Q-guidance

Q-guidance is a method of missile guidance used in some U.S. ballistic missiles and some civilian space flights. It was developed in the 1950s by J. Halcombe Laning and Richard Battin at the MIT Instrumentation Lab.

Q-guidance is used for missiles whose trajectory consists of a relatively short boost phase (or powered phase) during which the missile's propulsion system operates, followed by a ballistic phase during which the missile coasts to its target under the influence of gravity. (Cruise missiles use different guidance methods). The objective of Q-guidance is to hit a specified target at a specified time (if there is some flexibility as to the time the target should be hit then other types of guidance can be used).

At the time Q-guidance was developed the main competitive method was called Delta-guidance. According to Mackenzie,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. It appears, from monitoring of test launches, that early Soviet ICBMs used a variant of Delta-guidance.

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. In flight, the actual trajectory is modeled mathematically as a Taylor series expansion around the reference trajectory. The guidance system attempts to zero the linear terms of this expression, i.e. to bring the missile back to the planned trajectory. For this reason, Delta-guidance is sometimes referred to as "fly [along] the wire", where the (imaginary) wire refers to the reference trajectory.

In contrast, Q-guidance is a dynamic method, reminiscent of the theories dynamic programming or state based feedback. In essence, it says "never mind where we were supposed to be, given where we are what should we do to make progress towards the goal of reaching the required target at the required time". To do this it relies on the concept of "velocity to be gained".

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