Basic GPS Concept - Fundamentals of Global Positioning System Receivers: A Software Approach - page 9

FIGURE 2.2 Two-dimensional user position.
In GPS the position of the satellite is known from the ephemeris data trans-
mitted by the satellite. One can measure the distance from the receiver to the
satellite. Therefore, the position of the receiver can be determined.
In the above discussion, the distance measured from the user to the satellite
is assumed to be very accurate and there is no bias error. However, the distance
measured between the receiver and the satellite has a constant unknown bias,
because the user clock usually is different from the GPS clock. In order to
resolve this bias error one more satellite is required. Therefore, in order to find
the user position five satellites are needed.
If one uses four satellites and the measured distance with bias error to measure
a user position, two possible solutions can be obtained. Theoretically, one cannot
determine the user position. However, one of the solutions is close to the earth's
surface and the other one is in space. Since the user position is usually close to
the surface of the earth, it can be uniquely determined. Therefore, the general
statement is that four satellites can be used to determine a user position, even
though the distance measured has a bias error.
The method of solving the user position discussed in Sections 2.5 and 2.6 is
through iteration. The initial position is often selected at the center of the earth.
The iteration method will converge on the correct solution rather than the one
in space. In the following discussion four satellites are considered the minimum
number required in finding the user position.