Proportional navigation
This acceleration depends explicitly on the velocity difference vector, which may be difficult to obtain in practice.
By contrast, in the expressions that follow, dependence is only on the change of the line of sight and the magnitude of the closing velocity.
If acceleration normal to the instantaneous line of sight is desired (as in the initial description), then the following expression is valid: If energy conserving control is required (as is the case when only using control surfaces), the following acceleration, which is orthogonal to the missile velocity, may be used: A rather simple hardware implementation of this guidance law can be found in early AIM-9 Sidewinder missiles.
Since the mirror is in fact a gyroscope it will keep pointing at the same direction if no external force or moment is applied, regardless of the movements of the missile.
The voltage applied to the mirror while keeping it locked on the target is then also used (although amplified) to deflect the control surfaces that steer the missile, thereby making missile velocity vector rotation proportional to line of sight rotation.
Although this does not result in a rotation rate that is always exactly proportional to the LOS-rate (which would require a constant airspeed), this implementation is equally effective.
Commonly referred to as Constant Bearing Decreasing Range (CBDR), the concept continues to prove very useful for conning officers (the person in control of navigating the vessel at any point in time) because CBDR will result in a collision or near miss if action is not taken by one of the two vessels involved.
Simply altering course until a change in bearing (obtained by compass sighting) occurs, will provide some assurance of avoidance of collision, obviously not foolproof: the conning officer of the vessel having made the course change must continually monitor bearing lest the other vessel does the same.
[4] Holcocephala fusca and Coenosia attenuata are two species of predatory flies that use proportional navigation to reach their prey.
The former uses N ≈ 3 with a time delay of ≈ 28 ms, which is suitable for its long-range intercepts and minimizes the control effort required.
The latter uses N ≈ 1.5 with a time delay of ≈ 18 ms, which is adapted to its short-range hunts and helps reduce overcompensation.
By setting up the chase so that the predator either appears stationery relative to background while looming larger (real-point motion camouflage), or always appears at a fixed bearing (infinite-point motion camouflage), the predator reduces its chance of being detected.
