How many GPS satellites are required to yield a three dimensional position (latitude, longitude, and altitude) and time solution?

• A. 3 satellites
• B. 4 satellites
• C. 5 satellites
• D. 6 satellites

Answer: (B)

The essential idea is that to determine a full 3D position plus the receiver’s precise time, you must solve for four unknowns: the receiver’s x, y, z coordinates and the receiver clock bias relative to GPS time. Each GPS satellite provides one pseudorange measurement, which translates into an equation that relates these unknowns to the measured distance to that satellite (plus the clock error). Therefore, you need four independent equations to solve for four unknowns, which requires four satellites.

With only three satellites, you’d have three equations for three unknowns, but the receiver clock error remains unresolved, so you can’t obtain a complete 3D position and time. Having more than four satellites isn’t required for a basic solution, but those extra measurements improve accuracy and allow a more robust, redundant solution through least-squares processing.