The simple explanation: you know when McGyver is locked in a trunk and the bad guys drive him off to someplace, but he figures out where he is by keeping track of which way the car turns, and how long it goes at what speed? That, in a nutshell, is how the IRS works. You tell the system exactly where it is on startup, by programming in the coordinates of the stand, then a very high tech gyroscope keeps track of every change in motion from then on.
The technical explanation: It uses 'laser ring gyros.' Instead of having spinning mass like mechanical gyros do, the laser gyro has two homogeneous light beams following a circuit in opposite directions. There are two kinds of ring lasers, one with fibre optics, and a better one where the light follows a triangular path with mirrors. How does this act as a gyro?
Remember that nothing can travel faster than 'c', the speed of light, including light itself. (You have possibly been subjected to a thought experiment involving the headlights on relativistic trains. No matter how fast the train goes, the light from the headlight will not go faster than c, so that when the train is going at the speed of light, the headlight does not send a beam ahead of the train.) No matter how much of a "push" the light gets from its source, it won't go any faster than if it came from a stationary source.
When the aircraft is stationary, the light beams going in each direction a given ring gyro have exactly the same path length. Where they meet after a circuit of the instrument, they have a particular phase difference. I'm not certain that the instrument is tweaked to have it be zero, but without loss of generality, let's say that it is zero. The beams are perfectly in phase.
Working from these principles, consider what happens to the gyro in the horizontal plane, when the aircraft turns to the left. The gyro has turned around so as to reduce the path for the light beam going clockwise. The light going counterclockwise has had its path increased and it doesn't get a push from the turning motion. So the light beams will meet out of phase. Just as your VOR instrument works out what radial you are on by the phase difference between the two signals received, the computers associated with the ring laser gyro works out how much you turned, by the phase difference between the two beams.
The crew of an A319, who first told a disbelieving me about this system, swore up and down that it uses only inertial data.
(Oops, this post didn't actually answer the question that was asked. See below.)
[This message has been edited by Luftwaffle (edited 24 September 2000).]