Mathematically.
I was genuinely hoping for a more...complete answer.
The drift was very small and predictable from what I was told.
The drift is small, over short periods of time. The error arises from the signal itself, which is then integrated,
twice, providing an exponentially increasing position error.
Take for example, a good quality single axis accelerometer. It has an error of about a
milli-g. Now let's assume the government has extreme quality accelerometers and has done other, tricky stuff, to get the error down three orders of magnitude, to a
micro-g. If you were to turn this simple, one axis INS on and leave it alone in a ship in dry dock, it would begin to integrate the noise in the system. After one minute, the error in position is about .0018m. After an hour, it's grown to 6.48m. After a day, it's become 3.732km. In one year the error would grow to 297,260km. If the system was left alone for the four and a half years, it would be able to place the ship to somewhere out towards Venus, as the error is now at over 10 million kilometers!