This document is a certificate and report submitted by Harshit Bansal for their class project on the Global Positioning System (GPS). It includes an acknowledgement of their physics teacher, an index of topics to be covered, and sections on the introduction to GPS, the concept of using satellite signals and trilateration to determine position, how additional satellites improve accuracy, and common sources of error. The report provides an overview of how GPS works to allow devices to calculate their location using signals from multiple satellites.

1. Submitted by:- Harshit Bansal
Class :-XII A
Roll no.:- 15

2. Certificate
• This is here by to certify that the original and
genuine investigation work has been carried out to
investigate about the subject matter and related data
collection which has been completely solely,
sincerely and satisfactory done by Harshit
Bansal of class XII-A of global positioning
system(GPS). SIGNATURE

3. ACKNOWLEDGEMENT
It would my utmost pleasure to express my
sincere thanks to my physics teacher MR.
NITIN KHABRANI in providing a helping
hand in this project.
His valuable guidance and support and
supervision all through this project are
responsible for attaining its present form.

4. Index
Introduction
Review of GPS concept
Theory of positioning
Start with first satellite
Second satellite gives the points
Third satellite sets the location
Speed equation
Uses of gps
Gps source Error
Bibliography

5. • TheGLOBAL POSITIONING SYSTEM
(GPS) is a satellite based navigation system that
consists of 24 orbiting satellites, each of which
make two circuits around the Earth every 24 hrs.
• These satellite transmit three bits of information-
the satellite’s number, its position in space ,and
the time the information is sent.
• These signals are received by the GPS receiver ,
which uses this information to calculate the
distance between it and the gps satellite.
Introduction

6. Review of GPS
concept
The GPS concept is based on time . The satellites carry very
stable atomic clocks that are synchronized to each other and
to ground clocks . Any drift from true time maintained on the
ground is corrected daily . Likewise , the satellite locations
are monitored precisely GPS receivers have clocks as well –
however, they are not synchronized with true time, and are
less stable.. A GPS receiver monitors multiple satellites and
solves equation to determine the exact position of the receiver
and its deviation from true time. At a minimum, four
satellites must be in view of the receiver for it to compute four
unknown quantities (three position coordinates and clock
deviation from satellite time).

8. Theory of Positioning
Trilateration
Measuring distance
Accuracy of time and location
of satellite

9. • A method for determining the
intersections of the given sphere
surfaces given the centers and radii of
the three surfaces.
d?
α βl
r1
r2
r3
B
Trilateration

10. Let’s assume several factors for easy
understanding.
• GPS satellite are on the ground (3D-2D)
• We know the exact location of the
satellite.
• We can calculate the distance from each
of the satellite.

11. Start by determining your position
The receiver
is
somewhere
on this
sphere.

12. Adding more distance measurements to
satellites narrows down your possible
positions

13. A
Now you know that you are at
A

14. Trilateration is a common operation to find the
object location using its distances or range
measurements to three other known points or
stations.
Traditionally ,this problem has been solved either
by algebraic or numerical methods. These
methods involve long and complex geometric
computations which are usually implemented in
software. An approach that avoids this
complexity is proposed here.

15.  Simulation results show improvements of the proposed
approach in terms of computational cost and
implementation simplicity over the proposed approach is
based on vector rotations and uses only simple add and
shift operations and therefore can be easily implemented in
the hardware (or firmware) of the mobile.
 In geometry, trilateration is the process of determining
absolute or relative locations of points by measurement of
distances, using the geometry of circles, spheres or
triangles.
 In addition to its interest as a geometric problem,
trilateration does have practical applications in surveying
the navigation including global positioning system (GPS). In
contrast to triangulation, it does not involve the
measurement of angles.

16. In two-dimensional geometry, it is known that if a
point lies on two circles, then the circle centres on the
two radii provide sufficient information to narrow
the possible locations down to two.. Additional
information may narrow the possibilities down to
one unique location.
In three- dimensional geometry, when it is known
that a point lies on the surface of three spheres along
with their radii provide sufficient information to
narrow the possible locations done to no more than
two (unless the centers lie on a straight line).

17. The 4th satellite in trilateration is to resolve any
signal timing error
•Unlike GPS satellites, GPS receivers do not
contain an atomic clock
•To make sure the internal clock in the receiver is
set correctly we use the signal from the 4th
satellite

18. Three Dimensional (3D) Positioning

19. MEASURING THE DISTANCE
• Using the Pythagoreans theorem to calculate distances?
• First, both sets of coordinates need to be in UTM.
• Existing Geocaches have them on the cache detail page.
• Your personally retrieved coordinates in your GPS can be
converted by changing the setting on the GPS to UTM.
• Finally you can convert them using the online calculator at
JEEEP. Com conversion page .
• Once both sets of coordinates are in UTM assume the
following:
Northing 1= ‘N1” Easting 1=“E1”
Northing2= “N2” Easting2 = “E2”
• UTM uses meters from reference points , so the positions are
already metric .
• Subtracting the northing’s gives you the distance in meters
north to south(a)
• Subtracting the easting’s gives you the distance in meters east
to west(b).
• Since a²+b²=c², that translates into sqrt(a^2+b^2)=c
• C is the distance in meters. Divide by 1000 to get kilometres.

20. Speedequation
• GPS receiver uses speed equations to
calculate the distance to satellites.
•Distance = speed * duration
(time)

21. GPSsatellitesuseradiosignal
• Instead of throwing balls, the GPS satellites
send radio wave and GPS receivers catch
them.
• Radio wave fly at the same speed of light.
about 300,000 km/s.

22. SignalfromGPSsatellite
Each satellites continuously transmits
messages including :
The time the message was transmitted
Precise orbital information (location of itself).
Rough orbits of all GPS satellites (the
almanac)

23. UseofGPS
 GPS systems are extremely versatile and can be found in almost every
sector. They can be used to map forests, help farmers harvest their fields ,
and navigate airplanes on ground or in the air. GPS systems are used in
military applications and by emergency crews to locate people in need of
assistance. GPS technologies are often working in many areas that we do
not normally consider .
 GPS applications are generally fall into five major categories :
1) Location – determining a position
2) Navigation – getting from one location to another
3) Tracking - monitoring object or personal movements
4) Mapping – creating maps of the world
5) Timing – bringing precise timing to the world
 Some of the applications that GPS systems are currently being used for
around the world include mining, aviation, surveying ,agriculture, marine,
recreation and military. These days doctors , scientists, farmers, soldiers,
pilots, hikers, delivery drivers, sailors, fisherman, dispatchers, athletes,
and people from many others walks of life are using GPS systems in
ways that make their work more productive, safer and easier.

24. GPS Error Sources
 Satellite errors
Satellite position error (i.e., satellite not exactly where it’s
supposed to be)
Atomic clocks, though very accurate, are not perfect
 Atmospheric
Electro-magnetic waves travel at light speed only in a
vacuum
Atmospheric molecules, particularly those in the
ionosphere, change the signal speed
 Multi-path distortion
The signal may "bounce" off structures before reaching the
GPS receiver – the reflected signal arrives a little later

25. Bibliography