At over 20,000 kilometres above sea level (20,180 kilometres (12,540 miles)) is a constellation
of satellites, each orbiting Earth every 11 hours and 58 minutes.
These satellites are continuously beaming data down to us on earth, which in turn is
received by devices such as your phone or navigational units in your cars, allowing
you to see where you are on the planet.
There are a lot of misconceptions about how GPS’s actually work, an example being that
your phone and the GPS satellites are both talking to each other.
So let’s get down to it: how do GPS’s work?
GPS stands for Global Positioning System, which works through trilateration, not triangulation
or multilateration, which is commonly misconceived.
There are many different types of navigational satellite systems from countries across the
world, but the most popular and commonly used system is Navstar, which is the USA system.
There are however Russian, Indian, Chinese and European equivalent systems, although
the Indian and Chinese systems sit in a geosynchronous orbit above their countries which means they
are not worldwide systems.
The Navstar system, which is simply referred to as GPS, is what we will be focusing more
on – although most phones and devices tend to have the capabilities to use both GPS and
GLONASS.
GPS satellites are setup in such a way that from almost anywhere on the surface of Earth
you should have a direct line of sight of at least four GPS satellites.
This is quite important on the basis that GPS point positioning requires at least four
satellites to calculate three position coordinates and the clock deviation.
As GPS units are receivers, there needs to be something sending some sort of signal to
devices such as your phone to receive.
Each GPS satellite broadcasts a navigational message towards Earth which contains an extremely
accurate timestamp (obtained through atomic clocks on-board the satellites), and the satellites
also broadcast their position at the time of broadcast, with all GPS signals broadcasting
at 1.57542 GHz (L1 signal) and 1.2276 GHz (L2 signal).
These two bits of information allow you to begin to work out your position on Earth.
With the satellites all sending exceptionally accurate time down to Earth, your phone or
GPS receiver can compare the difference of time between the signal being sent and received
to work out the distance between you and the satellite.
By multiplying this time difference with the speed of light (as the signal is sent as the
speed of light), you can get the distance you are from the satellite.
As the satellites are also sending whereabouts they are, you can begin to draw spheres around
the satellites, with you being somewhere on the outside border of the sphere.
As we introduce more GPS satellites into the mix we begin to get closer to where we are.
By calculating the time differences between these satellites we move from having no idea
where we are, to being able to pinpoint where we are, typically down to five to ten minutes
on average, with the potential error being around 15 metres.
There are a lot of factors which escalate the potential error, but the most significant
is due to the ionosphere, a part of the upper atmosphere extending from 60 km to 2,000 km,
where free elections occur frequently enough to have an appreciable influence on the proportion
of electromagnetic waves passing through this layer.
This error is substantially smaller when satellites are directly overhead, compared to being larger
the closer satellites are to the horizon relative to you as the path between you and the GPS
satellites goes through more of the atmosphere compared to being directly overhead.
Even things such as small variations in the atomic clocks found on board these satellites
can case major errors.
A clock error of 1 nanosecond can translate through to a 1 foot or 30 centimetre miscalculation.
Then the theory of relativity kicks in with the atomic clocks (which are moving at GPS
orbital speeds) ticking ever so slightly slower than clocks which are stationary on the ground
which translates into a 7 microsecond a day delay.
General relativity then kicks in with the effect of the gravitational frequency shift
being far greater than the 7 microsecond per day delay due to the velocity relative to
Earth.
As the theory states that a clock which is closer to an object will be slower than a
clock further away, the atomic clocks on board the GPS’s are faster by about 45.9 microseconds
per day.
Combining the 7 microsecond a day delay due to the satellites velocity relative to Earth
and the GPS’s being further away from Earth, this adds up to a 38 microsecond delay, which
if left uncorrected would translate through to a 10 km/day pseduorange error, rendering
GPS’s invalid from the get go if this was not to be taken into consideration.
This is compensated by the GPS’s clocks frequencies being slightly slowed down from
10.23MHz to 10.22999999543 MHz to cancel out the effects of relativity.
So next time you turn on your GPS, you should realise just how much physics and maths is
going into you finding your own location.