GPS, Global Positioning System, is the most used geolocation system all around the world. As seen before in TFS, all GPS satellites have synchronized atomic clocks and orbit the Earth every 12 hours (twice a day). Thanks to that and the signal emitted from them, the GPS receivers (for example, a mobile phone) can be positioned no matter where on the globe. However, a small but essential point that could completely vary the measure is not being considered thus far
According to Einstein’s theory of relativity, clocks tick slower if an object is moving faster, this is known as time dilation. In other words, if a person is moving 1000 times faster than another, their time is passing differently than that of the other. The clock for the one who goes faster ticks slower than for the other person. Therefore, GPS satellite clocks, as they are moving faster than Earth in their orbit, are ticking around 7 µs slower than a clock on Earth, per day!
Nevertheless, this is not the only consequence of Einstein’s relativity theory. Actually, Einstein also stated that gravity curves space and time. This means, due to GPS satellites experiencing four times less gravity in their distant orbit than on Earth, their clocks are advancing 45 µs faster per day than on Earth. Thus, it can be concluded that the time difference experienced by a clock on Earth and one on a GPS satellite is 38 µs per day (45 – 7).
For a human being 38 µs is not even significant, so the question is, why is it so important to correct it? Well actually, not correcting those 38 µs can result in your GPS positioning you in Hong Kong when you’re in fact in New York. In other words, GPS receivers calculate the distance between GPS satellites and the same receiver, assuming that their orbit is perfectly known by all of the receivers and the signal received from them also contains the satellite time. From that data the distance is calculated, but those 38 µs of error would insert around 10km position error (38 µs is the time in which the light is able to go through 11km) and that’s why it is so important to correct it.
Despite this correction, GPS or other navigation systems are still not 100% accurate and this is because of the accuracy of timing. In fact, the GPS satellites have an accuracy timing of around 10ns (3m error), that is pretty small, as they use atomic clocks. Moreover, the other big issue is the receivers : as they could have an accuracy timing of 30ns. For example, for L1 GPS receivers, this implies, an error of 10m while trying to obtain positioning.
Some new alternative clock technologies are trying to be developed in the field of global positioning in order to achieve better performances, one of them is the Hydrogen masers used by Galileo but this will be treated in the next GNSS article.