Global positioning system and its mathematical form. By Mustahsan Khan _ BS(physics-Nanotechnology) (International Islamic University Islamabad) Pakistan.

1. GPS (Global Positioning
System)

2. Presented by:
 873- Mustahsan Khan
 - Akbar Shahis
 Abdul Wahab
 Mohsin Bin waqar
 Sohail Ahmad

3. What is GPS ?
GPS or Global
Positioning System is a
network of orbiting
satellites that send
precise details of their
position in space back to
earth. The signals are
obtained by GPS
receivers, such as
navigation devices and
are used to calculate the

4. When & Why it was Developed ?
The very first GPS system
was developed in the 1960s
to allow ships in the US
Navy to navigate the oceans
more accurately. The first
system had five satellites
and allowed ships to check
their location once every
hour.
GPS is well-known for its
military uses and was first

5. Segmentations of GPS
The Space Segment
The Control Segment
The User Segment

6. The Space Segment
Consists of 24 satellites in 6
orbits.
 a constellation of between
24 and 32 solar-powered
satellites orbiting the earth
in orbits at an altitude of
approximately 20000
kilometers,
Each satellites transmits low

7. The Control Segment :
A Master Control
Station
Unmanned
Monitor Stations
Large Ground-
antenna Stations

8. The User Segment :
 Users-Military and Civilians
 GPS Receivers
 Decodes the signals from Satellites.
 Calculate the distance.

9. What signal does GPS use :
 There are currently between 27 and 32 global positions
system (GPS) satellites in orbit around the earth. Of
these, three act as backups. Each satellite transmits a
regular GPS signal that is carried by radio waves in the
microwave part of the electromagnetic spectrum.
 microwave carrier frequency of approx 1600 MHz

10. How does GPS work?
 Each of the satellites is in an
orbit that allows a receiver to
detect at least four of the
operational satellites. The
satellites send out microwave
signals to a receiver where the
built-in computer uses these
signals to work out your precise
distance from each of the four
satellites and then triangulates
your exact position on the
planet to the nearest few meters
based on these distances.

11. What is Trilateration?
 A GPS receiver uses trilateration
(a more complex version of
triangulation) to determine its
position on the surface of the
earth by timing signals from three
satellites in the Global Positioning
System. The GPS is a network of
satellites that orbit the earth and
send a signal to GPS receivers
providing precise details of the
receiver's location, the time of
day, and the speed the device is
moving in relation to the three
satellites.

12. Determination of Position:
 By Triangalization.
 Triangulation is the
mathematical principle that
explains how GPS works.
 There are two types of
triangulation: 2-D and 3-D.
 GPS uses 3-D triangulation.
3-D has the capability to tell
altitude or height, while 2-D
doesn’t have that capability.

13. Calculation & Determination of a position :
 For determining the positions , Some relations are there :
 we let Delta ti = Ti' - Ti,
 X Y Z are the axis
 epsilon represent any error in our clock's time.

14. Calculation of Position :
 Satellites Location
 Almanac data
The GPS Almanac is a set of data to describe the orbits of the complete
active fleet of Satellites. GPS receivers use the almanac to determine
"approximately" where the satellites are relative to the local sky. It then uses
this information to determine what satellites it should track.
 Time is the essence
 Velocity * Time=distance

15. Sources of Error :
Ionosphere Delays
Troposphere Delays
Clock Error
Multi-path Error
Relativity Error

16. Applications and Industry
Agriculture
Mapping & GIS Data Collection
Public safety
Surveying
Telecommunication