The Global Positioning System (GPS) is one of the true wonders of modern science. It is one of the only human achievements that has combined both Einstein’s Special and General Relativity theories. Funded by the American Department of Defence (DoD), it is the cornerstone of most electronic navigation devices available to buy today.
The Global Positioning System or GPS for short, is a network of satellites above the Earth.
There are roughly 30 satellites in use at any time, orbiting at 11,500 miles above the Earth’s surface. The satellites zoom through the sky at over 9500mph. Because of their positions, any device is always in the line of sight of at least 4. This can be far higher with over twelve available at once if you are in the right spot.
The satellites broadcast a very accurate time signal, kept in check by the use of atomic clocks on board the satellites. Devices then receive and measure these signals. By differentiating between the minute differences in these timing signals from three or more satellites, the devices can determine your exact location, anywhere on the Earth’s surface. Positioning calculations are called triangulation.
Triangulation with three satellites can give an accurate two-dimensional position on the surface of the Earth, being your longitude and latitude. If you add in the data from a fourth satellite, you can then accurately determine your altitude as well. The more satellites you add, the greater the degree of accuracy you can expect. When GPS is in line with a reasonable number of satellites your device can give you an exact three-dimensional position, usually to within a few yards, anywhere on the planet. Expensive, or government/military devices can provide accuracy within inches.
There are also some ground-based stations that periodically check that the satellites are where they say they are. These though, are of general purpose and not specifically assigned to the GPS system, so we won’t delve too far into these.
So that covers the simple explanation. Now, to find out how a time signal sent from many thousands of miles above our Earth translates into a meaningful position on a map, we will have to look more in depth at the satellites and signals. As well we’ll take a look at how the effects of Einstein’s equations help to keep everything in check.
GPS – A More Technical Overview
The satellites broadcast a time signal, which is in turn received by the GPS device. In addition to this, the satellites also broadcast secondary streams of data, called Almanac and Ephemeris data. This data is then stored on your GPS device and referred to like a set of sky maps and is referred to when triangulating positions. Importantly, the validity (freshness) of these data sets is critical to the successful operation of your device. If your GPS doesn’t know where in the Sky the satellites are, then there is no way a timed signal can be used to judge your distance from them, relative to the other data points.
Devices from different sources, different manufacturers, or those of differing quality all have slightly different thresholds for how long this data should be stored on the device before it is considered inaccurate and in need of updating. For the Almanac data, this can vary from a few weeks to many months. The Ephemeris data is updated far more regularly.
The Almanac data
Each satellite in the sky broadcasts the orbital paths of every other satellite on the GPS network. With this information, your GPS device can determine which satellites it should expect to see in the sky. Such as those behind the Earth’s horizon. The Almanac data contains the standard orbits of the satellites and is considered non-precise information.
The Almanac data is not updated very often, mainly due to the size of the dataset that needs to be installed. Without an up to date Almanac, your GPS won’t attempt to start calculating your position as it won’t know which satellites from which to expect signals. Given that it can take between five and fifteen minutes (device dependant) to work, it is considered an unacceptable length of time to wait for your device to start. However, the standard orbit of each satellite changes very infrequently and so there is little need to update the Almanac information often.
You may have noticed the delay caused by almanac data being received if you have not used your GPS for a while. In the case of many months out of use, it can feel like an eternity waiting for it to start pinpointing your position.
The Ephemeris data
Unlike the Almanac data, which broadcasts information from every satellite, about every satellite, the Ephemeris data is unique to each satellite that is broadcasting. The Ephemeris data contains accurate information about the exact position of each satellite and where it should be at specific times of the day. As such, this data needs to be very accurate and so is broadcast by the satellites roughly every thirty seconds. Ephemeris data becomes quickly inaccurate compared to the Almanac data. Some manufacturers set the renewal time in minutes, with not many running into hours. The Ephemeris data, however, only takes around six seconds to download from each satellite, so is non-disruptive.
There is still a small start up delay when you first turn your device on, even after a few hours. For the first triangulation, your GPS still has to consult the Almanac (if current). It then starts to synchronise the Ephemeris data from the satellites and where it “thinks” they are in the sky. Once locked on to the satellites, it then starts it positioning calculations.
The process is quicker if you are standing still. It is harder to gain a relative perspective as each new satellite found and acquired if you are moving.
If you have a more technical device, you can usually find a screen showing the satellites. These devices will also show the signal strength from each.
Ships navigators of old would be amazed by GPS. A scientific miracle in a tiny handheld device.
So where does Einstein come into all this?
We did elude to the use of Einsteins Special and General Relativity theories playing a part in the calculations.
Those new to these theories, may not appreciate the sheer complexity of them. Suffice to say that Special Relativity is used to factor in the effect of time travel that the satellites go through. Caused by them moving at high speed around the Earth. Objects that are moving at any speed relative to another, but more noticeably at higher speeds, experience a difference in realtive time. The GPS system relies on time accuracy to within thousands/millionths of a second, and so these fluctuations need to be taken into account. GPS satellites lose around seven microseconds a day because of this.
General relativity produces a similar effect.
There is some more technical reading available from other sources at the bottom of the article.
Other systems are also being developed to compliment/replace GPS. These include the Russian GLONASS system, and European Galileo system. Both are reportedly more accurate than the ageing GPS system. At the time of writing this, GLONASS is starting to see its way into most mainstream systems. A lot of devices adopt both GPS and GLONASS combined. Galileo is still a few years away from being ready for use by the general public.