The global positioning system exemplifies the amazingly high sophistication of 21st century technology that we now take for granted.

Its roots date to LORAN, a primitive radar system used in World War II, and was based on “;Transit,”; a system implemented in 1960 that used five satellites to give a crude navigational fix once per hour. GPS began as a military system, mandated by President Reagan in 1983 after a Korean airliner was shot down as it allegedly strayed into Soviet airspace. It underwent much iteration before becoming fully operational in 1995.

GPS uses a radio trilateration system to calculate distance by measuring the travel time from a minimum of three satellites. It is similar to triangulation used in surveying to pinpoint a location based on the geometric fact that the intersection of three circles defines a point.

The GPS system consists of a constellation of 31 Earth satellites orbiting at altitudes of 12,550 miles. The array is such that at least six satellites are within line of sight from any location on the planet at all times.

The satellites each have atomic clocks aboard and transmit a unique course acquisition (CA) code that carries the satellite's position, the GPS system time that is provided by atomic clocks at the U.S. naval observatory, its own clock error, and the accuracy of the transmitted data. The signal also contains the satellite's precise orbital ephemeris as well as information about the overall system health and orbital information about all of the satellites. The satellites synchronize so that the signals are all transmitted at the same instant.

The GPS receiver uses these signals to calculate its position by matching each CA code with an identical copy in its database.

Because the speed of light is so great a very small clock error can result in a large error in position, so the more satellite CA codes the GPS can receive the smaller the error.

Most commercially available GPS receivers are accurate to 10 or 20 yards, but scientists and others who need more precise locations use Differential GPS (DGPS). DGPS uses one or more additional receivers at a known location nearby that can correct positions to an accuracy of a few inches, allowing measurements of movements such as the drifting of continents and the swelling of volcanoes before eruptions.

Earth's rotation under the orbiting satellites contributes a few hundred nanoseconds that introduces tens of yards of error if not corrected.

The detail of the science, mathematics, signal processing and computer science is beyond the level of most of us. But the incredible advances that converge all of this in a hand-held device allow even the worst navigator among us to find our way home.

Richard Brill is a professor of science at Honolulu Community College. E-mail questions and comments to .(JavaScript must be enabled to view this email address).