Global positioning system (gps)

Physics Investigatory

Project

Submitted by:- Harshit BansalClass :-XII ARoll no.:- 15

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

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.

Index Introduction

Review of GPS concept Theory of positioning Start with first satellite

Second satellite gives the points Third satellite sets the location

Speed equationUses of gps

Gps source ErrorBibliography

• The GLOBAL 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

Review of GPS conceptThe 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).

Theory of PositioningTrilateration

Measuring distance

Accuracy of time and location of satellite

TRILATERATION

• A method for determining the intersections of the given sphere surfaces given the centers and radii of the three surfaces.

d?

α βl

r1r2

r3

B

Trilateration

Simplifying the problemLet’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.

START WITH FIRST SATELLITE

Start by determining your position

The receiver is somewhere on this sphere.

Second satellite gives the points

Adding more distance measurements to satellites narrows down your possible positions

Third satellite sets the location

A

Now you know that you are at A

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.

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.

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).

Real Trilateration in 3-D space

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

Three Dimensional (3D) Positioning

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.

Speed equation

• GPS receiver uses speed equations to calculate the distance to satellites.

•Distance = speed * duration (time)

GPS satellites use radio signal

• 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.

Signal from GPS satelliteEach 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)

Use of GPS 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 another3) Tracking - monitoring object or personal movements4) Mapping – creating maps of the world5) 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.

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

AtmosphericElectro-magnetic waves travel at light speed only in a vacuumAtmospheric 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

Bibliography