SciTech

How Things Work: Global Positioning Systems

A GPS will utilize three or four different satellites to figure out its location. When the GPS determines a distance from a particular satellite, a sphere of possible locations is created. The GPS’ final location is determined by the point where the spheres generated from each satellite overlap. (credit: Michael Setzer/Acting SciTech Editor | Adelaide Cole/Art Editor) A GPS will utilize three or four different satellites to figure out its location. When the GPS determines a distance from a particular satellite, a sphere of possible locations is created. The GPS’ final location is determined by the point where the spheres generated from each satellite overlap. (credit: Michael Setzer/Acting SciTech Editor | Adelaide Cole/Art Editor)

The GPS, or Global Positioning System, is an efficient tool that one may utilize for myriad causes. It is an ubiquitous object that is able to identify a current location and destination, give directions, and calculate the time and distance of a journey. How does such a small object complete such complex tasks?

Broadly, the GPS function is supported by clocks, signals, and mathematical concepts. The GPS system involves the receiver as well as 27 Earth-orbiting satellites, three of which are backups in case one fails. According to howstuffworks.com, the satellites rotate around the Earth twice a day so that different sets of at least four satellites are visible through a telescope at all times and in all places. The GPS receiver calculates a specific point on Earth by analyzing radio signals from GPS satellites.

Through 3-D trilateration, a mathematical principle that involves overlapping areas, the GPS can identify its current location by relying on its distance from a relative point on Earth and from at least three satellites. Because a satellite cannot determine the exact direction it receives the signal from a GPS, a sphere of possible locations is created, with the radius being the distance between the GPS and the satellite. So if a GPS connects with three or four satellites, four spheres of possible locations are generated. The intersection of these spheres on Earth is the location of the GPS.

But how does the GPS calculate the distance from the receiver to the satellite? The satellite contains an atomic clock that can be synchronized to the nanosecond, while the receiver contains a household clock that constantly resets. Because the household clock in the receiver initially makes proportionally incorrect time measurements using its own clock, the receiver resets and syncs with the satellite's correct time. Syncing to a correct time causes all received signals to align at a single point in space, which causes the other three satellites to have the same time.

After syncing, the satellite transmits a pseudo-random code, or a digital pattern, and the receiver begins running the same pattern. As the satellite’s signal reaches the receiver, transmission lags behind the receiver’s pattern run. The receiver determines its distance from the satellite by multiplying the lag by the speed of light.

To use the distance information, the GPS receiver refers to an internal almanac that records every satellite position at any given time. Any slight changes in the satellite orbit will be corrected and sent to the receivers by the Department of Defense.

Despite the intricate processes that appear to guarantee accuracy, satellites sometimes transmit unclear signals and faulty almanac information. In those cases, a Differential GPS (DGPS) — which is separate from the ones that everyday people use — identifies inaccuracies by calculating its location via satellite signals at its stationary receiver station, and then compares it to a known location.

The DGPS provides correct signal information by broadcasting a radio signal from its station to all DGPS-equipped receivers in the area. As a result, those roving GPS receivers will receive signals that inform them of any differences in calculation from the DGPS station and correct any faulty information. From there, those DGPSs communicate correct signal information to GPSs that civilians use.

It then sends a radio signal to all DGPS-equipped receivers, informing them of correct signal information. In general, the GPS picks up transmissions from at least four satellites and combines them with information in the electronic almanac to figure out the receiver’s position on Earth. When the position is calculated, the GPS can tell users the longitude, latitude, and altitude of their current positions and future destinations.

So when you pull out your GPS help you get to your relative’s house for Thanksgiving, you can thank complex mathematical principals for getting you where you need to be.