GPS Explained

Paul Bertorelli

Originally published January - February 1996

This article was prepared for the Compuserve Aviation Special Interest Group (Avsig) by IFS magazine in 1992. 1 found it to be a good explanation of how GPS (that's Global Positioning System) really works so I present it for your enjoyment and education. I've taken the liberty of doing some editing here and there but the explanation should be worthwhile. I had the opportunity, 20 years ago when I first came out of graduate school, to work in the GPS program office as an engineer (yes, I was rocket scientist) so l can attest to the accuracy of what's presented here. >ed

You don't have to be a rocket scientist to understand it, but it helps.

Triangulation
Timing's The Thing
What Time Is It, Exactly?
Breaking The Code
Hey, Can You Hear Me?
Boys In Blue
Orbital Perturbations
Bit By Bit
What It's Doing
How Accurate, Anyway?
That's It!

Triangulation

GPS works by triangulation. You remember the concept, right? Back in the stone age, instructors used to send student pilots motoring off on cross countries with strict instructions to navigate by pilotage and, under no circumstances, to use the VORs. But, just in case they got lost, the students were taught how to triangulate with crossing radials. In the olden days, students actually followed the instructions and got lost a lot. They triangulated their way back to the land of the living, grew up, got out of flying and became GPS engineers.

GPS triangulation is different but the principle is the same. Think of triangulation with DME. If you had *just* DME and no VORs, could you fix your position? Of course! Tune one DME and draw a circle around it whose diameter equals your distance from the station. Tune another DME and do the same. Now you'd have two intersecting circles that intersect at two points. Your position would be at one of those two intersections. If you had even a vague idea of where you were, you could throw out the bogus position and there'd you'd be.

Better, though, is to take a third line of position from yet another DME. Now you'd have three intersecting circles and your position would be inside the little triangle formed by the intersection of the three circles.

Got the picture? This is basically how GPS triangulates, except instead of circles, we're dealing intersecting spheres. And by the way, there are navigation systems that mix DME information with other data (inertial, VOR, etc.) to arrive at a fix. The FAA's flight check aircraft use a system that does just that.

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Timing's The Thing

Think of GPS satellites as floating DME stations. They move along in orbit and that complicates things but forget about that for the moment. How the hell are we gonna measure distance?

Back to DME. You know how it works, right? Your aircraft DME unit is really a transceiver that interrogates a transponder in a VOR-DME station. When you tune the DME, your unit sends a signal to the ground station, which replies on a different frequency. The receiver multiplies half the total signal transmission time by the speed of light and converts it to distance. Subsequent fixes allow ground speed and time computations.

GPS does a version of that, but it's a one way deal; the satellites transmit, your receiver listens. And, as we said, the SVs are moving around up there at about five miles a second, so we have to account for that, too. You can see how it begins to get complicated.

Like DME, GPS measures the time that it takes the signal to reach the receiver. However, unlike DME, it doesn't have benefit of a returning pulse from an interrogation to act as a baseline. It relies purely on one-way timing. Let's see here...the satellites are 10,900 miles up...light (and radio waves) travel at 186,000 miles a second so...what?...it'll take 1/17th of a second for the signal to reach us.

The math is simple enough. All we need to know is *exactly* when the signal led the satellite. And we do mean *exactly.* A error of a mere 1/1000th of a second would trash the fix by a factor of 180 miles or so. Obviously, very accurate clocks are required.

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What Time Is It, Exactly?

Each satellite carries around four atomic clocks, which use the oscillation of cesium and rubidium atoms to keep very accurate time. How accurate are we talking about here? Well, your average GPS atomic frequency standard has to maintain accuracy of plus/minus a second over more than 30,000 years. (That's one part in 10 to the 13th for you scientific types.) All satellites in the system are synchronized at exactly the same time and it must be kept within 176 nanoseconds of UTC, plus accumulated jump seconds. Navigation messages from the SVs (SV stands for space vehicle, or in this case, satellite>ed) announce the difference between GPS time and UTC.

Okay, we have accurate clocks in the satellites. Now all we need are accurate clocks in the receivers, sync 'em up and we're in business. Of course, if your discount GPS receiver had to have a cesium clock, it'd cost about $200,000 and be about the size of a desktop computer. The way around that was to develop internal receiver clocks that are consistently accurate over relatively short periods of time, as long as they're reset often.

Here's how the receiver clocks are reset: Remember how we explained that DME business, with three intersecting circles? Well, GPS does the same thing only it uses three intersecting spheres to determine position.

Let's for a moment assume that the receiver clock and satellite clock are exactly in sync. The receiver times the signal, figures the distance from three satellites and where the three spheres intersect...voila...that's our position. But, the receiver doesn't know for sure that its clock is perfectly synced up with the satellites. Remember, a lousy millionth of a second translates to a thousand foot error. So, just to be sure, the receiver listens for a fourth satellite. If the fourth line of position doesn't pass through the other three, the receiver knows something is wrong; it's geometrically impossible for four mutually intersecting spheres to merge at the same point unless the clock is spot on. The receiver assumes, then, that because the fourth line doesn't jive with the others, it's internal clock must be out of sync.

The receiver then runs a simple little routine to adjust the clock until all four lines of position intersect the same point. This is known as correcting clock bias and it's how the receiver resets its clock. That's one of the things that's going on when your receiver has just been turned on and you're waiting for it to initialize.

(Once you know where you are in three dimensions using this approach, or four dimensions if you count time, you can measure the Doppler shift of the signal from each of the known, tracked satellites and get a three dimensional velocity vector as well. In practice the vertical velocity isn't very accurate due to the geometry of the satellites but the ground speed [that's what you're measuring] is quite accurate. >ed)

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Breaking The Code

So much for the clock synching. Pretty clever, eh? It gets better. We said that in order to measure distance, the receiver has to know *exactly* when the signal left the satellite. Just having a clock set exactly to satellite time isn't enough.

The receiver determines range using something called pseudo-random code. Think of the code as looking like the teeth on a carpenter's saw, with a few broken off at random points. Each satellite transmits its own random code. The receiver has a code generator pre-programmed to generate the exact same codes (in 32 variations).

When the receiver hears a satellite, it matches up the code--like aligning the patterns of broken teeth on two saws. Since it knows that the signal carrying the code left the satellite at a certain exact time, all the receiver does is generate its matching code at *exactly* the same time. It then measures how long it takes the random code from the satellite to arrive and...right...it converts this time lapse to a distance measurement. It does this for four satellites and the rest is simply math.

Earlier, we said four satellites are necessary, with the fourth required to sync the clock and three others for lines of position. Actually, if the receiver operator knows his altitude, he can plug that into the receiver and that serves as *one* line of position. Then, only two other SV ranges are required to determine position. The third satellite is used to sync the clock. This is known as two-dimensional navigation.

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Hey, Can You Hear Me?

There's another important reason for random code; it relates to some basic GPS design limitations. In order to be affordable, GPS satellites had to be relatively small and light--the Block II production SVs weigh just less than 2000 pounds. That means that power requirements are limited and the radiated signal power is also quite low, on the order of 40 watts.

Think about that. There's a 40-watt transmitter floating out there almost 11,000 miles away and it has to blanket a very large portion of the earth's surface with a receivable signal. Big problem.

For comparison, a typical communication satellite has much more power and it radiates a very directional signal that you need a satellite dish to receive. For obvious reasons, ships, planes, cars and other moving vehicles, can't have dishes. Who wants a plane that looks like a West Virginia sharecropper's double-wide trailer? Besides, they'd blow off in the slipstream.

Rather than directing a high power signal, then, a GPS satellite spreads a very low power signal over a large area. It's so low-powered that it's completely hidden in the background hash of cosmic rays, car ignitions, neon lighting, computer drive fuzz and so forth. That's where random code comes in.

The receiver starts generating its own code and listening for matches in the background noise. Once it has enough matches to recognize the SV's transmission, it drags the signal out of background muck and "locks on." When three SVs are locked up, navigation can begin.

This is why a receiver can get by with a very small, relatively non-directional antenna. Handheld GPS units have antennas that are only a couple of inches square or perhaps about the size of a cigar. One other thing: using pseudo-random code and low, low power makes it very hard to jam a GPS signal. For military purposes, this is obviously very desirable.

That's the theory. It works. It works very well, as a matter of fact. But it takes a whole lot of effort and money to keep it working.

The GPS system consists of three major parts-the user segment (that's us), the ground or control segment (the DOD nerds who run the thing) and the space segment. The space segment will eventually be composed of 21 satellites, with three on-orbit spares. Right now, as this is being written in August of 1992, there are 19 SVs in orbit, 18 usable. Three more are due for launch by the end of the year.

The satellites are now being launched by Delta II expendable rockets. At one time, the Shuttle was supposed to launch GPS satellites but that plan went down with the Challenger. There have been no successful launches of GPS satellites by the Shuttle and probably never will be.

You'll hear the term "Block I" and "Block II" used to describe satellites. Block Is were the initial R and D birds and a few (four or five) are still operating. They're smaller than the Block II production satellites and don't have the same amount of military spook stuff aboard. They're also not selective-availability equipped.

The full constellation of GPS satellites is due to be in orbit by 1993, if all goes according to plan (No guarantee there). Until then. the system is deemed by the Defense Department to be under construction.

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Boys In Blue

The U.S. Air Force's 2nd Satellite Operations squadron at Falcon AFB in Colorado maintains the GPS system These guys are the ground segment They have monitoring stations at several points on the globe, from which they keep track of satellite health, maintenance and so forth.

Make no mistake about it, GPS is a high maintenance system The satellites require regular tweaking including data uploads, orbital positioning adjustments and clock maintenance. If the ground segment stopped doing this constant maintenance, it's said that the system would "gracefully degrade" to complete uselessness in about two weeks time.

So, as each satellite whizzes along and completes one earth orbit every 12 hours, the Boys in Blue from Falcon talk to it every few hours. What do the ground guys tell the satellites?

Well, we mentioned basic maintenance items,. including clock commands, power and attitude messages, new programming instructions. Occasionally, the SV must undergo what's called a "momentum dump." Each SV has a series of gyroscopic wheels for stabilization. In space, these wheels tend to accelerate and would do so indefinitely, eventually disintegrating. By dumping the wheel energy periodically, this unpleasant scenario is avoided.

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Orbital Perturbations

Most of the uploading relates to routine navigation data. including almanac and ephemeris information. Probably the most important is the ephemeris, which compensates for the SV's normal orbital perturbations

As it circles the earth. each satellite is subject to several major influences which cause its orbit to be less than perfectly circular. The major influence is the earth's equatorial bulge, but solar wind and other effects also take a toll. The GPS orbital perturbations are defined by 16 constants and these are updated and uploaded at least once a day (maybe more often) along with clock correction data. The satellite then rebroadcasts this and your receiver decodes it as ephemeris data. The ephemeris tells the receiver exactly where the satellite is in space so,. when the receiver calculates distance, it'll know exactly where the source of the signal is; each SV broadcasts its own ephemeris data.

In addition. each SV also broadcasts what's called an almanac. In more general terms than does the ephemeris, the almanac tells the receiver the location of all of the SVs in the GPS constellation. This lets the receiver know when and where to look for satellites, as it's attempting to establish a fix. Your receiver stores an almanac in its memory and that data is constantly updated when the receiver is tracking satellites. If the receiver is turned off for several months, the almanac will usually remain usable enough for the receiver to find satellites and upload a new almanac.

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Bit By Bit

Of course. all this data we've been blithely describing here has to find its way through 10,900 miles of space and into your receiver's computer memory. This is another one of GPS's elegant design features.

Remember how we explained that a communication satellite uses a relatively high powered, directional signal? Such a signal allows for a rather dense data stream, which, when you think about it, is just what a multi-channel comm satellite needs. Lottsa phone calls, fax bits, video pixels and so on streaming down from space. The GPS data stream is just the opposite; very little information spread out over a wide, nondirectional signal. If satellite signals were soup, a comm bird would be a rich, thick minestrone, GPS would be chicken broth, and a pretty thin one at that.

The GPS data stream trickles down from each SV in 1500-bit frames, each composed of five subframes 300 bits long. Subframes 4 and 5 are subcommutated 25 times each, which is a fancy way of saying that to get a complete data message, requires that 25 full frames be sent. A full 1500-bit frame takes 30 seconds to send. Do the math here and you'll realize that the GPS data rate is slower than slow--it's 50 baud. If your computer downloaded this article at 50 baud, it would take about six hours. You could read the damn thing c-h-a-r-a-c-t-e-r by c-h-a-r-a-c-t-e-r.

The data subframes contain various information. Subframes 1,2 and 3 contain time and date information. user range accuracy, satellite health status messages, clock correction. ephemeris data and some other odds and ends. Subframes 4 and 5 contain the almanac, which, as we noted. is the location in space of *all* of the satellites. It's a fair amount of data and that's why it's subcommutated. If it weren't and the almanac were transmitted continuously until complete, a GPS receiver would take about 12 minutes to initialize, every time you turned it on. Oh...and no navigating while you're waiting.

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What It's Doing

So you just bought a brand new Garmin or Trimble. You take it out of the box, turn it on and it doesn't work. You read the instructions and learn that it needs a current almanac if one wasn't downloaded within the past nine months or so or if the receiver was moved more than a 1000 miles.

You go outside, turn it on and it just sits there. What's it doing? Well, for one thing, it's looking for a satellite so it can grab an almanac, which it must have in order to find the three or four satellites it needs to fix position. If the receiver is "dumb" and has no almanac at all or an outdated almanac, it'll take 12 1/2 minutes to download. Why?

Well, remember the almanac is in subframes 4 and 5, each of which takes 6 seconds to send. Because there are five subframes, though, almanac is coming through only 2/5ths of the time. It takes 25 full data frames to get a full almanac. Each full frame takes 30 seconds so 25 frames takes 12 1/2 minutes, which is why your receiver manual gives 12 1/2 minutes as the download time.

Once the receiver's got it, it can locate other SVs in the sky, download the ephemeris and other data and tell you where you are, within a few feet or so.

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How Accurate, Anyway?

Which brings us to the question of accuracy. You hear all kinds of incredible claims about GPS being accurate enough to locate a gnat's ass while others say its only good for about 100 meters, give or take. Which is true? Well, it depends.

GPS is generally said to be available in two forms, PPS and SPS. Depending on whose figures you want to believe, PPS or precision positioning service is accurate to about 29 meters with single-frequency receivers. SPS or standard positioning service is actually capable of the same accuracy except...the DOD invokes something called selective availability. SA is currently on and that degrades the SPS accuracy to about 100 meters. GPS usually delivers on that promise, too.

SA, by the way, is an intentional "dithering" of the clock accuracy and perhaps a contamination of the ephemeris data. Why the DOD thinks this makes any difference to a potential enemy is beyond us.

A number of factors go into making that 100-meter potential error. Break these factors down and they might look like this:

Throw in the statistical average and the ability to repeat a fix reliably over and over and the error gets up around 300 feet or so, with SA on. With SA off, it's around 60 to 200 feet.

One last note about errors: We mentioned something called a single-frequency receiver That's a bit confusing because we didn't explain that GPS satellites broadcast on two frequencies called L1 and L2. L1 is at 1575 MHz. L2 is 1227 MHz. Military receivers generally receive both L1 and L2. They compare the results from each and use this information to greatly reduce the ionospheric errors GPS signal are subject to when passing through the atmosphere. Single frequency receivers--our Garmins and Trimbles--use a fixed mathematical model to allow for iono errors.

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That's It!

So, that's how GPS works. Take it from us, a buncha cynical and hardbitten journalists who've seen it all, this is hot stuff. The people who designed this system were smart and clever and have created a fantastic navigation system. No kidding.

Like the Pepsi ads say, you gotta have it!

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Contents of The Leading Edge and these web pages are the viewpoints of the authors. No claim is made and no liability is assumed, expressed or implied as to the technical accuracy or safety of the material presented. The viewpoints expressed are not necessarily those of Chapter 1000 or the Experimental Aircraft Association.
Revised -- 22 February 1997