The flight computer knows the aircraft’s altitude, orientation (pitch,roll,yaw), and velocity & acceleration vector magnitudes and directions, the DMT/ARBS knows the angles from boresight to the designation and the angular rates of change.
With some trig and calculus figuring out and updating the slant range isn’t so bad and from that you can work out the math that leads to the AUTO release mode features.
But don’t take my word for it, read it for yourself! 