In this chapter, we present the fundamentals used in the analysis and design of midcourse guidance systems. These systems are predicated on the following assumptions:

1. In mission planning, a set of nominal trajectories that meet mission specifications is determined.

2. During flight, corrections are continually applied to the trajectory to return it to nominal. This sustained application of control authority is the distinguishing feature of midcourse guidance.

We consider three methods for midcourse guidance. In the first method, the set of nominal trajectories is parametrized by initial position and initial time, which specify the required velocity. This leads to the formalism of velocity-to-be-gained guidance, also known as Q-guidance. In the second method, a single nominal trajectory is determined and control is applied to return the trajectory to it. This leads to the formalism of state feedback guidance, also known as Delta-guidance. The third method combines state feedback guidance with navigation in that it uses Delta-guidance based on an estimate of the state vector rather than the true state vector.

Midcourse guidance is related to work presented in the previous two chapters. Indeed, in Chapter 5, the primary purpose of homing is to come close to a target - in other words, homing is a “final-value” problem. However, constant bearing guidance can be viewed as a form of midcourse guidance where the nominal trajectory is defined by β = 0.