Global Positioning System – Clive VK6CSW

The inquisitive nature of man has always driven him to explore and to widen his horizons in both the physical and mental sense, and over the ages he has developed ever more sophisticated means of navigating. Navigation by compass and star has served man for centuries with steady refinement of technique, but the earth’s magnetic field changes constantly and dense cloud cover makes astro-nav impossible. Self-contained inertial navigation systems are much better but, unless they can be periodically updated, their accuracy diminishes with elapsed running time. The latest navigation system is the Global Positioning System – GPS – which has the potential to give the navigator his position at all times with extreme accuracy. Here is a brief outline of the system.

Tha accuracy of any navigational system depends largely upon how often the basic information is updated. Take, for example, an aircraft flying from Los Angeles to Sydney using an inertial navigation system, INS. In principle, INS works by measuring all the accelerating forces acting on the aircraft (or other vehicle) and converting these into a vector which is then compared with a known pre-planned programme. The point of departure is accurately known, but the gyroscopes which measure the various forces will have errors, and tiny though these may be, over a flight of thirteen hours or more these may translate into significant position errors of several tens of kilometres. Provided that the aircraft can be placed safely within range of radio-navigation aids which will finally guide it to its destination, this error is not necessarily a problem.

Later INS systems incorporate updating techniques from ground-based distance measuring equipment (DME stations) which largely eliminate the accrued errors and permit terminal airfield area navigation, but not reliable final-approach guidance using INS alone. Separation of aircraft travelling along the same track at the same height will depend to a large extent on the likely errors in the system; over land masses with adequate DME availability this may be as little as four minutes, over oceanic regions 15 minutes or more. A more accurate system would permit greater traffic densities.

INS is not just used by aircraft, of course. The 1969 Apollo moon flight was INS guided; in 1958 the first underwater crossing of the Arctic Ocean by the nuclear submarine Nautilus relied on INS, and today many ships still use the system. In the early 1970’s the US Airforce proposed a system whereby a number of satellites would be placed in orbits which could be used to give pinpoint navigational accuracy anywhere on earth. In principle the system is simple.

If, on a flat surface, you can measure the distance that you are from a point, then you must be somewhere on a radius centred on that point. If you can do the same with a second point, then you must be at the intersection of the two radii or position lines. In most cases this will give two possible positions, so a third line is needed to resolve the ambiguity. GPS is a time-delay triangulation ranging system, using signals transmitted from the satellites on carrier frequencies between 1227.6 Mhz and 1575.42 Mhz. Twenty-four satellites orbit the earth at an altitude of 10,900 NM or 20,000 km. Four ground stations around the world monitor, update, and control the system, which is owned by the American Department of Defense. (Their spelling, not mine).

Put simply, GPS satellites transmit a very accurate time signal which the GPS receiver compares with its own internal clock. Since the speed of propagation of radio waves in space is accurately known, then the difference between the time signal received from the satellite and the receiver time signal can be translated into distance. However, rather than a circle in a flat plane as in Fig.1, we now have a SPHERE centred on the satellite in space and we could be anywhere on that spherical surface. By taking two such measurements we get two spheres which intersect, so our position could be anywhere on a CIRCLE formed by this intersection. By using a third satellite we can derive two positions where the three spheres intersect. One of these will usually be ridiculous (at least for a terrestrial or atmospheric vehicle) and will be rejected by the receiver’s computing system.

Accurate time-keeping is the essence of this system, and each satellite carries a highly accurate on-board atomic clock to control the transmitted signals. To use an atomic clock within the receiver would be both impracticable and expensive, so a GPS receiver uses a clever technique to derive an accurate time from the satellite system, and thus an accurate position. To do this it takes a distance measurement from a fourth satellite; if the receiver clock is incorrect, there will be no point in space where all the distance measurements will intersect. The difference between receiver and satellite clock times will cause an error to each measurement, but this error will be the same for each measurement. The receiver computer then works out a common correction which causes all distance measurements to intersect at just one point; this translates to a known clock error and the appropriate correction is applied.

Satellite signals are sent in a special pseudo-random binary code sequences (PRBS) and each satellite has its own characteristic PRBS thus allowing some frequency sharing. Digital auto-correlation techniques are used in GPS receivers to perform averaging of the PRBS codes and to enable operation at very low received signal levels, thus permitting the use of very small receiving antennas.

If you have followed the argument thus far, you should be able to see that we can determine a point in space, but how does this relate to a point on the earth’s surface? The satellites are placed in orbits which are very precise and predictable, and each one in its twelve hour orbit-time passes over one of the four monitoring points twice a day. These monitoring stations accurately determine the satellite’s position, altitude, and speed, and send this data to the satellite as an update of its own position. Satellites transmit their position with respect to the earth’s centre together with the time signal, and the GPS receiver uses this information together with its own internal mathematical model of the earth to calculate its position which is then displayed as a latitude and longitude.

Earlier, I mentioned that the system uses twenty four satellites. This has not always been so and for some years the system worked with a lesser number, due to Department of Defense cutbacks followed by the disaster to the space shuttle service used to launch the satellites. This meant that there were often long gaps in the time that satellite acquisition was possible and thus in position updates, often of the order of several hours.

As more satellites were launched, so the accuracy improved. With all satellites commissioned, continuous updating is achieved. However, no system is totally error free. The most significant source of error is likely to be the ionosphere, because as the signals pass through this region they are slowed by an amount which is determined by the ever changing state of that region. Ionospheric prediction can be used to partially offset this error, but, as we all know, this is not totally accurate.

Signals are also slowed by atmospheric water-vapour, again unpredictable, and there will always be a very small inaccuracies in the actual measurement of the satellite position and in the satellite’s clocks. The angles of the satellites relative both to themselves and to the receiver can be such as to introduce areas of uncertainty of position, known as Position Dilution Of Precision. Most importantly, the US Department of Defense can introduce deliberate errors to deny use of the system to an enemy.

How accurate is the system? Potentially, the maximum error may be as little as one metre for military use. To off-set the enormous cost of setting up the system, the USAF agreed to allow anyone to purchase and use a GPS receiver, but only in the “clear acquisition” mode. The “protected mode” is available only to specific military users and, as hinted at earlier, this mode is not only the most accurate but may also have deliberate coding errors introduced which would prevent use by the enemy in time of hostilities. It is believed that this was done during the Gulf War to safeguard American installations. Receiver quality has a direct bearing on accuracy.

The simpler compact receivers, small enough to be hand-held and costing around $1000, generally have a single receiving channel and use time-multiplexing to receive and compare signals, while the more expensive and complex receivers have multiple receiving channels and can compare several signals simultaneously, giving much faster updates. A good civilian receiver when stationary should give a position to within about 20 to 30 metres, and about 30 to 300 metres when moving. Often, results may be much more precise. Additionally, it is possible to improve position accuracy by using the “differential mode”. This works by having receivers at known fixed locations which compare the GPS position to their known position, calculate the differential and advise local receivers of the necessary correction to be applied.

In aviation, this now means that the possibility exists to guide an aircraft down to about 200 feet on final approach to any runway in the world, independent of any ground aids. However, the system is not yet accurate enough in C/A mode to provide guaranteed guidance along the runway centre-line. Uses of the system are virtually unlimited and with the ever decreasing cost of receivers, maybe every bush-walker should have one to supplement his visual map reading! Although the absolute accuracy is less than perfect, the relative accuracy is astounding. Experiments are going on which indicate that with antennas attached to each wing-tip it is possible to measure accurately  angle of bank. Further development could see auto-pilots using GPS for flight control, rather than self-contained gyros, and ultimately automatic landings using GPS as primary guidance are likely.I hope that this simplified explanation of GPS has been of some value in outlining the principles of operation of the system.

Clive – VK6CSW

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