L-1011 Navigation: Inertial Navigation System (34-43-4)

Once alignment is complete and the aircraft starts moving, the computer converts acceleration signals to a series of vectors. By algebraically summing the vector, the computer measures distance traveled in north-south and east-west directions. The computer upgrades position extremely rapidly (in terms of microseconds) and is therefore capable of detaching very small variations in velocity.
In the short term, INS computers are very accurate. OVer the long term, however, the computer accumulates computations errors. The magnitude of these errors becomes progressively greater with time. When two or more INSs are operations, the crew can observe the present positions slowly drift apart. Since the computers do drift, there is a built-in compensation circuit. When the INS is shutdown, the position is recorded. When the set is next aligned, the difference between shutdown position and alignment position is measured and an appropriate correction favor is then applied to further computations.