**2. Overview of GPS**

GPS provides three-dimensional positioning and navigation services for both civilian and military users [2]. The GPS receivers use the TOA ranging to generate code pseudorange to determine the user's position. They also monitor changes in signal frequency to produce a rate of change of range measurements to determine velocity [3]. The time between the transmission of the signal and its arrival at the receiver is measured. The transmitter-to-receiver distance can then be obtained by scaling the signal transit time by the speed of light. Using the concept of trilateration, a GPS receiver can determine its position using the measured travel time along with the satellites' locations that are obtained from the navigation message carried by the signal. Though three satellites can be used to determine the user's position, at least four are required owing to an additional estimation of the receiver clock offset.

**Figure 1** illustrates the concept of position fixing by trilateration by using the range to three satellites. Using four satellites to find the position improves the accuracy of the solution by eliminating the receiver clock offset. The first and second user-to-satellite range measurements define two spheres on two different satellites, and the intersection of these two spheres defines a circle of possible receiver positions. A third range measurement, intersecting with the first two, narrows those receiver positions to an ambiguous pair, while the fourth measurement resolves this ambiguity and determines the clock bias. The GPS positioning equations are found in [1–6]. Military GPS signals are more robust against interference and spoofing than civilian signals [3]; hence, the position determined by military signals is more precise than the position determined using civilian signals.

**Figure 1.** The concept of position fixing by trilateration using signals from three satellites. The user's position is indicated by the red dot [4].
