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A GPS receiver calculates its position by carefully timing the signals sent by the constellation of GPS satellites high above the Earth. Each satellite continually transmits messages containing the time the message was sent, a precise orbit for the satellite sending the message (the ephemeris), and the general system health and rough orbits of all GPS satellites (the almanac). These signals travel at the speed of light (which varies between vacuum and the atmosphere). The receiver uses the arrival time of each message to measure the distance to each satellite, from which it determines the position of the receiver (conceptually the intersection of spheres - see trilateration[5]). The resulting coordinates are converted to more user-friendly forms such as latitude and longitude, or location on a map, then displayed to the user.

It might seem that three satellites would be enough to solve for a position, since space has three dimensions. However, a three-satellite solution requires the time be known to a nanosecond or so, far better than any non-laboratory clock can provide. Using four or more satellites allows the receiver to solve for time as well as geographical position, eliminating the need for a very accurate clock. In other words, the receiver uses four measurements to solve for four variables: x, y, z, and t. While most GPS applications use the computed location and not the (very accurate) computed time, the time is used in some GPS applications such as time transfer and traffic signal timing.

Although four satellites are required for normal operation, fewer may be needed in some special cases. If one variable is already known (for example, a ship or plane may already know its altitude), a receiver can determine its position using only three satellites. Some GPS receivers may use additional clues or assumptions (such as re-using the last known altitude, dead reckoning, inertial navigation, or including information from the vehicle computer) to give degraded answers when fewer than four satellites are visible.[6][7][8]


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