1. T215A Communication and information technologies (I) Block 2 Exploring and enquiring Session 12 Arab Open University 1

2. Session Outline Part 5: How the Global Positioning System works Introduction Basic principles Dealing with errors GPS receivers Conclusion 2 Arab Open University

3. 1. Introduction Currently, the only fully functional global navigation satellite system (GNSS) is the US’s GPS system based on a set of Navstar satellites. However, that this is not the only GNSS; others already exist or are being planned. Russia has a system, Glonass, that is currently being brought back into functional use after having been allowed to run down. In addition, a European system named Galileo is on its way. It began in-orbit testing of pilot satellites in 2008 and is expected to become operational, offering a greater accuracy than the US system, some time in the early–mid 2010s. China has also indicated its intention to build a GNSS system, and Japan and India are planning regional systems. 3 Arab Open University

4. 2. Basic principles [1] How GPS enables a receiver’s location to be determined? GPS satellites transmit radio signals that are picked up by the GPS receiver. The GPS receiver can calculate its distance from each of three satellites based on the speed of radio signals and the times taken for the signals from each satellite to reach the receiver. For each satellite, the GPS receiver must be located somewhere on the surface of a sphere centred on the satellite, and whose radius is the calculated distance from the satellite. The intersection of the spheres from two satellites restricts the possible location of the receiver to a circle. 4 Arab Open University

5. 2. Basic principles [2] How GPS enables a receiver’s location to be determined? (Cont.) The surface of the third sphere intersects this circle at just two points, and only one of these will be on the Earth’s surface. In theory, only three satellites are needed, but a fourth satellite is used in practice to provide the required level of measurement accuracy. In practice, the process is much more sophisticated. For instance, as well as measuring the propagation time very precisely, it is also necessary to allow for the fact that the speed of the radio signals from the satellites to the receiver is not constant but varies slightly within the Earth’s atmosphere. 5 Arab Open University

6. 2. Basic principles [3] One important requirement in GPS is that a GPS receiver needs to be able to locate the GPS satellites in the sky in order to lock on to the signals they are transmitting. How can it do that, given the satellites are moving continuously in relation to the surface of the Earth?! The answer is that the US Department of Defense, which is responsible for the satellites, publishes tables of the satellites’ positions at any given time, and these tables are programmed into each GPS receiver. 6 Arab Open University

7. 2. Basic principles [4] In details, how GPS enables a receiver’s location to be determined? 7 Arab Open University

8. 2. Basic principles [5] Step 1: Measurement of Propagation Time: This will show that the location obtained from the simple three-satellite triangulation is not as accurate as is needed for many purposes. This is the reason that four satellites are used. The signal that is transmitted from a satellite to a GPS receiver contains a sequence of code that runs continuously at both the GPS receiver and the GPS satellite transmitter. 8 Arab Open University

9. 2. Basic principles [6] The code in Figure 5.1 is a pseudo-random binary sequence, and it repeats every 1023 bits. 9 Arab Open University

10. 2. Basic principles [7] What is “Pseudo-random binary sequences”? A random binary sequence is a pattern of 1s and 0s that has no obvious pattern to it. A pseudo-random binary sequence is a random binary sequence that repeats over and over again. Pseudorandom binary sequences are useful because they combine some of the properties of random signals with some of the properties of signals that repeat regularly. 10 Arab Open University

11. 2. Basic principles [8] Step 2: Each satellite transmits its own dedicated pseudo-random binary sequence, which makes it possible to detect which satellite’s signal is being received. Further, pseudo-random binary sequences have some special properties that make it easier to detect and amplify the very weak signals reliably at the GPS receiver on the ground. The receiver therefore does not need the large antenna that would otherwise be needed for such weak signals. 11 Arab Open University

12. 2. Basic principles [9] 12 Arab Open University

13. 2. Basic principles [10] 13 Arab Open University

14. 2. Basic principles [11] Step 3: Assuming that the code sequences at both the transmitter and the receiver are running in perfect synchronism, the GPS receiver can compare the received code with the code already running at the receiver. The received code will appear delayed by the amount of time that it has taken to propagate from the transmitter – that is, it will appear to have been shifted in time. Step 4: adjustment in time is needed to bring the received and the receiver code sequences back into alignment. This is the adjustment for the time it takes for the signal to travel from the satellite transmitter to the receiver. 14 Arab Open University

15. 2. Basic principles [12] 15 Arab Open University

16. 2. Basic principles [13] Note: GPS needs to measure a time delay of somewhere around 60 or 70 ms to a precision of about 3 ns for a resolution of 1 m to be achieved. Note: A key assumption in the explanation of how the time the signal takes to travel to Earth is calculated is that the code sequences at the receiver are running in perfect synchronism with those at the transmitter.  This assumes very accurate clocks in both the satellite and the receiver  High accuracy atomic clocks are available, but they are very expensive! 16 Arab Open University

17. 2. Basic principles [14] The cost of such a clock can be justified on a GPS satellite (of which there are only a few), but not in a low-cost GPS receiver. The clocks in GPS receivers are, therefore, not sufficiently accurate to hold perfect synchronism with the clocks in the satellites and hence identify a precise location from three satellites. A solution to this problem lies in using a fourth satellite. A fourth satellite enables a correction to be made for the fact that the clock in the receiver may well not be in perfect synchronism. 17 Arab Open University

18. 2. Basic principles [15] Step 5: The position from three satellites is found based on three spheres centred on the three satellites, with the radius of each sphere equal to the measured distance between receiver and satellite. These three spheres meet at just two points, of which only one will be on the Earth’s surface. However, if the radii are slightly inaccurate (because they have been calculated from slightly inaccurate times) then the spheres won’t be in exactly the right place and so the point of intersection won’t be at the right place on the Earth’s surface. The GPS receiver will, therefore, report an erroneous position. It may only be a few metres in error, but the inevitable consequence of errors in the time measurements will be an erroneous position. This is where the fourth satellite comes in. 18 Arab Open University

19. 2. Basic principles [16] The GPS receiver uses this lack of coincidence as an indication that it needs to make a correction. It does this by searching for one single correction that it can make to all four of its timing measurements such that the fourth satellite measurement gives the same position as the other three. This brings the receiver’s clock back into synchronism with the satellite’s precise atomic clock and allows an accurate position value to be given. 19 Arab Open University

20. 3. Dealing with errors 3.1 Sources of errors [1] We saw how one sort of error, the error caused by inaccurate clocks in GPS receivers, is overcome. However, other ways in which errors can occur in GPS position measurements!! One important source of error is that the radio signals from the satellite do not travel at a constant speed on their journey to the Earth’s surface. Far more important is the fact that not all of the signal’s journey is in a vacuum. As the radio signal travels down from the satellite it begins to meet the Earth’s atmosphere, which slows it down slightly  The nearer to the Earth’s surface it gets, the denser the atmosphere is and the more slowly it travels. 20 Arab Open University

21. 3.1 Sources of errors [2] A further problem is that the radio signal’s speed depends on the weather conditions in the lower atmosphere. The speed on one day will be different from the speed on another day; indeed, the speed at one time on a particular day may be different from the speed at a different time on that day. There is no way of correcting completely for the speed variations, but the GPS system does have a built-in correction factor for an average situation, and GPS receivers apply this correction factor. 21 Arab Open University

22. 3.1 Sources of errors [3] Another error: because not all of the satellites from which a signal is being used will be overhead, then some of the signals will travel through more of the Earth’s atmosphere than others. NOTE: In fact, it would be very undesirable for them to be so, as a more accurate position value can be found when the satellites are well spread out around the sky. 22 Arab Open University

23. 3.1 Sources of errors [4] The signal from satellite A, which is fairly low in the sky, travels through more of the Earth’s atmosphere than does the signal from satellite B, which is overhead. 23 Arab Open University

24. 3.1 Sources of errors [5] Errors due to this problem can be corrected for, to some extent at least, provided the GPS receiver knows where each satellite is. GPS receivers have stored in them tables showing where the satellites are at any given time. This is useful not only for obtaining a ‘fix’ on a signal, but also for being able to calculate how much of the Earth’s atmosphere the signal will be travelling through, in order to make a suitable allowance for the speed of the radio signal in the atmosphere. 24 Arab Open University

25. 3.1 Sources of errors [6] Another error: the satellite may not be exactly where the stored tables say it should be! Satellites do not behave perfectly and may stray slightly from their planned orbit. This will affect any corrections the GPS receiver makes to allow for the radio signal’s journey through the Earth’s atmosphere. This source of errors is dealt with as follows: The US authorities constantly check the orbital paths of the satellites; when errors are detected in any satellite’s path, signals are sent to that satellite indicating its current path. The satellite then transmits this data and any GPS receiver on Earth can pick it up and use it to correct for the satellite’s position. 25 Arab Open University

26. 3.1 Sources of errors [7] Another source of errors is multipath propagation. This problem is caused by radio signals reflecting off nearby buildings or other objects at or near the ground. Good-quality GPS receivers employ sophisticated techniques to sort out the principal signal from the reflected ones so that they can reject the latter. 26 Arab Open University

27. 3.2 Differential GPS [1] Differential GPS is a relatively simple solution to some of the problems and errors described earlier. It requires a stationary GPS receiver in the vicinity of moving GPS receivers. The process works like this: The stationary receiver knows exactly where it is. Therefore, if, when it calculates its position from four satellites, it obtains an inaccurate position value it can work out what correction factor to apply to get the correct position value. It can then make this correction factor available to the other GPS receivers in its vicinity, which are effectively receiving the same satellite signals. These moving receivers can use the correction factor to make appropriate corrections to their calculated positions. 27 Arab Open University

28. 3.2 Differential GPS [2] Differential GPS is a very simple yet powerful idea. It can significantly reduce the position error in a GPS position reading. But it does depend on there being a stationary GPS receiver in the vicinity, and on the moving receiver being able to access the stationary GPS receiver’s correction data. Some private companies, for example security firms, have their own networks of stationary receivers. 28 Arab Open University

29. 3.2 Differential GPS [3] For the public, however, it’s a case of in some places it is possible to access data from stationary receivers while in others it is not – either because there are none or because they do not make the data available to the public. One exception to this is when mobile phones feature GPS receivers. In this case the mobile network operator can provide the correction data, using some of its base stations as sites for stationary receivers. Another way in which mobile telephone companies can support subscribers whose phones incorporate GPS receivers is to make their first fix on their position faster than it would otherwise be. This is known as assisted GPS (A-GPS), and is not a matter of error correction, but of providing a faster GPS service on start- up. 29 Arab Open University

30. 3.2 Differential GPS [4] Activity 5.6 : Which of the following sources of errors (from Section 3.1) would you expect differential GPS to correct, partially or wholly? Why? (a) The variable speed of radio signals in the Earth’s atmosphere. (b) The fact that a particular satellite may have strayed slightly from its orbit. (c) Multipath propagation. Solution (a) Errors due to the variable speed of radio signals should be very much reduced. This because the distances travelled from the satellites are nearly the same from the stationary and roving receivers, and the atmospheric conditions very likely the same too. But the errors will probably not be removed entirely: the distances are not identical and there may be local weather conditions (e.g. a localised rainstorm). 30 Arab Open University

31. 3.2 Differential GPS [5] (b) Although the differential GPS system could possibly correct errors due to inaccurate satellite position, there is no need for it to do so. This is because, as you saw in Section 3.1, each satellite transmits information about where it actually is, and roving GPS receivers can use this data to make corrections without reference to a stationary GPS receiver. (c) There will be no effect on errors due to multipath propagation, which is a highly local problem. 31 Arab Open University

32. 4. GPS receivers [1] Functional block diagram of a GPS receiver 32 Arab Open University

33. 4. GPS receivers [2] As with a mobile telephone, therefore, the radio signals are captured by an antenna, manipulated, converted to digital format and then processed. All of this is under the control of a processor that also deals with user inputs, the display and any synthesised speech output. Just as specialised integrated circuits are sold to perform all of the major functions of a mobile telephone, so they are sold to perform all of the major functions of a GPS receiver. This is one of the ways in which GPS receivers have been able to become smaller and lighter since their inception. In fact, they could not become much smaller without the screen becoming too small for convenience. And as with all mobile devices, the battery’s size, weight and capacity are important issues. 33 Arab Open University

34. 5. Conclusion The GPS system enables one’s location to be determined through signals from four satellites: three to fix a position and the fourth to supply the necessary correction. Inaccuracies in this position are due to variations in the speed of radio signals in the Earth’s atmosphere, to small variations in the orbits of the satellites and to multipath fading near the GPS receiver. Differential GPS, where available, can help to overcome the first of these three sources of inaccuracy. Although a GPS receiver performs many of the same functions as a mobile telephone, at the detailed level the functional blocks perform their tasks differently. 34 Arab Open University