Global Positioning System receivers require a minimum of four visible satellites to determine a precise, three-dimensional position encompassing latitude, longitude, and altitude, while simultaneously correcting receiver clock bias. Mathematically, three intersecting spheres derived from distance measurements to three satellites can pinpoint two potential points in space, one of which is typically discarded as invalid far above or below the Earth. However, because standard consumer GPS receivers contain inexpensive quartz clocks rather than atomic clocks, a severe timing discrepancy exists between the receiver's internal clock and the ultra-precise atomic clocks onboard the satellites. A fourth satellite measurement is strictly required to solve for this clock error variable, allowing the receiver to calculate accurate three-dimensional coordinates and precise time.