Satellite navigation systems have come to affect countless aspects of our daily lives, from directing our holiday aeroplanes to enabling us to drive round an unfamiliar city without any map other than the one on our mobile phone. Most new cars sold today have an inbuilt Sat Nav and you can buy trackers relatively cheaply to enable you to track the whereabouts of your children and pets.
Some of the many Sat Nav Devices
I for one am heavily reliant on this technology to find my way from A to B. Although I enjoy using paper maps, they have the major limitation that they don’t tell you your current location!
If we also know that we are 35000 km from satellite B then our location must be on the ring of points where the two spheres intersect
If we also know that we are 21 000 km from satellite C then our location must be where the three spheres intersect. So it must be at either location x or location y.
Although there are two possible locations (x and y) only one of these will be at a sensible location on or near the surface of the Earth.
Because the GPS receiver does not have an accurate atomic clock it cannot know the current time as accurately as the GPS satellites. The clock on the GPS receiver will be fast or slow by a small fraction of a second. To get an accurate measure of the time taken for the signal to arrive, the clock on the GPS receiver must synchronise perfectly with the clocks on the GPS satellites. The way it gets around this is by using the time signal from a fourth satellite to work out the amount of time by the which the receiver is fast or slow. (The signal from the fourth satellite also confirms which of the possible locations (x and y) in the diagram above is correct)
Because the satellites are in space orbiting the Earth at 14 000 km/h, their atomic clocks run at slightly different speeds compared to atomic clocks on the Earth’s surface. There are two separate effects which work in opposite directions.
- Einstein’s theory of special relativity predicts that moving clocks run slow and means that the so the atomic clocks on the satellites should run at a slower rate than identical stationary clocks.
- However, Einstein’s theory of general relativity tells us that clocks run more slowly in proximity to a massive object (in this case the Earth) so the atomic clocks on the satellites should run at a faster rate than identical clocks on the Earth’s surface.
Taken together, the two effects mean that time on a GPS satellite runs slightly faster than it does at the surface of the Earth at the incredibly small rate of just under 46 millionths of a second per day. Because of this GPS satellites’ atomic clocks need to be slowed down to keep them in step with atomic clocks on the surface of the Earth.
Limitations of Sat Nav
There are limitations to the accuracy of position provided by GPS (or indeed any Sat Nav system). One is that the speed of radio waves is not constant. Conditions in a region of the upper atmosphere, known as the ionosphere, can cause them to slow down slightly. This makes the time taken for the signal to arrive at the receiver slightly longer, implying that a satellite is further away than it actually is. Another factor is that large objects such as trees between the receiver and the GPS satellite may weaken the signal or even block it altogether.
An additional false signal can also be generated when a GPS signal is reflected off tall buildings. This effect, which is known as a multi-path error, is shown in the diagram below. The receiver receives two signals from the same satellite: a direct signal (the yellow line) and a reflected signal (the pink line). The two signals have travelled different distances, so the GPS receiver calculates two different distances to the same satellite. This can result in an incorrect distance if the wrong signal is chosen by the receiver. Alternatively, the two signals can interfere and cancel each other out so no signal is received.
Errors could also be caused by slight inaccuracies in the atomic clocks on the satellites or by the satellite making an error when calculating its own exact position. Nevertheless, even taking all these factors into account, a GPS receiver should be able to work out its position to an accuracy of within 10 metres. This, however, only applies to locations outdoors and above ground, as the signal cannot travel through buildings with thick walls.
Improving Sat Nav Accuracy
For non-civilian users, who need to know their position to greater precision Sat Nav can be augmented in a number of ways to provide better accuracy. For example, satellites transmit on multiple frequencies and more than one of these frequencies can be used. This is too large a topic to fit in this post, but if you want to know about one system, WAAS used by the US Federal Aviation Authority, please click on the link belowhttps://www.faa.gov/about/office_org/headquarters_offices/ato/service_units/techops/navservices/gnss/waas/howitworks/