GPS Simulation

8/4/2019 GPS Simulation

1/16

GLOBAL POSITIONINGSYSTEM

PROJECT ON MATLAB BY THETEAM: Amar Kashyap.S

Ayush SharmaJayanth Kumar.AAbhimanyu Kohli

Mohd.Sharief


2/16

What is GPS?

The Global Positioning System (GPS) is aspace based radio positioning/navigationsystem that will provide three-dimensionalposition, velocity and time information tosuitably equipped users anywhere on ornear the surface of the earth.


3/16

GPS SIMULATION-COURTESY MATLAB

The satellites share a common time system known as GPS timeand transmit (broadcast) a precise time reference as a spreadspectrum signal at two frequencies in L-Band: L1=1575,42 MHz,L2=1227,6 MHz. Two spread spectrum codes are used: a civil

coarse acquasition (C/A) code and a military precise (P) code. L1contains both a P band a C/A code, while L2 contains only the Pcode.

The accuracy of both codes is different. The receiver of the civilcode cannot decode the military P code when the security statusSelective Availability in GPS satellites is turned on.

With selective availability turned on, military users determinetheir location within 17,8 m, while civilian users determine theirposition within an accuracy of 100m; hence selective availabilitydegrades the navigation information to all civil users.


4/16


5/16

We are trying to write a code using MATLABwhich is the same as used in GPS receivers.The code will take the distances (as inputs)send by satellites which is between thesatellite and the point. Also the code willknow the position of satellites in space.


6/16

But there is one problem: we cannot determine the d i

distances exactly. There is an error term. As a result of these errors, the circles do not intersect at one exact

point. Each circle intersects the other circle at twodifferent points. From the below figure, we can seethat an area biguity area) is formed as a result of theintersection of the circles. We know that our point P

lies in this area but we do not know its exact location.(ambiguity area) is formed as a result of theintersection of the circles. We know that our point Plies in this area but we do not know its exact location


7/16


8/16


9/16

P is the location where we read GPS outputs. Ris the radius of the earth. E r i is the distance of the satellite i from the center of coordinate

system. o is the center of earth and center of our coordinate system. dis the distance at any time send from the satellite to our

point P. i

When we read output from GPS receiver, dio

is the data sentfrom GPS satellite. d i is a random variable and we assume that d i has a normal pdf

with = d io and = 50m. (normally this can be 10m but to be

on the safe side we take this as 50m).


10/16


11/16

Inputs and outputs of the reciever When the user of GPS receiver wants the output as lateral and

longitudinal coordinates on earth, the inputs of the receiverwill be

1. Radius of the earth; r = RE (Assumption: Earth is assumedto be spherical).

2. Place of satellite i (for i =1,,N); i, i, ri in sphericalcoordinates.

3. Distance between satellite i (i =1,,N) and our location; dio.(Taken from satellite i, by the GPS gadget).

4. Probability distribution of di and we assume that di has anormal pdf with = dio and = 50m.


12/16

Inputs to the code

Inputs to the code Enter the latitude of point 29.0523611 Enter the longitude of point 41.0835 Enter the number of satellites 2


13/16

Enter the height of the satellite 1 in meters 20243200 Enter the alpha of the satellite 1 in degrees 25.6 Enter the beta of the satellite 1 in degrees 9 Enter the distance between the satellite 1 and the point where we take

measurement, send from satellite 1(1)

15237610


14/16

Enter the height of the satellite 2 in meters 20197500 Enter the alpha of the satellite 2 in degrees -42.2 Enter the beta of the satellite 2 in degrees 43.3 Enter the distance between the satellite 2 and the point where we take

measurement, send from satellite 2(2)

16945900 note about (1),(2): These are the figures that we get from the GPS receiver. But they are not the exact

values. The exact ones are: (1). 15237604, (2). 16945895.


15/16

outputs

Your position estimation using mass center 41 5 6.486010e-002 North 29 3 1.152029e-001 East Your position estimation using most probable point 41 5 6.486028e-002 North 29 3 1.152027e-001 East Error of the estimation 6.451908e+001


16/16

Thank You

GPS Simulation

Documents