How did GPS originate?

In the latter days of the arms race, the targeting of ICBMs became such a fine art that they could be expected to land right on an enemy's missile silos. Such a direct hit would destroy the silo and any missile in it. The ability to take out your opponent's missiles had a profound effect on the balance of power. But you could only expect to hit a silo if you knew exactly where you were launching from. That's not hard if your missiles are on land as most of the targeted silos were in the Soviet Union.  But most of the U.S. nuclear arsenal was at sea on subs. To maintain the balance of power, the U.S. had to come up with a way to allow those subs to surface and fix their exact position in a matter of minutes anywhere in the world.

The US department of Defense solved this problem by developing GPS – the global positioning system. They spent 12 billion dollars to place 24 satellites into geo-synchronous orbit around the Earth, and built monitoring stations to support them. These ground stations monitor the GPS satellites, checking both their operational health and their exact position in space. The master ground station transmits corrections for the satellite's ephemeris constants and clock offsets back to the satellites themselves. The satellites can then incorporate these updates in the signals they send to GPS receivers. There are five monitor stations: in Hawaii, Ascension Island, Diego Garcia, Kwajalein, and Colorado Springs.

What is GPS?

GPS uses these "man-made stars" (satellites) as reference points to calculate positions accurate to a matter of meters. In fact, with advanced forms of GPS, you can make measurements to better than a centimeter! In a sense it's like giving every square meter on the planet a unique address.

GPS receivers have been miniaturized to just a few integrated circuits and so are becoming very economical. And 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 even laptop computers.

How GPS Works

 Satellite Triangulation

Improbable as it may seem, the whole idea behind GPS is to use satellites in space as reference points for locations here on earth. That's right, by very, very accurately measuring our distance from three satellites, we can triangulate our position anywhere on earth. Forget for a moment how a GPS receiver measures this distance. We'll get to that later. First consider how distance measurements from three satellites can pinpoint you 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. A fourth measurement does come in very handy for another reason however, but we'll tell you about that later.  But how 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.

In a sense, the whole thing boils down to those "velocity times travel time" math problems we did in high school. Remember the old: "If a car goes 60 miles per hour for two hours, how far does it travel?"

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. The 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 we're going to need some really precise clocks. We'll talk about those soon. But assuming we have precise clocks, how do we measure travel time? To explain it let's use a goofy analogy:

Suppose there was a way to get both the satellite and the receiver to start playing "The Star Spangled Banner" at precisely 12 noon. If sound could reach us from space (which, of course, is ridiculous) then standing at the receiver we'd hear two versions of the Star Spangled Banner, one from our receiver and one from the satellite.  These two versions would be out of sync. The version coming from the satellite would be a little delayed because it had to travel more than 11,000 miles. If we wanted to see just how delayed the satellite's version was, we could start delaying the receiver's version until they fell into perfect sync. The amount we have to shift back the receiver's version is equal to the travel time of the satellite's version. So we just multiply that time times the speed of light and BINGO! we've got our distance to the satellite.

That's basically how GPS works. Only instead of the Star Spangled Banner the satellites and receivers use something called a "Pseudo Random Code" - which is probably easier to sing than the Star Spangled Banner.

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 Department of Defense a way to control access to the system.

But 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.

We glossed over one point in our goofy Star-Spangled Banner analogy. It assumes that we can guarantee that both the satellite and the receiver start generating their codes at exactly the same time. But how do we make sure everybody is perfectly synced?

 Measuring a 4^th Satellite

If measuring the travel time of a radio signal is the key to GPS, then our stop watches had better be darn good, because if their timing is off by just a thousandth of a second, at the speed of light, that translates into almost 200 miles of error!

On the satellite side, timing is almost perfect because they have incredibly precise atomic clocks on board. But what about our receivers here on the ground? Remember that both the satellite and the GPS receiver need to be able to precisely synchronize their pseudo-random codes to make the system work.  If our receivers needed atomic clocks (which cost upwards of $50K to $100K) GPS would be a lame duck technology. Nobody could afford it.

Luckily the designers of GPS came up with a brilliant little trick that lets us get by with much less accurate clocks in our receivers. This trick is one of the key elements of GPS and, as an added side benefit, it means that every GPS receiver is essentially an atomic accuracy clock.

The secret to perfect timing is to make an extra satellite measurement. That's right, if three perfect measurements can locate a point in 3-dimensional space, then four imperfect measurements can do the same thing.

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. So the receiver's computer says "Uh-oh! there is a discrepancy in my measurements. I must not be perfectly synced with universal time."

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.

That correction brings the receiver's clock back into sync with universal time, and bingo! - you've got atomic accuracy time right in the palm of your hand.

Once it has that correction it applies to all the rest of its measurements and now we've got precise positioning.

One consequence of this principle is that any decent GPS receiver will need to have at least four channels so that it can make the four measurements simultaneously.

With the pseudo-random code as a rock solid timing sync pulse, and this extra measurement trick to get us perfectly synced to universal time, we have got everything we need to measure our distance to a satellite in space. But for the triangulation to work we not only need to know distance, we also need to know exactly where the satellites are.

Finding Satellites

That 11,000 mile altitude is actually a benefit in this case, because something that high is well clear of the atmosphere. And that means it will orbit according to very simple mathematics. The Air Force has injected each GPS satellite into a very precise orbit, according to the GPS master plan. 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.

The 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.  The errors are usually very slight, but if you want great accuracy, they must be taken into account.

Once the Department of Defense has measured a satellite's exact position, they relay that information back up to the satellite itself. The satellite then includes this new corrected position information in the timing signals it's broadcasting. So a GPS signal is more than just pseudo-random code for timing purposes. It also contains a navigation message with ephemeris information as well. With perfect timing and the satellite's exact position, you'd think we'd be ready to make perfect position calculations. But there's even more to it than that.

Correcting GPS Errors

Up to now we've been treating the calculations that go into GPS very abstractly, as if the whole thing were happening in a vacuum. But in the real world there are lots of things that can happen to a GPS signal that will make its life less than mathematically perfect. To get the most out of the system, a good GPS receiver needs to take a wide variety of possible errors into account. Here's what they've got to deal with.

First, one of the basic assumptions we've been using throughout this document is not exactly true. We've been saying that you calculate distance to a satellite by multiplying a signal's travel time by the speed of light. But the speed of light is only constant in a vacuum.

As a GPS signal passes through the charged particles of the ionosphere and then through the water vapor in the troposphere, it gets slowed down a bit, and this creates the same kind of error as bad clocks. There are a couple of ways to minimize this kind of error.

For one thing we can predict what a typical delay might be on a typical day. This is called modeling and it helps but, of course, 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.

Trouble for the GPS signal doesn't end when it gets down to the ground. The signal may bounce off various local obstructions before it gets to our receiver. This is called multi-path error and is similar to the ghosting you might see on a TV. Good receivers use sophisticated signal rejection techniques to minimize this problem.

And even though the satellites are very sophisticated, they do account for some tiny errors in the system. The atomic clocks they use are very, very precise, but they're not perfect. Minute discrepancies can occur, and these translate into travel time measurement errors. And even though the satellites positions are constantly monitored, they can't be watched every second. So slight position errors can sneak in between monitoring times.

Also, basic geometry itself can magnify these other errors with a principle called "Geometric Dilution of Precision" or GDOP. It sounds complicated but the principle is quite simple. There are usually more satellites available than a receiver needs to fix a position, so the receiver picks a few and ignores the rest.  If it picks satellites that are close together in the sky, the intersecting circles that define a position will cross at very shallow angles. That increases the gray area or error margin around a position. If it picks satellites that are widely separated, the circles intersect at almost right angles, and that minimizes the error region. Good receivers determine which satellites will give the lowest GDOP.

Basic GPS is the most accurate radio-based navigation system ever developed. And for many applications it's plenty accurate. But it's human nature to want MORE!

Differential GPS involves the cooperation of two receivers, one that's stationary, and another that's roving around making position measurements. The stationary receiver is the key. It ties all the satellite measurements into a solid local reference.

Here's how it works:

Remember that GPS receivers use timing signals from at least four satellites to establish a position. Each of those timing signals is going to have some error or delay -- depending on what sort of perils have befallen it on its trip down to us.

Since each of the timing signals that go into a position calculation has some errors, the final calculation is going to be a compounding of those errors.

Luckily the sheer scale of the GPS system comes to our rescue. The 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.

That's the idea behind differential GPS: We have one receiver measure the timing errors and then provide correction information to the other receivers that are roving around. That way virtually all errors can be eliminated from the system, even the pesky Selective Availability error -- that the Department of Defense puts in on purpose.

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.

Since the reference receiver has no way of knowing which of the many available satellites a roving receiver might be using to calculate its position, the reference receiver quickly runs through all the visible satellites and computes each of their errors. Then it encodes this information into a standard format and transmits it to the roving receivers. It's as if the reference receiver is saying: "OK everybody, right now the signal from satellite #1 is ten nanoseconds delayed, satellite #2 is three nanoseconds delayed, satellite #3 is sixteen nanoseconds delayed..." and so on. The roving receivers get the complete list of errors and apply the corrections for the particular satellites they're using.

Inverted Differential GPS

There's another permutation of Differential GPS , called "inverted DGPS," that can save money in certain tracking applications.

Let's say you've got a fleet of buses and you'd like to pinpoint them on street maps with very high accuracy (maybe so you can see which side of an intersection they're parked on or whatever). Anyway, you'd like this accuracy but you don't want to buy expensive "differential-ready" receivers for every bus.

With an inverted DGPS system the buses would be equipped with standard GPS receivers and a transmitter and would transmit their standard GPS positions back to the OCC. Then at the OCC the corrections would be applied to the received positions. It requires a computer to do the calculations and a transmitter to transmit the data, but it gives you a fleet of very accurate positions for the cost of one reference station, a computer, and a lot of standard GPS receivers.

GPS Summary

GPS technology has matured into a resource that goes far beyond its original design goals. These days scientists, sportsmen, farmers, soldiers, pilots, surveyors, hikers, delivery drivers, sailors, dispatchers, lumberjacks, fire-fighters, and people from many other walks of life are using GPS in ways that make their work more productive, safer, and sometimes even easier.