I'm sure you already know what GPS is
but have you ever wondered how GPS
actually calculates your position or
what sort of limitations there are to
its accuracy? in its most basic form GPS
triangulate your position by measuring
how far away it is from different
satellites it knows the position of each
satellites and by drawing an imaginary
ring around each one it can calculate
its position as the point where all the
Rings intersect it sounds simple enough
but in this video we're going to explore
exactly how it measures our distance and
what sort of errors can creep in
throughout the process let's look at
this diagram to keep things simple I'm
going to only work on a 2d image for 3d
like in real life you just need to add
an extra satellite to work out the extra
dimension this satellite will broadcast
its code at a set time let's call that
time T equals zero the transmission will
travel out from the satellite at the
speed of light obviously I've slowed it
down here as it travels out time ticks
away a time T equals five the receiver
picks up the signal if the time on the
receiver and the time on the satellite
are perfectly in sync the receiver could
easily calculate the precise distance to
the satellite using the equation
distance equals speed times time time
was measured at five and the speed is
the speed of light with that distance it
can draw a ring around the satellite and
know that it is somewhere along that
ring repeating the process with a second
satellite gives us a second ring the GPS
knows it is at the location where the
two rings intersect you'll notice that
there are two points where these circles
intersect but if we add in the
additional restraint that the position
has to be near the surface of the earth
then we can eliminate one of those
points of course all this only works if
their receiver and the satellites keep
perfect time for the satellites that's
easy each one carries multiple atomic
clocks atomic clocks use the atomic
oscillations of atoms to maintain time
accurate
within less than a second over millions
of years this sort of accuracy is
necessary when you consider the signal
travels at the speed of light which is
300,000 kilometers per second if time
was out by as little as one second the
position would be 300,000 kilometers
away from where it should be
GPS receivers however do not have
built-in atomic clocks
they've only got normal clocks which are
nowhere near as accurate as is needed
what this means is that instead of
knowing the precise time as is kept by
the satellites they have their estimated
time based on their own clock to turn
this into the same precise time that the
satellites use they need to apply an
unknown offset in our previous example
instead of the receiver knowing that as
time equals 5 it would now think that
the time equals 5 plus some offset which
we're just going to call alpha for now
the equations that we use to calculate
the distance their satellites now
becomes distance equals speed times time
which equals speed times 5 plus alpha
this offset is going to be the same for
all equations as the time offset is
constant the receivers clock is wrong by
a set amount we just don't know what
that amount is with the additional
unknown is no longer possible to find
our position using only two satellites
two satellites worked when we needed two
unknowns our x and our y coordinate now
that we have three unknowns X Y and
alpha we need to resettle ice to solve
the required equations of course we've
only been working in two dimensions so
far in real life there is an additional
dimension we actually want latitude
longitude altitude and time the same
principle applies which just means we
need four satellites to produce enough
simultaneous equations it is this reason
that GPS receivers all lock onto a
minimum of four satellites before
they're able to give you your position
even after completing all these
calculations there are still limitations
and errors that can creep in propagation
these are errors that arise due to
signals from satellites slowing down as
they
passed through different layers of the
atmosphere different atmospheric layers
are made of different elements creating
different densities as signals passed
through these layers the speed at which
they trouble might reduce slightly
normally GPS signals travel at the speed
of light but if they slow down in places
they're going to take longer than
expected to reach the receiver this
results in a slightly airiness
measurement of pseudo range to the
satellite which results in slight
inaccuracies to the final calculated
position remember we've already said
that for every second of error our
position is out by 300,000 kilometers
one millionth of a second is going to
result in an accuracy of 300 meters
which is still way bigger than we need
GPS can compensate for some propagation
errors by transmitting a second signal
that's a different frequency to the
first different frequencies are
disrupted differently when passing
through layers of the atmosphere
comparing the second frequency to the
original gives enough information to
work out a correction to apply multipath
errors are caused by signals from
satellites not taking a direct path to
the receiver
maybe they bounce off a building or a
cliff face before reaching the receiver
again this results in the signal taking
a longer time to reach the receiver then
it would have taken if it had traveled
along the direct route again this
results in an errand assistance being
calculated in terms of marine GPS units
these errors are not so common there are
not so many structures at sea they
result in multipath errors and GPS
aerials are placed high up on the ship's
superstructure improving the visibility
of satellites ephemeris or orbital
errors are due to slight variations in
satellite orbits if the orbit was
precise all the numbers would tie in
perfectly as the orbit of the satellites
varies slightly small errors can creep
into the calculated positions ephemeris
errors are correctable because satellite
positions are observed by ground
stations ground stations calculate the
difference between the satellites
expected position and their actual
position so they can apply the
correction receiver noise refers to
errors resulting from electronic signals
within the GPS
receive a unit itself the receiver is a
small level of interference much like
the static you can sometimes see on your
TV screen this can effect signals
received and in turn affects that
calculated pseudo ranges to each of the
satellites a lot of this can be solved
with just quality of equipment you
generally find more expensive equipment
will suffer from less noise relativistic
errors are errors that result from
relativistic effects within the
satellites themselves there are loads of
videos about Einstein's theory of
relativity but the part we're interested
in is the part that describes how time
runs at different speeds depending on
the relative speed between two observers
this is important for us because
satellites orbiting the Earth travels so
much faster than observers on the earth
about 9,000 miles per hour time on each
satellite appears to run differently to
time on earth on satellites it actually
runs slightly faster so all the clocks
will be turning that little bit quicker
to compensate for this the clocks are
programmed to run slightly slower than
they would do on earth from the point of
view of an observer on earth the clock
is actually running at the right speed
relativistic effects are still monitored
from stations on earth to ensure the
system maintains is accuracy and finally
differential GPS now differential GPS
was a system originally developed a
combat selective availability selective
availability which degraded the accuracy
of signals randomly it made positional
accuracy less precise for users that
were not past the US military and did
not have access to the key to decode the
errors the theory behind D GPS was that
you could build a receiver in a fixed
location and compare its GPS position to
his actual position the difference
between the two was due to selective
availability the difference could be
broadcast as a correction to all
receivers in the area they are equipped
to receive D GPS Corrections the
correction effectively eliminated
selective availability contributing to
its eventual termination today even
though selective availability is no
longer an issue d GPS is still
use to provide corrections to GPS
signals and increase its overall
accuracy and that brings us to the end
of todays video if you've enjoyed the
content this video is actually based on
an article that I've written for my new
website I'm going to add the link down
in the description below otherwise
hopefully you've found the content