 time to all of you. I am Mr. Sheshikant B. Gosavi, Assistant Professor, Department of Civil Engineering, Valchan, the Institute of Technology, Sulapur. Today we are going to discuss regarding global positioning system coordinates based on which we will have some learning outcomes. At the end of this session, students will be able to explain the coordinate systems. They will be able to compare various coordinate systems used in global positioning system. The student will also be able to convert one coordinate system into the other coordinate system. Wow, this is a wonderful picture of how the global positioning system works. The conventional nav star used to have around 24 number of satellites into the space placed in a systematic manner. And the orbits of various satellites is beautifully displayed in this picture. The total satellites were 24 plus and the distance of the satellites from the earth was around 20,200 kilometers. The inclination used to be 55 degrees and orbital period of each of the satellite was 12 hours. There were five ground control stations to enable data exchange with these satellites. Each satellite passes over a ground monitoring station every 12 hours. The GPS is supposed to have three components, ground control point, the space segment and the user segment. At the bottom, you can see the planimetric view of the whole world around which the satellite used to move. This is the classical example of how exactly the GPS functions. This is a geometrical explanation. The earth itself is a big sphere. The distance of the satellite from the earth is what we call as the range. At a given time when the instrument transmits the wave, the satellite, whatever are the waves which are sent will be received by the instrument. And based on the time traveled between the transmission and reception, gives us an idea about what should be the distance or range of each of the satellite from the earth. Each satellite will give their respective range. So, satellite number one will be having this much distance from the ground point. Satellite two will be having this much distance from the ground point. Satellite three will be having this much distance from the ground point. And therefore, intersection of all these spheres actually enables us to get exact data of coordinates of a point on earth. As has already been told, it is a spherical trigonometry which is dominant in this case. This is the principle of geolocation with GPS. So, because of the trial iteration, we are able to find out position of each of the object on earth with the help of the satellites. And then later on, GPRS or GSM technique allows us to exchange the data. Finally, the things can go into the cartography or mapping science. The Cartesian coordinate system, all of us are familiar. That is a planar coordinate system. We are very much familiar about the y coordinate and x coordinate quadrant. And then in the first quadrant, positive, positive. In the second quadrant, x axis will be positive, y will be negative and so on and so forth. This is one of the very, very well known coordinate system which we are familiar with. This is particularly true for the planar drawings. Map projection is one of the very important part of GPS coordinates. Because what we are actually doing is the spherical surface of the earth we are supposed to project onto the plane drawing sheet or the computer screen. There are several ways of doing that. You can have a shape like a cone, you can have a shape like a sphere and accordingly there will be variation in the projection system. So, projection system is very, very important for us to make our positioning of the point on earth valid in terms of geodetic coordinates. Just now I have spoken regarding geodetic coordinates. All of us are familiar that there are planar coordinates wherein x and y coordinates were there. In geodetic coordinates however, we are working on the surface of earth which is a sphere. So, here the spherical trigonometry plays major role. WJS84 is the most reliable coordinate system with the help of which we can get exact idea about how the things can be done in relevance to the respective thing. Here you can see the shape of this particular sphere. It is ellipsoid while this is the conventional spheroid. Of course, both of them are having their shapes. This is oblate and this is prolet. Oblate is the one which is used in case of the world geographic coordinate system. Here the classical coordinates like latitude, longitude, altitude in reference to WJS84 system have been shown. Here you can see 0 meridian is assumed to be over here. All of us are familiar that through the green which the geographic meridian goes with reference to which the longitudes of the various points on earth are recorded. And equatorial plane is most often taken as the respective 0 latitude plane. Above the equator towards north the respective points are assumed to be taken with positive coordinates and on the lower side with the negative coordinates. So, it will have plus in the northern side minus on the south side. Similarly with reference to the meridian towards east and towards west we will have certain coordinates. This is again another classical way of showing the word geodetic system. You can see that earth is not perfectly sphere. So, it is ellipsoid having the variation into radius almost everywhere. Along the equatorial plane the radius is largest while perpendicular to east it is smallest. So, here it is 6378.137 kilometer while towards the polar axis it is 6356.7523 kilometer. The mean radius of the earth if we will assume it to make up a sphere in that particular case comes out to be 6371.0088 kilometer. This is very important for us to know. So, a measurement is equatorial measurement, b is a polar measurement and mean earth radius which is shown here in red is another way of presenting it. There are several ways of having the coordinates. This is earth centered earth fixed coordinate system. Here the center of the earth is taken as the origin and with reference to that distance a, distance b and radius etcetera are worked out. This is the radius along the prime vertical which we can easily work out by knowing the values of a and b as well as we can work it out with reference to the angle phi. So, n phi that is radius of the prime vertical plane will be equal to a square divided by square root of a square cos square phi plus b square sin square phi. ECEF coordinate system are better version of presentation of geodetic coordinates. We have a liberty of conversion of units of geodetic coordinate system. The numerical value of latitude and longitude can occur in a number of different units of format. The classical is sex as decimal degree which is degree minute and second system 40 degree 26 minute 46 second is an example of how we can present it. A degree and decimal minute is keeping the degree same, but the minutes are converted into the decimal. So, you can see the minutes represented over here as 26.767. The decimal degree actually converts everything into decimal and present it in front of you. Coordinate system conversion is at most important. pq which is a prime vertical radius as has been shown over here. This is p, this is q. So, this pq is said to be n phi. The length iq this particular distance is e square n phi that is e square multiplied by the radius at prime vertical and r is classical coordinate system of x, y, z. So, what we are aiming at is converting x, y, z are getting the x, y, z from the geodetic coordinates of phi, l and the respective height h. These are the equations corresponding to that. If you have the knowledge of n phi, h phi and lambda you can obviously convert it to the x, y, z coordinates. Please pause the video for a while and answer following questions. Comment about what are different coordinate systems. Similarly, how can we convert the formats of coordinate systems? The answers have been given in this particular slide for your information. I have used the reference of this websites for getting the information into this online educational resource. Thank you very much.