Guidance systems work by determining the projectile’s position and velocity vector (its direction and speed, usually via GPS/INS, but also by radar tracking), determining the target’s position and velocity vector (either known in advance, or acquired by radar, or infrared/electro-optical camera, or passive EM detection), calculating what corrections are needed to make both vectors meet, then applying these corrections to whatever maneuvering system with which the projectile is equipped.
This cycle happens many times per second.
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