GPS (very) Basics

The geodetic positioning system (GPS) is based on satellite ranging. Any GPS receiver can identify signals from any of 24 satellites; each satellite broadcasts its identity and location. GPS receivers analyze signals from visible satellites and determine the distance from them. Because a receiver's clock is not nearly as accurate as the atomic clocks in the satellites, a GPS receiver determines how far it is from four GPS satellites to solve for four unknowns: northing, easting, elevation, and time.

Standard, utility grade GPS receivers work on the code phase, in megahertz, broadcast by the satellites. Travelling at about the speed of light, these waves have nominal wavelengths greater than about 10² meters. Thus resolution is limited to an accuracy of tens of meters. As a demonstration, I positioned a Trimble Geoexplorer GPS receiver on my garage roof and collected positions for a couple of hours. The thumbnail on the right leads to the result and some accompanying (quick, dirty, and not rigorous) statistics. The result is representative of what you can expect from code-phase receivers operating on a stand-alone basis. That is, with any individual reading you might be off by tens of meters. Several averaged readings, collected over an hour or more, will produce a more accurate result.

Notice that many of the positions in the figure are on loopy tracks that end; that's what happens when a different satellite is picked up and used by the GPS receiver. Differential corrections, essentially comparing our observations to observations from a nearby fixed base station and assuming the errors are highly correlated, will significantly collapse the error envelope. Using Missoula County's community base station to differentially correct the readings from my garage roof reduced the standard error by nearly an order of magnitude.

To further reduce the standard error of GPS observations requires using the gigahertz carrier phase rather than the megahertz code-phase broadcast from the satellites. Going from megahertz to gigahertz improves results by about 10³ but requires occupation times of at least ten minutes using the Trimble Geoexplorers.