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What is GPS below
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GPS and Map Apps
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Recreation:
  Using a Handheld GPS
  Geocaching
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Location & Mapping for mobile phones

What is GPS?
The Global Positioning System (GPS) (also called NAVSTAR, the official U.S. Department of Defense name for GPS) is a satellite-based navigation system made up of a network of 24 satellites placed into orbit by the U.S. Department of Defense. GPS was originally intended for military applications, but in the 1980s, the government made the system available for civilian use. GPS works in any weather conditions, anywhere in the world, 24 hours a day. There are no subscription fees or setup charges to use GPS.

How it works:
GPS satellites circle the earth twice a day in a very precise Semi-Synchronous orbit and transmit signal information to earth. GPS receivers take this information and use triangulation to calculate the user's exact location. Essentially, the GPS receiver compares the time a signal was transmitted by a satellite with the time it was received. The time difference tells the GPS receiver how far away the satellite is. Now, with distance measurements from a few more satellites, the receiver can determine the user's position and display it on the unit's electronic map.

In some places 12 satellites are visible simultaneously. Any location on earth will have, at the minimum, four satellites visible to it.
A given GPS satellite will be accessible for 5-10 hours. Less if visibility of the horizon is obscured.

gps orbit
LEO - Low Earth Orbit, MEO - Medium Earth Orbit

Accuracy:
Usually within 25-50 ft.
Receivers with WAAS (Wide Area Augmentation System) capability can improve accuracy to less than 10 ft. on average.
WAAS is an air navigation aid developed by the Federal Aviation Administration to augment the Global Positioning System (GPS). WAAS uses a network of ground-based reference stations, to measure small variations in the GPS satellites' signals. Correction messages are sent to geostationary WAAS satellites. Those satellites broadcast the correction messages back to Earth.

To get more accuracy you can take several reading 90 minutes apart and average them.

Sources of error:

Code noise, receiver noise, satellite clock - 1 m each
Ephemeris data error, troposphere delay - 1 m each
Unmodeled ionosphere delay - 10 m, multipath - 1 m
Satellite constellation geometry - 10 m

Some receivers also use GLONASS, the Russian version of GPS, which also improves accuracy.


Glossary:
2D RMS or 2drms - Twice-distance Root Mean Square - A horizontal measure of accuracy representing
the radius of a circle within which the true value lies at least 95 percent of the time.
Anywhere fix - The ability of a receiver to start position calculations without
  being given an approximate location and approximate time.

A-GPS - Assisted GPS uses Cell tower triangulation to provide an immediate approximation of your location, even while indoors. Based off of this data it can very quickly lock onto the correct satellites to provide true GPS data. 
A-GPS - Assisted GPS - Provides supplementary information enabling reduced 
 'time to first fix' so that users get position very quickly at power on.
DGPS - Differential GPS - A form of corrected GPS giving enhanced accuracy
  in the few decimeter range. EGNOS is a dGPS service.
(better than stand alone GPS, not as good as RTK).
ARNS - Aeronautical radio-navigation service - Uses a special GPS frequency.
C/A Code (Coarse/Acquisition Code) - The standard positioning signal for the civilian user.
DMRs - Delay-mapping receiver - Special GPS which measures signal reflected from the earth.
DOP - Dilution of Precision - A factor based on signal strength and location of
  satellites that indicates accuracy.  DOP of 2 is really good, 20 is really bad.
EGNOS - European Geostationary Navigation Overlay Service - Provides GNSS
 augmentation. Consisting of three geostationary satellites and a network of ground
 stations.
ETA - Estimated time of arrival
ETE - Estimated-Time-Enroute
Galileo - A European operated GNSS scheduled to start in 2008.
 Galileo and GPS combined will lead to improvements in position quality,
 even in very harsh environments.
GDOP - Geometric dilution of recision - See DOP.
GLASNOSS - Similar Russian System
GLONASS - Global Navigation Satellite System
GNSS -  Global Navigation Satellite System - Generic term for systems
 such as GPS and Galileo.
GPS - Global Positioning System - System of 24 U.S. Satellites.
  10-20 m accuracy w/o WAAS.
GPS III - A new initiative by the U. S. government to upgrade the current GPS system,
  which includes replacing all current satellites.
GPX - GPS eXchange format -  An XML schema designed for transferring GPS data between
   software applications. It can be used to describe waypoints, tracks, and routes.
Marlin A-GPS Chip Set - Acquires satellites with signals down to \0x2212160dBm.
  Enables position availability in harsh signal environments
  (deep indoor and urban canyon). For use in mobil phones.
Multi-channel receiver - A GPS receiver that can simultaneously track more than one satellite signal.
   Even though you only need 4 satellites a 12-channel system will keep track
   of others so when one disappears over the horizon it can quickly switch.
NEMA - National Marine Electronics Association -
   Interface Standard (NMEA 0183) for data exchange between marine electronic devices.
PPS - Precise Positioning Service - The highest level of military dynamic positioning
  accuracy provided by GPS, using the dual-frequency encrypted P-code. Was military only.
  SA is turned off.  Accuracy of at least 22m (2d rms, 95%) in the horizontal plane and
   27.7m (95%) in the vertical plane. Users in mid latitudes (especially in North America) 
  can expect significantly better horizontal accuracy (less than 10 meters) 
Quadrifilar Helix Antenna - Also known as Quadhelix Antenna. A type of antenna in which four
spiraling elements form the receiving surface of the antenna. 
Unlike Patch Antennas which are flat, Quadrifilar Helix Antennas are encased either
in a plastic cylinder or within the GPS unit itself, resulting in a GPS unit that gets
the best reception possible.
P-Code - The precise code of the GPS signal typically used only by the U.S. military.
RNSS - Radionavigation satellite service 
RTK - Real Time Kinematic - A form of corrected GPS giving accuracy down around 20 mm.
SA - Selective Availability - A policy adopted by the Department of Defense to introduce
some intentional clock noise into the GPS satellite signals thereby degrading their accuracy
for civilian users. This policy was discontinued as of May 1, 2000, and now SA is turned off.
SPS - Standard Positioning Service - Uses single frequency C/A code.
  Accuracy is 100 m 2DRMS (95% of the time.)
SBAS - Space Based Augmentation System - Any system that uses a network of
 geostationary satellites and ground stations to enhance the performance of a GNSS.
SiRF - Fast acquisition GPS chipset from SiRF techlology
Static positioning - Location determination when the receiver's antenna is presumed to be
 stationary on the earth. This allows the use of various averaging techniques that improve
 accuracy by factors of over 1,000.
UTM - Universal Transverse Mercator - A nearly worldwide coordinate projection system using
  north and east distance measurements from reference point(s). UTM is the primary coordinate
  system used on U.S. Geological Survey topographic maps. 
WAAS - Wide Area Augmentation System. Developed by FAA for aircraft navigation.  
  Provides accuracy of better than 3 m. 95% of the time.
WGS-84 - World Geodetic System, 1984 - The primary map datum used by GPS.

A Glossary of GPS Terms at U. New South Wales, AU
Map GPS Glossary at maps-gps-info.com

Links:
GPS_sat_constellation
Satellite Orbits
What is the major technological change that has dramatically improved GPS acquire time? - Electrical Engineering
Garmin | What is GPS?
Map coordinate Systems
GPS's in Products
Geocaching in Recreation
Goecaching to GPS and Map Apps for tablets and smart phones
Todd Humphreys: Millimeter GPS using carrier phase technology with current signals - Spoofing GPSs | Video on TED.com