Quantifying Gyro Noise Coefficients from Allan Variance Data
Quantify gyro noise coefficients by fitting specific logarithmic slope asymptotes to overlapped Allan deviation curves gathered in thermally stabilized static rigs.
Allan Variance Regression
Stochastic Noise Estimation
A statistical procedure identifies noise parameters in inertial sensor output by fitting observed variance data to established noise models. Allan variance regression characterizes the time domain stability of oscillators and gyroscopes by decomposing the total error into discrete sources like white noise or random walk. Calculations proceed through the generation of an Allan deviation plot from sampled raw data followed by the application of least squares fitting to identify the slope of specific segments.
Each slope corresponds to a distinct physical phenomenon such as quantization noise or bias instability. Fitting errors arise when data lengths do not match the expected time constants for these individual noise processes.
Regression Mechanics
Linear estimation techniques minimize the squared distance between the computed log-log slope of the data and the theoretical model of the device. Software executes this analysis across multiple tau intervals to isolate the gain or intensity coefficients of identified noise components. Numerical solvers process the data to ensure convergence toward a singular noise coefficient for every targeted slope.
Accuracy degrades when sampling frequencies or time horizons fall outside the operating range of the underlying sensor electronics.
Data Qualification
Input sequences require calibration under stable thermal and environmental conditions to avoid the coupling of non-stationary drift with intrinsic stochastic noise. Laboratory verification confirms that temperature fluctuations do not bias the slope segments used for the calculation of the noise coefficients. Precise isolation of the white noise floor depends upon a sufficiently long observation period to reach the necessary statistical confidence for high tau values.
Drift in the bias during measurement introduces systematic errors that mimic random walk behavior and masks the true performance of the hardware.
Calibration Boundary
Sensor specifications limit the validity of this estimation to the frequency range where the physical mechanism of the noise remains constant. Deviations occur if the hardware undergoes mode switching or if internal thermal compensation loops engage during the collection of the sample. Verification of the results necessitates comparison against a known reference standard to confirm that the regression model correctly identifies the actual noise signature rather than artifacts from digital filtering or quantization.
Proper interpretation of the slope values provides the only reliable metric for predicting long term sensor reliability.