Global Positioning System (GPS) is the system which is used for navigation purpose.  Previously many systems like TRANSIT, LORAN and VOR are there for navigation purpose. But GPS is highly efficient than all other systems. Now GPS is the primary system for all navigation like ships, aircrafts and surveying etc.

GPS used L-band signals. L-band signals are in the frequency range 1-2 GHz. GPS transmits two codes. One is C/A code and other one is P code. P code is used for the military purposes and C/A code is available for the public usage. In military purposes, sensitive data is transmitted. So the data should be highly secured. So the P code is encrypted and transmitted as Y code. So the receiver must know the decryption algorithm for decoding the position of the satellite. So normal receiver can’t decode the code because it doesn’t know the decryption algorithm. Using GPS, we can find the position with a typical accuracy of 30m.

GPS system consists of 24 satellites which are placed in medium earth orbits. They are at an height of 20,200 Km from the surface of the earth. The satellites are inclined at an angle of 55° with the equatorial plane. And the groups of four satellites are called as constellation. Each constellation separated by a 60° in longitude. The orbital period of the GPS satellite is one half of the side real day. i.e., 11 hours 58 minutes. So a typical satellite appears in the same position in the sky for two times. The GPS system is designed such that receiver at any place can pickup signals from at least 4 satellites. It can receive signals from 12 satellites too. Sometimes due to some problems, satellites stop functioning. For this purpose, backup satellites are also launched in their orbit. If any of the satellite stops functioning, then this backup satellite serves the users. In general around 30 satellites are there in the orbit.


Figure: GPS system with satellites

The GPS system is controlled by master control station (MCS) which is present in the Falcon Air Force Base in Colorado Springs, Colorado. Some subsidiary stations are also used for the monitoring purposes. Master control station and other stations calculate atomic clock error, ephemeris data for each satellite and other factors which are needed for the navigation message.  By using ephemeris data, we can know the position of satellite in the space. The master control station transmits the data to the satellites by using S-band link. If any error is present, then these master control station sends the data within 1.5s for the navigation purpose.

Position of the GPS receiver is found by using the method called trilateration.   It is the one of the simplest method for finding the unknown position. In this method, three satellites are selected and by considering the satellite as the centre of the sphere and the distance between the satellite and the receiver as radius, a sphere is drawn. So from three satellites three spheres are drawn. These three spheres intersect at two points. By eliminating one point during the calculation purpose, we find the position of the receiver.

Sometimes enemies target the GPS system. So to avoid that, a process called selective availability is used. The accuracy of a GPS receiver is degraded some of the time by a process called selective availability. Selective Availability causes variations in the C/A code transmissions and that result in inaccurate calculation of the position of the receiver.  If SA is used, then the position may be shifted up to 200m. But this process is now switched off by the US government. If in case of emergency, then it will be reinstituted if the US president permits it.

The distance between the satellite and the receiver is called as range. Range is calculated from the time delay introduced by the signal travelling from the GPS satellite to the GPS receiver. The waves are EM waves which travel with velocity of light.

Each GPS satellite has 4 atomic clocks. Atomic clock has 1 in 1011 accuracy. Atomic clocks are very costly. So GPS receiver use crystal oscillator. Crystal oscillator has 1 in 105 or 1 in 106 accuracy. So the receiver clock is allowed to have an offset relative to the Satellite clocks. Due to this, when time delay is measured, the receiver clock has an offset error. If the clock offset is 10msm, then the position of the receiver may be shifted up to 3000km. So it is important to synchronize the GPS satellite time and the GPS receiver time.

So for finding this offset error we consider 4 satellites during the position calculation. Then from 4 equations, we find the latitude, longitude, elevation and the clock offset.

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