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ArticlesHow Triangulation Works


April 1995 / Solutions Focus / On-Road, On-Time, and On-Line / How Triangulation Works

GPS (Global Positioning System) location technology uses a trigonometric formula known as triangulation. There are two methods of triangulation; one uses an unknown location, and the other uses a known location. Vehicle-location systems such as the one used by Day & Night use the unknown-location method.

A transceiver in a truck receives signals from three satellites. From these signals, the software in the transceiver can determine the truck's position. The satellites orbit the earth at about 12,000 miles from its surface, but a satellite is rarely directly overhead. The varying positions of a satellite in its orbit create a variety of distances from the transceiver.

If a truck receives a sign al from a satellite located 13,000 miles away, the location of the truck is narrowed down to a 13,000-mile sphere centered on that satellite. If another signal comes from another satellite located 18,000 miles away, the location is narrowed further to the points where the 13,000-mile and 18,000-mile spheres intersect. Add a third satellite, located 16,000 miles away, and the area of intersection is narrowed to two points--one on the ground and one impossibly high above the earth.

The distance between a truck's transceiver and a satellite is calculated with the old "velocity times travel time" formula you may have learned in school. The satellite signal contains the time it was sent from the satellite.

To work correctly in a GPS, each clock in every transceiver has to be synchronized to the nanosecond. Each satellite has four atomic clocks: One is the working clock, one serves as a backup, and the other two are responsible for keeping the first two in sync.

When the transceiver receives a signal, the time included in the signal is immediately recorded. The GPS's software then calculates the difference between the send time and the current time to determine the lapse. For example, the transceiver might find that the lapse is 0.1 second. Using the aforementioned formula, velocity (186,000) time traveled (0.1) equals the distance from the satellite (18,600 miles).

After determining the transceiver's distance from all three satellites, the software in a GPS can accurately determine the transceiver's latitude, longitude, and altitude. Then, based on the transceiver's unique identity number, it can transmit its position using a different geosynchronous satellite communications network.

How long does all this take? If a truck uses the same three satellites during the operation, it can take as little as 2 seconds. Otherwise, the calculation can take up to 30 seconds.

Triangulation is an old concept: Celestial navigation uses triangulation with the position of three stars. But it looks like triangulation will be around for years to come. Even the starships Enterprise and Voyager use triangulation to plot courses for strange, new worlds.


Location, Location, Location

illustration_link (74 Kbytes)

A truck-mounted transceiver relays positioning information to three Navstar satellites that orbit the earth at an altitude of 12,000 miles. The satellites collate the positioning data to determine the truck's geographic location. A communications satellite links the truck and the company headquarters via the system provider's base station(s).


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