A guided missile engagement is a highly dynamic process. The conditions that determine how close the missile comes to the target are continuously changing, sometimes at a very high rate. A guidance sensor measures one or more parameters of the path of the missile relative to the target. A logical process is needed to determine the required flight path corrections based on the sensor measurements.

This logical process is called a guidance law. The objective of a guidance law is to cause the missile to come as close as possible to the target. Guidance laws usually can be expressed in mathematical terms and are implemented through a combination of electrical circuits and mechanical control functions.

The two basic criteria on which guidance laws are based are that the guidance must (1) be effective under anticipated conditions of use and (2) be able to be implemented using the particular sensor configuration selected. A number of different schemes and their many variations have been used for missile guidance, chief among which are intercept point prediction, pursuit, beam-rider, proportional navigation, and methods based on modem control theory.

If a surface-to-air missile system is being used to defend a relatively small area the intercept ranges can be short enough that the accuracy from a ground-based sensor is acceptable, thus the cost and complexity of an onboard target sensor are eliminated. The missile system can be simplified further by eliminating the ground-based missile tracker; however, such elimination leaves only one way to keep track of the missile and that is to keep it within the target-track sensor beam. As the missile begins to move away from the beam, this movement is sensed either by the ground sensor or by antennas on the missile, and control commands are provided to hold the missile in the beam. This is called beam-rider guidance and is illustrated in Figure 4.

Fig. 4 Beam-Rider Guidance

The guidance scheme that has proven to be extremely effective is proportional navigation. In proportional navigation the missile is steered so as to cause the angular rate of the missile flight path to be proportional to the angular rate of the line-of-sight from the missile to the target. The proportionality factor, called the navigation ratio, is usually set between 3 and S, i.e., the turn rate of the missile is three to five times the angular rate of the line of-sight. The result is that the angular line-of-sight rate is driven toward zero, and the missile is steered to a flight path in which the bearing angle to the target tends to remain constant as shown In Figure 5.

One basic tenet of Ship piloting is that “constant bearing means collision”. It can be shown that under the conditions of constant target velocity and constant missile velocity, proportional navigation does indeed lead to an Intercept.

Fig. 5 Proportional Navigation Guidance