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Global Positioning System. Trey Brown September 19, 2000. Forms of Navigation. Navigation and positioning are crucial to so many activities and yet the process has always been quite cumbersome.

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Global Positioning SystemTrey BrownSeptember 19, 2000Forms of NavigationNavigation and positioning are crucial to so many activities and yet the process has always been quite cumbersome. Over the years all kinds of technologies have tried to simplify the task but every one has had some disadvantage. U.S. Department of DefenseThe DOD decided that the military had to have a super precise form of worldwide positioning. And fortunately they had the kind of money ($12 billion) it took to build something really good. Global Positioning SystemWorldwide radio-navigation system formed from a constellation of 24 satellites and their ground stations. GPS uses these "man-made stars" as reference points to calculate positions accurate to a matter of meters. With advanced forms of GPS you can make measurements to better than a centimeter Global Positioning SystemGPS receivers have been miniaturized to just a few integrated circuits and so are becoming very economical. That makes the technology accessible to virtually everyone. These days GPS is finding its way into cars, boats, planes, construction equipment, movie making gear, farm machinery, and laptop computers. GPS works in three logical stepsThe basis of GPS is "triangulation" from satellites. To "triangulate," a GPS receiver measures distance using the travel time of radio signals. To measure travel time, GPS needs very accurate timing which it achieves with some tricks. Along with distance, you need to know exactly where the satellites are in space. High orbits and careful monitoring are the secret. Finally you must correct for any delays the signal experiences as it travels through the atmosphere. Triangulation?The word "triangulation" is used very loosely with GPS because it's a word most people can understand Purists would not call what GPS does "triangulation" because no angles are involved. It's really "trilateration" or "resection." First StepSuppose we measure our distance from a satellite and find it to be 11,000 miles. Knowing that we're 11,000 miles from a particular satellite narrows down all the possible locations we could be in the whole universe to the surface of a sphere that is centered on this satellite and has a radius of 11,000 miles. Second StepNext, say we measure our distance to a second satellite and find out that it's 12,000 miles away. That tells us that we're not only on the first sphere but we're also on a sphere that's 12,000 miles from the second satellite. Or in other words, we're somewhere on the circle where these two spheres intersect. Third StepIf we then make a measurement from a third satellite and find that we're 13,000 miles from that one, that narrows our position down even further, to the two points where the 13,000 mile sphere cuts through the circle that's the intersection of the first two spheres. So by ranging from three satellites we can narrow our position to just two points in space. To decide which one is our true location we could make a fourth measurement. But usually one of the two points is a ridiculous answer (either too far from Earth or moving at an impossible velocity) and can be rejected without a measurement. TimingHow can you measure the distance to something that's floating around in space? We do it by timing how long it takes for a signal sent from the satellite to arrive at our receiver. TimingIn a sense, the whole thing boils down to Velocity (60 mph) x Time (2 hours) = Distance (120 miles) In the case of GPS we're measuring a radio signal so the velocity is going to be the speed of light or roughly 186,000 miles per second. The problem is measuring the travel time. TimingThe timing problem is tricky. First, the times are going to be awfully short. If a satellite were right overhead the travel time would be something like 0.06 seconds. So there is a need for a really precise clocks. Measuring travel time Satellites and receivers use something called a "Pseudo Random Code" TimingDistance to a satellite is determined by measuring how long a radio signal takes to reach us from that satellite. To make the measurement we assume that both the satellite and our receiver are generating the same pseudo-random codes at exactly the same time. By comparing how late the satellite's pseudo-random code appears compared to our receiver's code, we determine how long it took to reach us. Multiply that travel time by the speed of light and you've got distance. TimingDistance to a satellite is determined by measuring how long a radio signal takes to reach us from that satellite. To make the measurement we assume that both the satellite and our receiver are generating the same pseudo-random codes at exactly the same time. By comparing how late the satellite's pseudo-random code appears compared to our receiver's code, we determine how long it took to reach us. Multiply that travel time by the speed of light and you've got distance. Error CorrectionUse a fourth satellite If our receiver's clocks were perfect, then all our satellite ranges would intersect at a single point (which is our position). But with imperfect clocks, a fourth measurement, done as a cross-check, will NOT intersect with the first three. Since any offset from universal time will affect all of our measurements, the receiver looks for a single correction factor that it can subtract from all its timing measurements that would cause them all to intersect at a single point. Satellite LocationThe Air Force has put each GPS satellite into a very precise orbit, according to the GPS master plan. 11,000 mile altitude is important because something that high is well clear of the atmosphere and it will orbit according to very simple mathematics. On the ground all GPS receivers have an almanac programmed into their computers that tells them where in the sky each satellite is, moment by moment. Satellite LocationThe basic orbits are quite exact but just to make things perfect the GPS satellites are constantly monitored by the Department of Defense. They use very precise radar to check each satellite's exact altitude, position and speed. The errors they're checking for are called "ephemeris errors" because they affect the satellite's orbit or "ephemeris.” These errors are caused by gravitational pulls from the moon and sun and by the pressure of solar radiation on the satellites. Real World ConditionsThe Speed of Light Modeling can predict what a typical delay might be on a typical day, but atmospheric conditions are rarely exactly typical. Another way to get a handle on these atmosphere-induced errors is to compare the relative speeds of two different signals. This " dual frequency” measurement is very sophisticated and is only possible with advanced receivers. Real World ConditionsSignal Bounce The signal may bounce off various local obstructions before it gets to our receiver. This is called multipath error and is similar to the ghosting you might see on a TV. Good receivers use sophisticated signal rejection techniques to minimize this problem. Intentional ErrorThe U.S. government is intentionally degrading its accuracy in a policy called "Selective Availability" or "SA” and the idea behind it is to make sure that no hostile force can use GPS to make accurate weapons. Basically the DoD introduces some "noise" into the satellite's clock data which, in turn, adds noise (or inaccuracy) into position calculations. The DoD may also be sending slightly erroneous orbital data to the satellites which they transmit back to receivers on the ground as part of a status message. Together these factors make SA the biggest single source of inaccuracy in the system. Military receivers use a decryption key to remove the SA errors and so they're much more accurate. Differential GPSDifferential GPS or "DGPS" can yield measurements good to a couple of meters in moving applications and even better in stationary situations. That improved accuracy has a profound effect on the importance of GPS as a resource. With it, GPS becomes more than just a system for navigating boats and planes around the world. It becomes a universal measurement system capable of positioning things on a very precise scale. Differential GPSThe satellites are so far out in space that the little distances we travel here on earth are insignificant. So if two receivers are fairly close to each other, say within a few hundred kilometers, the signals that reach both of them will have traveled through virtually the same slice of atmosphere, and so will have virtually the same errors The idea is simple.Put the reference receiver on a point that's been very accurately surveyed and keep it there. This reference station receives the same GPS signals as the roving receiver but instead of working like a normal GPS receiver it attacks the equations backwards. Instead of using timing signals to calculate its position, it uses its known position to calculate timing. It figures out what the travel time of the GPS signals should be, and compares it with what they actually are. The difference is an "error correction" factor. The receiver then transmits this error information to the roving receiver so it can use it to correct its measurements. PRCPhysically it's just a very complicated digital code, The signal is so complicated that it almost looks like random electrical noise. Hence the name. There are several good reasons for that complexity: First, the complex pattern helps make sure that the receiver doesn't accidentally sync up to some other signal. The patterns are so complex that it's highly unlikely that a stray signal will have exactly the same shape. Since each satellite has its own unique Pseudo-Random Code this complexity also guarantees that the receiver won't accidentally pick up another satellite's signal. So all the satellites can use the same frequency without jamming each other. And it makes it more difficult for a hostile force to jam the system. In fact the Pseudo Random Code gives the DoD a way to control access to the system. PRCBut there's another reason for the complexity of the Pseudo Random Code, a reason that's crucial to making GPS economical. The codes make it possible to use "information theory" to " amplify " the GPS signal. And that's why GPS receivers don't need big satellite dishes to receive the GPS signals. CarriersThe GPS satellites transmit signals on two carrier frequencies. The L1 carrier is 1575.42 MHz and carries both the status message and a pseudo-random code for timing. The L2 carrier is 1227.60 MHz and is used for the more precise military pseudo-random code. There are two types of pseudo-random codeThe first pseudo-random code is called the C/A (Coarse Acquisition) code. It modulates the L1 carrier. It repeats every 1023 bits and modulates at a 1MHz rate. Each satellite has a unique pseudo-random code. The C/A code is the basis for civilian GPS use. The second pseudo-random code is called the P (Precise) code. It repeats on a seven day cycle and modulates both the L1 and L2 carriers at a 10MHz rate. This code is intended for military users and can be encrypted. When it's encrypted it's called "Y" code. Since P code is more complicated than C/A it's more difficult for receivers to acquire. That's why many military receivers start by acquiring the C/A code first and then move on to P code. Navigation MessageThere is a low frequency signal added to the L1 codes that gives information about the satellite's orbits, their clock corrections and other system status.

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