Errors

(Ephemeris)• Atmospheric

– Delays & Signal Strength

• Multipath• Receiver Clock

Page 11: GPS: A Primer - MITweb.mit.edu/ncfmtc/pubs/Pugh_GPSPrimer.pdf© 2007, EMH&T, Inc. GPS: A Primer •GPS = G lobal Positioning System • 24 Satellites in Orbit around Earth • Each

© 2007, EMH&T, Inc.

GPS ErrorGPS Error

• Satellite Clocks• Selective Availability

(SA)• Orbital Errors

(Ephemeris)• Atmospheric

– Delays & Signal Strength

• Multipath• Receiver Clock

• Satellite Clocks• Selective Availability

(SA)• Orbital Errors

(Ephemeris)• Atmospheric

– Delays & Signal Strength

• Multipath• Receiver Clock

Minimal – atomic clocksDisabled – was upwards

of 300 feet7 feet

13 feet

3 feet13 feet

Minimal – atomic clocksDisabled – was upwards

of 300 feet7 feet

13 feet

3 feet13 feet

Page 12: GPS: A Primer - MITweb.mit.edu/ncfmtc/pubs/Pugh_GPSPrimer.pdf© 2007, EMH&T, Inc. GPS: A Primer •GPS = G lobal Positioning System • 24 Satellites in Orbit around Earth • Each

© 2007, EMH&T, Inc.

EphemerisEphemeris

• Satellite location• Monitored by DoD

– Updated Constantly

• Almanac: all SV’s• Adjusted

– Orbit– Altitude– Speed

• Satellite location• Monitored by DoD

– Updated Constantly

• Almanac: all SV’s• Adjusted

– Orbit– Altitude– Speed

Page 13: GPS: A Primer - MITweb.mit.edu/ncfmtc/pubs/Pugh_GPSPrimer.pdf© 2007, EMH&T, Inc. GPS: A Primer •GPS = G lobal Positioning System • 24 Satellites in Orbit around Earth • Each

© 2007, EMH&T, Inc.

MultipathMultipath

• Signal reflects off Objects

• Travels further and delayed

• Corrected with improved antenna and processors

• “First one wins”

• Signal reflects off Objects

• Travels further and delayed

• Corrected with improved antenna and processors

• “First one wins”

Page 14: GPS: A Primer - MITweb.mit.edu/ncfmtc/pubs/Pugh_GPSPrimer.pdf© 2007, EMH&T, Inc. GPS: A Primer •GPS = G lobal Positioning System • 24 Satellites in Orbit around Earth • Each

© 2007, EMH&T, Inc.

Dilution of Precision (DOP)Dilution of Precision (DOP)

• Includes:– Horizontal (HDOP)– Vertical (VDOP)– Position (PDOP)

• √HDOP² +VDOP²• Generally below 6

– Time (TDOP)– Geometry (GDOP)

• √PDOP² + TDOP²

• Includes:– Horizontal (HDOP)– Vertical (VDOP)– Position (PDOP)

• √HDOP² +VDOP²• Generally below 6

– Time (TDOP)– Geometry (GDOP)

• √PDOP² + TDOP²

Poor DOP

Page 15: GPS: A Primer - MITweb.mit.edu/ncfmtc/pubs/Pugh_GPSPrimer.pdf© 2007, EMH&T, Inc. GPS: A Primer •GPS = G lobal Positioning System • 24 Satellites in Orbit around Earth • Each

© 2007, EMH&T, Inc.

Dilution of Precision (DOP)Dilution of Precision (DOP)

• Includes:– Horizontal (HDOP)– Vertical (VDOP)– Position (PDOP)

• √HDOP² +VDOP²• Generally below 6

– Time (TDOP)– Geometry (GDOP)

• √PDOP² + TDOP²

• Includes:– Horizontal (HDOP)– Vertical (VDOP)– Position (PDOP)

• √HDOP² +VDOP²• Generally below 6

– Time (TDOP)– Geometry (GDOP)

• √PDOP² + TDOP²

Good DOP

Page 16: GPS: A Primer - MITweb.mit.edu/ncfmtc/pubs/Pugh_GPSPrimer.pdf© 2007, EMH&T, Inc. GPS: A Primer •GPS = G lobal Positioning System • 24 Satellites in Orbit around Earth • Each

© 2007, EMH&T, Inc.

When to go?When to go?

Page 17: GPS: A Primer - MITweb.mit.edu/ncfmtc/pubs/Pugh_GPSPrimer.pdf© 2007, EMH&T, Inc. GPS: A Primer •GPS = G lobal Positioning System • 24 Satellites in Orbit around Earth • Each

© 2007, EMH&T, Inc.

Differential CorrectionDifferential Correction

Base Station Rover

Page 18: GPS: A Primer - MITweb.mit.edu/ncfmtc/pubs/Pugh_GPSPrimer.pdf© 2007, EMH&T, Inc. GPS: A Primer •GPS = G lobal Positioning System • 24 Satellites in Orbit around Earth • Each

© 2007, EMH&T, Inc.

Differential CorrectionDifferential Correction

Known PositionAll SatellitesCalculate Error

Known PositionAll SatellitesCalculate Error

Unknown ErrorCompare to Base

Apply offset Error

Unknown ErrorCompare to Base

Apply offset Error

Base Station Rover“Post Processing”

Page 19: GPS: A Primer - MITweb.mit.edu/ncfmtc/pubs/Pugh_GPSPrimer.pdf© 2007, EMH&T, Inc. GPS: A Primer •GPS = G lobal Positioning System • 24 Satellites in Orbit around Earth • Each

© 2007, EMH&T, Inc.

Differential CorrectionDifferential Correction

Base Station Rover“DGPS”“RTK”

Page 20: GPS: A Primer - MITweb.mit.edu/ncfmtc/pubs/Pugh_GPSPrimer.pdf© 2007, EMH&T, Inc. GPS: A Primer •GPS = G lobal Positioning System • 24 Satellites in Orbit around Earth • Each

© 2007, EMH&T, Inc.

Differential CorrectionDifferential Correction

• National Public Base Station Network

• National Public Base Station Network

Page 21: GPS: A Primer - MITweb.mit.edu/ncfmtc/pubs/Pugh_GPSPrimer.pdf© 2007, EMH&T, Inc. GPS: A Primer •GPS = G lobal Positioning System • 24 Satellites in Orbit around Earth • Each

© 2007, EMH&T, Inc.

Types of GPSTypes of GPS

• Recreational Grade± 30 - 100 feet

• Mapping Grade± 1 – 3 feet

• Survey Grade< 0.04 feet (1 cm)

Vertical 2-5 times horizontal accuracy

• Recreational Grade± 30 - 100 feet

• Mapping Grade± 1 – 3 feet

• Survey Grade< 0.04 feet (1 cm)

Vertical 2-5 times horizontal accuracy

Page 22: GPS: A Primer - MITweb.mit.edu/ncfmtc/pubs/Pugh_GPSPrimer.pdf© 2007, EMH&T, Inc. GPS: A Primer •GPS = G lobal Positioning System • 24 Satellites in Orbit around Earth • Each

© 2007, EMH&T, Inc.

Types of GPSTypes of GPS

• Recreational Grade± 30 - 100 feet

• Mapping Grade± 1 – 3 feet

• Survey Grade< 0.04 feet (1 cm)

Purchased for $100-800

• Recreational Grade± 30 - 100 feet

• Mapping Grade± 1 – 3 feet

• Survey Grade< 0.04 feet (1 cm)

Purchased for $100-800

Page 23: GPS: A Primer - MITweb.mit.edu/ncfmtc/pubs/Pugh_GPSPrimer.pdf© 2007, EMH&T, Inc. GPS: A Primer •GPS = G lobal Positioning System • 24 Satellites in Orbit around Earth • Each

© 2007, EMH&T, Inc.

Types of GPSTypes of GPS

• Recreational Grade± 30 - 100 feet

• Mapping Grade± 1 – 3 feet

• Survey Grade< 0.04 feet (1 cm)

Purchased for $3,000-5,000+

• Recreational Grade± 30 - 100 feet

• Mapping Grade± 1 – 3 feet

• Survey Grade< 0.04 feet (1 cm)

Purchased for $3,000-5,000+

Page 24: GPS: A Primer - MITweb.mit.edu/ncfmtc/pubs/Pugh_GPSPrimer.pdf© 2007, EMH&T, Inc. GPS: A Primer •GPS = G lobal Positioning System • 24 Satellites in Orbit around Earth • Each

© 2007, EMH&T, Inc.

Types of GPSTypes of GPS

• Recreational Grade± 30 - 100 feet

• Mapping Grade± 1 – 3 feet

• Survey Grade< 0.04 feet (1 cm)

Purchased for $15,000-50,000++

• Recreational Grade± 30 - 100 feet

• Mapping Grade± 1 – 3 feet

• Survey Grade< 0.04 feet (1 cm)

Purchased for $15,000-50,000++

Page 25: GPS: A Primer - MITweb.mit.edu/ncfmtc/pubs/Pugh_GPSPrimer.pdf© 2007, EMH&T, Inc. GPS: A Primer •GPS = G lobal Positioning System • 24 Satellites in Orbit around Earth • Each

© 2007, EMH&T, Inc.

Types of GPSTypes of GPS

• Recreational Grade± 30 - 100 feet

• Mapping Grade± 1 – 3 feet

• Survey Grade< 0.04 feet (1 cm)

What do you get?Better clocks, receivers, filters,

processors.

• Recreational Grade± 30 - 100 feet

• Mapping Grade± 1 – 3 feet

• Survey Grade< 0.04 feet (1 cm)

What do you get?Better clocks, receivers, filters,

processors.

Page 26: GPS: A Primer - MITweb.mit.edu/ncfmtc/pubs/Pugh_GPSPrimer.pdf© 2007, EMH&T, Inc. GPS: A Primer •GPS = G lobal Positioning System • 24 Satellites in Orbit around Earth • Each

© 2007, EMH&T, Inc.

Types of GPSTypes of GPS

• Recreational Grade± 30 - 100 feet

• Mapping Grade± 1 – 3 feet

• Survey Grade< 0.04 feet (1 cm)

• Recreational Grade± 30 - 100 feet

• Mapping Grade± 1 – 3 feet

• Survey Grade< 0.04 feet (1 cm)

Page 27: GPS: A Primer - MITweb.mit.edu/ncfmtc/pubs/Pugh_GPSPrimer.pdf© 2007, EMH&T, Inc. GPS: A Primer •GPS = G lobal Positioning System • 24 Satellites in Orbit around Earth • Each

© 2007, EMH&T, Inc.

So what can you do with it?So what can you do with it?

• Tree – Horticulture Inventory

• Ponds – Streams• Historical -

Archeological

• Tree – Horticulture Inventory

• Ponds – Streams• Historical -

Archeological

Page 28: GPS: A Primer - MITweb.mit.edu/ncfmtc/pubs/Pugh_GPSPrimer.pdf© 2007, EMH&T, Inc. GPS: A Primer •GPS = G lobal Positioning System • 24 Satellites in Orbit around Earth • Each

© 2007, EMH&T, Inc.

UtilitiesUtilities

• Manholes • Storm Drains• Sprinkler Heads• Power / Light Poles

– Not to “locate”underground utilities!

• Manholes • Storm Drains• Sprinkler Heads• Power / Light Poles

– Not to “locate”underground utilities!

Page 29: GPS: A Primer - MITweb.mit.edu/ncfmtc/pubs/Pugh_GPSPrimer.pdf© 2007, EMH&T, Inc. GPS: A Primer •GPS = G lobal Positioning System • 24 Satellites in Orbit around Earth • Each

© 2007, EMH&T, Inc.

PlanimetricPlanimetric

• Building Corners• Walls• Trails – Footpaths• Bike Racks• Benches – Bus Stops• Signage

• Building Corners• Walls• Trails – Footpaths• Bike Racks• Benches – Bus Stops• Signage

Page 30: GPS: A Primer - MITweb.mit.edu/ncfmtc/pubs/Pugh_GPSPrimer.pdf© 2007, EMH&T, Inc. GPS: A Primer •GPS = G lobal Positioning System • 24 Satellites in Orbit around Earth • Each

© 2007, EMH&T, Inc.

Emergency ManagementEmergency Management

• GPS is also for Navigation

• Hydrants• Emergency Call

Boxes• Valves

• GPS is also for Navigation

• Hydrants• Emergency Call

Boxes• Valves

Page 31: GPS: A Primer - MITweb.mit.edu/ncfmtc/pubs/Pugh_GPSPrimer.pdf© 2007, EMH&T, Inc. GPS: A Primer •GPS = G lobal Positioning System • 24 Satellites in Orbit around Earth • Each

© 2007, EMH&T, Inc.

AttributesAttributes

• While you’re collecting location, collect data!

• Pull-down menus• Valid Values –

Ranges• Required Fields

• While you’re collecting location, collect data!

• Pull-down menus• Valid Values –

Ranges• Required Fields

Page 32: GPS: A Primer - MITweb.mit.edu/ncfmtc/pubs/Pugh_GPSPrimer.pdf© 2007, EMH&T, Inc. GPS: A Primer •GPS = G lobal Positioning System • 24 Satellites in Orbit around Earth • Each

© 2007, EMH&T, Inc.

Base MapBase Map

Page 33: GPS: A Primer - MITweb.mit.edu/ncfmtc/pubs/Pugh_GPSPrimer.pdf© 2007, EMH&T, Inc. GPS: A Primer •GPS = G lobal Positioning System • 24 Satellites in Orbit around Earth • Each

© 2007, EMH&T, Inc.

Ground ControlGround Control

Page 34: GPS: A Primer - MITweb.mit.edu/ncfmtc/pubs/Pugh_GPSPrimer.pdf© 2007, EMH&T, Inc. GPS: A Primer •GPS = G lobal Positioning System • 24 Satellites in Orbit around Earth • Each

© 2007, EMH&T, Inc.

Cool Tools you can Use!Cool Tools you can Use!

Page 35: GPS: A Primer - MITweb.mit.edu/ncfmtc/pubs/Pugh_GPSPrimer.pdf© 2007, EMH&T, Inc. GPS: A Primer •GPS = G lobal Positioning System • 24 Satellites in Orbit around Earth • Each

© 2007, EMH&T, Inc.

ESRI ArcPad™ESRI ArcPad™

• Mini-GIS Integrates with GPS

• Draw, edit• Enhanced menus,

attribute collection• Works with many

Systems• Customizable

• Mini-GIS Integrates with GPS

• Draw, edit• Enhanced menus,

attribute collection• Works with many

Systems• Customizable

Page 36: GPS: A Primer - MITweb.mit.edu/ncfmtc/pubs/Pugh_GPSPrimer.pdf© 2007, EMH&T, Inc. GPS: A Primer •GPS = G lobal Positioning System • 24 Satellites in Orbit around Earth • Each

© 2007, EMH&T, Inc.

Laser RangefinderLaser Rangefinder

OffsetOffset

GPS LocationGPS Location

• Remote Positions– Under Canopy or

Overhang– In Trees

• Remote Positions– Under Canopy or

Overhang– In Trees

OffsetOffset

GPS LocationGPS Location

Page 37: GPS: A Primer - MITweb.mit.edu/ncfmtc/pubs/Pugh_GPSPrimer.pdf© 2007, EMH&T, Inc. GPS: A Primer •GPS = G lobal Positioning System • 24 Satellites in Orbit around Earth • Each

© 2007, EMH&T, Inc.

LaserCraft™ RangefinderLaserCraft™ Rangefinder

• Remote Positions– Under Canopy or

Overhang– In Trees

• Remote Positions– Under Canopy or

Overhang– In Trees

• Remote Measurements– Horizontal– Vertical

• Remote Measurements– Horizontal– Vertical

OffsetOffset

GPS LocationGPS Location

Pt 1Pt 1

Pt 2Pt 2

Page 38: GPS: A Primer - MITweb.mit.edu/ncfmtc/pubs/Pugh_GPSPrimer.pdf© 2007, EMH&T, Inc. GPS: A Primer •GPS = G lobal Positioning System • 24 Satellites in Orbit around Earth • Each

© 2007, EMH&T, Inc.

Ricoh GPS CameraRicoh GPS Camera

• GPS Ready• Data Embedded in

Digital Image• “Talks” with

Bluetooth enabled GPS and Rangefinders

• GPS Ready• Data Embedded in

Digital Image• “Talks” with

Bluetooth enabled GPS and Rangefinders

Page 39: GPS: A Primer - MITweb.mit.edu/ncfmtc/pubs/Pugh_GPSPrimer.pdf© 2007, EMH&T, Inc. GPS: A Primer •GPS = G lobal Positioning System • 24 Satellites in Orbit around Earth • Each

© 2007, EMH&T, Inc.

GPS: A PrimerGPS: A PrimerReferences:

• ArcPad, ESRI. http://www.esri.com/software/arcgis/arcpad/index.html

• Contour XLR, LaserCraft, Inc. http://www.lasercraftinc.com

• “General Information on GPS,”U.S. Coast Guard Navigation Center. http://www.navcen.uscg.gov/gps/default.htm

• “Global Positioning System: The Role of Atomic Clocks,” National Academy of Science. http://www.beyonddiscovery.org/content/view.article.asp?a=458

• “Global Positioning System Overview,” Peter H. Dana, The Geographer's Craft Project, Department of Geography, The University of Colorado at Boulder. http://www.colorado.edu/geography/gcraft/notes/gps/gps_f.html

• Ricoh Corporation. http://www.ricohsolutions.com/geo/

• Trimble, Inc. http://www.trimble.com/gps/index.shtml

References:• ArcPad, ESRI. http://www.esri.com/software/arcgis/arcpad/index.html

• Contour XLR, LaserCraft, Inc. http://www.lasercraftinc.com

• “General Information on GPS,”U.S. Coast Guard Navigation Center. http://www.navcen.uscg.gov/gps/default.htm

• “Global Positioning System: The Role of Atomic Clocks,” National Academy of Science. http://www.beyonddiscovery.org/content/view.article.asp?a=458

• “Global Positioning System Overview,” Peter H. Dana, The Geographer's Craft Project, Department of Geography, The University of Colorado at Boulder. http://www.colorado.edu/geography/gcraft/notes/gps/gps_f.html

• Ricoh Corporation. http://www.ricohsolutions.com/geo/

• Trimble, Inc. http://www.trimble.com/gps/index.shtml

Product names, logos, brands, and other trademarks featured or referred to within this presentation are the property of their respective trademark holders. These trademark holders are not necessarily affiliated with

EMH&T products or services nor sponsor or endorse these materials.

Page 40: GPS: A Primer - MITweb.mit.edu/ncfmtc/pubs/Pugh_GPSPrimer.pdf© 2007, EMH&T, Inc. GPS: A Primer •GPS = G lobal Positioning System • 24 Satellites in Orbit around Earth • Each

© 2007, EMH&T, Inc.

GPS: A PrimerGPS: A Primer

Thank you! Questions?For more information or a copy of this presentation,

please email [email protected]

Thank you! Questions?For more information or a copy of this presentation,

please email [email protected]