Question 28C6

To determine a receiver's precise three-dimensional position (latitude, longitude, and altitude) and to achieve the highest accuracy, four satellites are the minimum required. Here's why: * Each satellite signal provides a pseudorange measurement, indicating the distance to that satellite. * To solve for a receiver's 3D position (three unknown variables: x, y, z coordinates), three distance measurements from three different satellites are geometrically needed, assuming perfect synchronization. * However, a typical GPS receiver's internal clock is not perfectly synchronized with the atomic clocks on the satellites. This clock offset introduces a fourth unknown variable. * Therefore, to solve for all four unknowns (x, y, z, and the receiver's time offset), a minimum of four independent distance measurements from four satellites are necessary. This allows the receiver to accurately calculate its 3D position while simultaneously correcting its internal clock error. Receiving fewer than four satellites makes it impossible to accurately determine 3D position and correct for time. While more than four satellites can improve accuracy by providing redundant data and better geometric dilution of precision (GDOP), four is the fundamental minimum for the initial calculation of highest accuracy.