Proportional navigation

Proportional navigation (also known as PN or Pro-Nav) is a guidance law (analogous to proportional control) used in some form or another by most homing air target missiles. It is based on the fact that two vehicles are on a collision course when their direct Line-of-Sight does not change direction as the range closes. PN dictates that the missile velocity vector should rotate at a rate proportional to the rotation rate of the line of sight (Line-Of-Sight rate or LOS-rate), and in the same direction.

Where ${\displaystyle a_{n}}$ is the acceleration perpendicular to instantaneous line of sight, ${\displaystyle N}$ is the proportionality constant generally having an integer value 3-5 (dimensionless), ${\displaystyle {\dot {\lambda }}}$ is the line of sight rate, and V is the closing velocity.

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