According to Mackenzie,[1] Titan, some versions of Atlas, Minuteman I and II used Delta-guidance, while Q-guidance was used for Thor IRBM and Polaris, and presumably Poseidon.
Delta-guidance is based on adherence to a planned reference trajectory, which is developed before the flight using ground-based computers and stored in the missile's guidance system.
The guidance system attempts to zero the linear terms of this expression, i.e. to bring the missile back to the planned trajectory.
The velocity to be gained is defined as the difference between Vc and Vm: A simple guidance strategy is to apply acceleration (i.e. engine thrust) in the direction of VTBG.
(The vertical bar refers to the fact that the derivative must be evaluated for a given target position rT and time of free flight tf.
Information about vehicle acceleration, velocity and position is supplied by the onboard inertial measurement unit.
A somewhat more clever strategy can be designed that takes into account the rate of time change of VTBG as well, since this is available from the differential equation above.