Question 3-98P5

To provide a complete three-dimensional position (latitude, longitude, and altitude) and precise time, a GPS receiver needs to receive signals from at least four satellites. Each satellite transmits a signal containing its precise location and the exact time the signal was sent. By measuring the time it takes for these signals to reach the receiver, the receiver can calculate its distance (pseudorange) from each satellite. Three satellites are theoretically enough to determine a 3D position through trilateration. However, this assumes the receiver's internal clock is perfectly synchronized with the atomic clocks on the satellites. Since typical GPS receivers have less precise, inexpensive clocks, there will be an unknown error in their timing. The fourth satellite provides an additional measurement, creating enough data to solve for this receiver clock error simultaneously with the three unknown position coordinates (X, Y, Z). Thus, the fourth satellite is essential for achieving both accurate position and precise time synchronization.