Lirnpt p t

where pt(t) is either stationary or moving by a (non-zero and bounded) velocity vt(f) 4 p t(t)e R2.

Concerning tracking of moving targets, the missile guidance community probably has the most comprehensive experience. They commonly refer to the object that is supposed to destroy another object as either a missile, an interceptor, or a pursuer. Conversely, the threatened object is typically called a target or an evader. Here, the designations interceptor and target will be used.

An interceptor typically undergoes 3 phases during its operation; a launch phase, a midcourse phase, and a terminal phase. The greatest accuracy demand is associated with the terminal phase, where the interceptor guidance system must compensate for the accumulated errors from the previous phases to achieve a smallest possible final miss distance to the target. Thus, 3 terminal guidance strategies will be presented in the following, namely line of sight, pure pursuit, and constant bearing. The associated geometric principles are illustrated in Fig. 4.

Note that while the main objective of a guided missile is to hit (and destroy) a physical target in finite time, we recognize the analogy of hitting (converging to) a virtual target asymptotically, i.e., the concept of asymptotic interception, as stated in (1).

3.1 Line of sight guidance

Line of sight (LOS) guidance is classified as a so-called three-point guidance scheme since it involves a (typically stationary) reference point in addition to the interceptor and the target. The LOS denotation stems from the fact that the interceptor is supposed to achieve an intercept by constraining its motion along the line of sight between the reference point and the target. LOS guidance has typically been employed for surface-to-air missiles, often mechanized by a ground station which illuminates the target with a beam that the guided missile is supposed to ride, also known as beam-rider guidance. The LOS guidance principle is illustrated in Fig. 4, where the associated velocity command is represented by a vector pointing to the left of the target.

3.2 Pure pursuit guidance

Pure pursuit (PP) guidance belongs to the so-called two-point guidance schemes, where only the interceptor and the target are considered in the engagement geometry. Simply put, the interceptor is supposed to align its velocity along the line of sight between the interceptor and the target. This strategy is equivalent to a predator chasing a prey in the animal world, and very often results in a tail chase. PP guidance has typically been employed for air-to-surface missiles. The PP guidance principle is represented in Fig. 4 by a vector pointing directly at the target.

Fig. 4. The interceptor velocity commands that are associated with the classical guidance principles line of sight (LOS), pure pursuit (PP), and constant bearing (CB)

Deviated pursuit guidance is a variant of PP guidance where the velocity of the interceptor is supposed to lead the interceptor-target line of sight by a constant angle in the direction of the target movement. An equivalent term is fixed-lead navigation.

3.3 Constant bearing guidance

Constant bearing (CB) guidance is also a two-point guidance scheme, with the same engagement geometry as PP guidance. However, in a CB engagement, the interceptor is supposed to align the relative interceptor-target velocity along the line of sight between the interceptor and the target. This goal is equivalent to reducing the LOS rotation rate to zero such that the interceptor perceives the target at a constant bearing, closing in on a direct collision course. CB guidance is often referred to as parallel navigation, and has typically been employed for air-to-air missiles. Also, the CB rule has been used for centuries by mariners to avoid collisions at sea; steering away from a situation where another vessel approaches at a constant bearing. Thus, guidance principles can just as well be applied to avoid collisions as to achieve them. The CB guidance principle is indicated in Fig. 4 by a vector pointing to the right of the target.

The most common method of implementing CB guidance is to make the rotation rate of the interceptor velocity directly proportional to the rotation rate of the interceptor-target LOS, which is widely known as proportional navigation (PN).

CB guidance can also be implemented through the direct velocity assignment

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