Why can small measurement errors create large errors in inertial guidance?

Inertial guidance systems determine a vehicle's position and velocity by performing two successive numerical integrations of acceleration data. Because the system relies on these cumulative calculations, even minute errors in the measuring capabilities of accelerometers or in the balance of gyroscopes can lead to significant departures from the intended trajectory over time.123

Essentially, because the system functions as a sophisticated form of dead reckoning, any initial inaccuracy is compounded during the integration process. As the computer continuously sums these measurements to track movement from a starting point, small discrepancies in the sensed acceleration or turning rates accumulate, resulting in large errors in the final calculated position. To mitigate these cumulative effects, such systems must be constructed to strict tolerances and are often reinitialized or corrected using independent navigation sources, such as the global positioning system (GPS) or star trackers.213