GPS Tutorial

 

Here's how GPS works in five logical steps:

 

   1.The basis of GPS is "triangulation" from satellites.

 

   2.To "triangulate," a GPS receiver measures distance using the travel time of radio signals.

 

   3.To measure travel time, GPS needs very accurate timing which it achieves with some tricks.

 

   4.Along with distance, you need to know exactly where the satellites are in space. High orbits and careful monitoring are the secret.

 

   5.Finally you must correct for any delays the signal experiences as it travels through the atmosphere.

 

Trying to figure out where you are and where you're going is probably one of man's oldest pastimes.

 

 Navigation 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.

 

Disadvantages of other navigation systems

 

 Landmarks:

             Only work in local area. Subject to movement or destruction by environmental factors.

 Dead Reckoning:

             Very complicated. Accuracy depends on measurement tools which are usually relatively crude. Errors accumulate quickly.

 Celestial:

             Complicated. Only works at night in good weather. Limited precision.

 OMEGA:

             Based on relatively few radio direction beacons. Accuracy limited and subject to radio interference.

 LORAN:

             Limited coverage (mostly coastal). Accuracy variable,

             affected by geographic situation. Easy to jam or disturb.

 SatNav:

             Based on low-frequency doppler measurements so it's

             sensitive to small movements at receiver. Few satellites so

             updates are infrequent.

 Back to the tutorial...

 

Finally, the U.S. Department of Defense 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.

 

 The result is the Global Positioning System, a system that's changed

 navigation forever.

 

Why did the Department of Defense develop GPS?

 

 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 them

 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......Hello GPS!

 

The Global Positioning System (GPS) is a worldwide 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. 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, even laptop computers.

 

 Soon GPS will become almost as basic as the telephone. Indeed, at Trimble, we

 think it just may become a universal utility.

 

 

GPS Satellites

 

 Name: NAVSTAR

 

 Manufacturer: Rockwell International

 

 Altitude: 10,900 nautical miles

 

 Weight:1900 lbs (in orbit)

 

 Size:17 ft with solar panels extended

 

 Orbital Period: 12 hours

 

 Orbital Plane: 55 degrees to equitorial plane

 

 Planned Lifespan: 7.5 years

 

 Current constellation: 24 Block II production satellites

 

 Future satellites: 21 Block IIrs developed by Martin Marietta.

 

 

Ground Stations

 

 (also known as the "Control Segment")

 

 These 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: Hawaii, Ascension Island, Diego Garcia,

 Kwajalein, and Colorado Springs.

 

 

Advanced Forms of GPS

 

 The quest for greater and greater accuracy has spawned an assortment of

 variations on basic GPS technology. One technique, called "Differential

 GPS," involves the use of two ground-based receivers. One monitors

 variations in the GPS signal and communicates those variations to the other

 receiver. The second receiver can then correct its calculations for better

 accuracy.

 

 Another technique called "Carrier-phase GPS" takes advantage of the GPS

 signal's carrier signal to improve accuracy. The carrier frequency is much

 higher than the GPS signal which means it can be used for more precise timing

 measurements.

 

 The aviation industry is developing a type of GPS called "Augmented GPS"

 which involves the use of a geostationary satellite as a relay station for the

 transmission of differential corrections and GPS satellite status information.

 These corrections are necessary if GPS is to be used for instrument landings.

 The geostationary satellite would provide corrections across an entire

 continent.

 

 All of these technologies are covered in more detail later in this tutorial.

 

 

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 our receiver measures this distance. We'll get to that

 later. First consider how distance measurements from three satellites can

 pinpoint you in space.

 

 The Big Idea Geometrically:

 

 Suppose 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.

 

Next, 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.

 

If 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.

 

 A fourth measurement does come in very handy for another reason however,

 but we'll tell you about that later.

 

 Next we'll see how the system measures distances to satellites

 

In Review: Triangulating

 

   1.Position is calculated from distance measurements (ranges) to

      satellites.

 

   2.Mathematically we need four satellite ranges to determine exact

      position.

 

   3.Three ranges are enough if we reject ridiculous answers or use other

      tricks.

 

   4.Another range is required for technical reasons to be discussed later.

 

 

We saw in the last section that a position is calculated from distance

 measurements to at least three satellites.

 

 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.

 

The Big Idea Mathematically

 

 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.

 

A Random Code?

 

 The Pseudo Random Code (PRC, shown above) is a fundamental part of GPS.

 Physically it's just a very complicated digital code, or in other words, a

 complicated sequence of "on" and "off" pulses as shown here:

 

 The signal is so complicated that it almost looks like random electrical noise.

 Hence the name "Pseudo-Random."

 

 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.

 

GPS Signals in detail

 

 Carriers

 

 The 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.

 

 Pseudo-Random Codes

 

 There are two types of pseudo-random code (see tutorial for explanation of

 pseudo random codes in general). The 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 Message

 

 There 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.

 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? Stay tuned and see.

 

 

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.

 

Encrypted GPS

 

 GPS was developed by the Defense Department primarily for military purposes.

 And even though it's been estimated that there are ten times as many civilian

 receivers as military ones the system still has considerable military

 significance.

 

 To that end the military maintains exclusive access to the more accurate

 "P-code" pseudo random code. It's ten times the frequency of the civilian C/A

 code (and so potentially much more accurate) and much harder to jam. When

 it's encrypted it's called "Y-code" and only military receivers with the

 encryption key can receive it. Because this code is modulated on two carriers,

 sophisticated games can be played with the frequencies to help eliminate

 errors caused by the atmosphere.

 

 It almost makes you want to enlist, doesn't it?

 

 

 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.

 

Expanded Topic:

 Using the Pseudo Random Code as an amplifier.

 

 The pseudo random code is one of the brilliant ideas behind GPS. It not only

 acts as a great timing signal but it also gives us a way to "amplify" the very

 weak satellite signals.

 

 Here's how that amplification process works:

 

 The world is awash in random electrical noise. If we tuned our receivers to the

 GPS frequency and graphed what we picked up, we'd just see a randomly

 varying line --- the earth's background noise. The GPS signal would be buried

 in that noise.

 

                           

 

 The pseudo random code looks a lot like the background noise but with one

 important difference: we know the pattern of its fluctuations.

 

 What if we compare a section of our PRC with the background noise and look

 for areas where they're both doing the same thing?

 

 We can divide the signal up into time periods (called "chipping the signal")

 and then mark all the periods where they match (i.e. where the background is

 high when the PRC is high).

 

                           

 

 Since both signals are basically random patterns, probability says that about

 half the time they'll match and half the time they won't.

 

 If we set up a scoring system and give ourselves a point when they match and

 take away a point when they don't, over the long run we'll end up with a score

 of zero because the -1's will cancel out the 1's.

 

 But now if a GPS satellite starts transmitting pulses in the same pattern as our

 pseudo random code, those signals, even though they're weak, will tend to

 boost the random background noise in the same pattern we're using for our

 comparison.

 

 Background signals that were right on the border of being a "1" will get

 boosted over the border and we'll start to see more matches. And our "score"

 will start to go up.

 

                            

 

 Even if that tiny boost only puts one in a hundred background pulses over the

 line, we can make our score as high as we want by comparing over a longer

 time. If we use the 1 in 100 figure, we could run our score up to ten by

 comparing over a thousand time periods.

 

 If we compared the PRC to pure random noise over a thousand time periods

 our score would still be zero, so this represents a ten times amplification.

 

 This explanation is a greatly simplified but the basic concept is significant. It

 means that the system can get away with less powerful satellites and our

 receivers don't need big antennas like satellite TV.

 

 You may wonder why satellite TV doesn't use the same concept and eliminate

 those big dishes. The reason is speed.

 

 The GPS signal has very little information in it. It's basically just a timing pulse,

 so we can afford to compare the signal over many time periods. A TV signal

 carries a lot of information and changes rapidly. The comparison system would

 be too slow and cumbersome.

 

 

 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? Stay tuned and see.

 

 

In Review: Measuring Distance

 

   1.Distance to a satellite is determined by measuring how long a radio

      signal takes to reach us from that satellite.

 

   2.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.

 

   3.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.

 

   4.Multiply that travel time by the speed of light and you've got distance.

 

 

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.

 

Atomic Clocks

 

 Atomic clocks don't run on atomic energy. They get the name because they

 use the oscillations of a particular atom as their "metronome." This form of

 timing is the most stable and accurate reference man has ever developed.

 

 

 But what about our receivers here on the ground?

 

 Remember that both the satellite and the receiver need to be able to precisely

 synchronize their pseudo-random codes to make the system work. ( to review

 this point click here )

 

 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.

 

Using GPS for Timing

 

 We generally think of GPS as a navigation or positioning resource but the fact

 that every GPS receiver is synchronized to universal time makes it the most

 widely available source of precise time.

 

 This opens up a wide range of applications beyond positioning. GPS is being

 used to synchronize computer networks, calibrate other navigation systems,

 synchronize motion picture equipment and much more.

 

 And it's a great resource at 11:59 on New Year's Eve!

 

 

 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.

 

 This idea is so fundamental to the working of GPS that we have a separate

 illustrated section that shows how it works. If you have time, cruise through

 that.

 

If you don't have time here's a quick summary:

 

 Extra Measurement Cures Timing Offset

 

 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.

 

In Review: Getting Perfect Timing

 

   1.Accurate timing is the key to measuring distance to satellites.

 

   2.Satellites are accurate because they have atomic clocks on board.

 

   3.Receiver clocks don't have to be too accurate because an extra satellite

      range measurement can remove errors.

 

In this tutorial we've been assuming that we know where the GPS satellites are

 so we can use them as reference points.

 

 But how do we know exactly where they are? After all they're floating around

 11,000 miles up in space.

 

A high satellite gathers no moss

 

 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.

 

GPS Master Plan

 

 The launch of the 24th block II satellite in March of 1994 completed the GPS

 constellation.

 

 Four additional satellites are in reserve to be launched "on need."

 

 The spacings of the satellites are arranged so that a minimum of five satellites

 are in view from every point on the globe.

 

 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.

 

Ground Stations

 

 (also known as the "Control Segment")

 

 These 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: Hawaii, Ascension Island, Diego Garcia,

 Kwajalein, and Colorado Springs.

 

 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 DoD 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 trouble afoot. Check out the

 next section to see what's up.

 

In Review: Satellite Positions

 

   1.To use the satellites as references for range measurementswe need to

      know exactly where they are.

 

   2.GPS satellites are so high up their orbits are very predictable.

 

   3.Minor variations in their orbits are measured by the Department of

      Defense.

 

   4.The error information is sent to the satellites, to be transmitted along

      with the timing signals.

 

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 tutorial

 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.

 

Ionosphere

 

 The ionosphere is the layer of the atmosphere ranging in altitude from 50 to

 500 km.

 

 It consists largely of ionized particles which can exert a perturbing effect on

 GPS signals.

 

 While much of the error induced by the ionosphere can be removed through

 mathematical modeling, it is still one of the most significant error sources.

 

Troposphere

 

 The troposphere is the lower part of the earth's atmosphere that encompasses

 our weather.

 

 It's full of water vapor and varies in temperature and pressure.

 

 But as messy as it is, it causes relatively little error.

 

 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.

 

Error Modeling

 

 Much of the delay caused by a signal's trip through our atmosphere can be

 predicted.

 

 Mathematical models of the atmosphere take into account the charged

 particles in the ionosphere and the varying gaseous content of the

 troposphere.

 

 On top of that, the satellites constantly transmit updates to the basic

 ionospheric model.

 

 A GPS receiver must factor in the angle each signal is taking as it enters the

 atmosphere because that angle determines the length of the trip through the

 perturbing medium.

 

 Hey, THIS IS ROCKET SCIENCE!

 

 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.

 

Dual Frequency Measurements

 

 Physics says that as light moves through a given medium, low-frequency

 signals get "refracted" or slowed more than high-frequency signals.

 

 By comparing the delays of the two different carrier frequencies of the GPS

 signal, L1 and L2, we can deduce what the medium (i.e. atmosphere) is, and we

 can correct for it.

 

 Unfortunately this requires a very sophisticated receiver since only the military

 has access to the signals on the L2 carrier.

 

 Civilian companies have worked around this problem with some tricky

 strategies.

 

 Unfortunately they're so secret if we told you how they work we'd have to kill

 you.

 

 

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 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.

 

Multipath error

 

 The whole concept of GPS relies on the idea that a GPS signal flies straight

 from the satellite to the receiver.

 

 Unfortunately, in the real world the signal will also bounce around on just

 about everything in the local environment and get to the receiver that way too.

 

 The result is a barrage of signals arriving at the receiver: first the direct one,

 then a bunch of delayed reflected ones. This creates a messy signal.

 

 If the bounced signals are strong enough they can confuse the receiver and

 cause erroneous measurements.

 

 Sophisticated receivers use a variety of signal processing tricks to make sure

 that they only consider the earliest arriving signals (which are the direct ones).

 

 

Problems at the satellite

 

 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 or " ephemeris" errors can sneak

 in between monitoring times.

 

Ephemeris errors

 

 Ephemeris (or orbital) data is constantly being transmitted by the satellites.

 

 Receivers maintain an "almanac" of this data for all satellites and they update

 these almanacs as new data comes in.

 

 Typically, ephemeris data is updated hourly.

 

 

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.

 

The bottom line

 

 Fortunately all of these inaccuracies still don't add up to much of an error. And

 a form of GPS called "Differential GPS" can significantly reduce these

 problems. We'll cover this type of GPS later.

 

 To get an idea of the impact of these errors click here for a typical error budget:

 

Summary of GPS Error Sources

 

 Typical Error in Meters

                    (per satellite)

                    Standard GPS

                              Differential GPS

 Satellite Clocks

                           1.5

                                       0

 Orbit Errors

                           2.5

                                       0

 Ionosphere

                           5.0

                                      0.4

 Troposphere

                           0.5

                                      0.2

 Receiver Noise

                           0.3

                                      0.3

 Multipath

                           0.6

                                      0.6

 SA

                           30

                                       0

 Typical Position Accuracy

 Horizontal

                           50

                                      1.3

 Vertical

                           78

                                      2.0

 3-D

                           93

                                      2.8

 

In Review: Correcting Errors

 

   1.The earth's ionosphere and atmosphere cause delays in the GPS signal

      that translate into position errors.

 

   2.Some errors can be factored out using mathematics and modeling.

 

   3.The configuration of the satellites in the sky can magnify other errors.

 

   4.Differential GPS can eliminate almost all error.

 

 

On to Differential GPS...