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...