Bias Instability Figures That Decide Whether Dead Reckoning Holds
Inertial dead reckoning holds only while gyroscope bias instability bounds cubic tilt divergence within allowable spatial position tolerance thresholds.
Quadratic Acceleration Drift
Navigation Error
Error in an inertial navigation system where the position deviation increases as the square of the elapsed time due to a constant acceleration bias. Precise guidance units experience quadratic acceleration drift when a small offset in the accelerometer output is integrated twice into a distance measurement. It represents a fundamental limit on the autonomous accuracy of a device when external positioning signals are unavailable.
Bias Stability
Small errors in the zero point of an accelerometer lead to a growing velocity error which then produces the non-linear position shift. In systems affected by quadratic acceleration drift, even a few micro-g of bias can result in hundreds of metres of error over an hour of operation. High quality sensors use oven controlled enclosures to maintain a stable temperature and minimize this bias shift.
Mathematical Integration
Double integration of a constant value results in a parabolic curve when plotted against time. This characteristic of quadratic acceleration drift makes it easy to distinguish from linear velocity drift or random walk noise. Kalman filters are used in the navigation software to estimate and subtract the bias in real time by comparing the inertial data with occasional external updates.
The frequency of these updates determines the maximum allowable drift of the internal components.
Calibration Precision
Measuring the bias to the required level of accuracy requires a stable tilt table and a long period of averaging. This initial calibration for quadratic acceleration drift is performed at the factory under reference conditions. Field performance may vary if the sensor is subjected to shocks that alter the mechanical alignment of the sensing element.