Gyroscope Allan Variance Analysis Function

Gyroscope Allan variance analysis is a classical method for evaluating inertial sensor performance, particularly suitable for analyzing gyroscope noise characteristics. The Allan variance curve helps identify different types of noise sources in gyroscopes and quantify their contributions.

Core Noise Parameter Analysis Angle Random Walk (ARW): Reflects the high-frequency white noise characteristic of gyroscopes, appearing in the -1/2 slope region of the Allan variance curve, typically measured in °/√h. This parameter directly affects short-term angle integration errors. Rate Random Walk (RRW): Manifests as low-frequency noise, corresponding to the +1/2 slope region of the Allan variance curve, usually expressed in °/h/√h. It characterizes error accumulation trends during long-term operation. Bias Instability (BI): Appears at the curve's trough region, measured in °/h, representing long-term drift characteristics in gyroscope output that determine the minimum error boundary during steady-state operation.

Implementation Logic Key Points Data Segmentation Processing: Divide raw angular rate sampling data into groups based on different time intervals τ, then calculate the average variance for each group. Code implementation typically involves creating overlapping time clusters and computing variance for each cluster. Logarithmic Coordinate Fitting: Identify characteristic slope regions using the Allan variance curve in double logarithmic coordinates, then extract noise coefficients through least squares fitting. The algorithm should implement slope detection and linear regression on log-transformed data. Visualization Presentation: When plotting τ-σ(τ) graphs, pay special attention to logarithmic transformation of both x-axis (time interval) and y-axis (standard deviation), and mark identification positions of key noise parameters. The code should include proper axis scaling and annotation functions.

Application Value This method can not only be used for gyroscope factory performance calibration but also for regular detection of sensor degradation in practical applications like drones and inertial navigation systems. By analyzing changes in Allan variance curve morphology, one can predict whether sensors require calibration or replacement.

(Note: During implementation, pay attention to the relationship between sampling frequency and maximum correlation time to avoid unreliable statistics in long τ intervals due to insufficient data volume. The code should validate data length against maximum τ requirements.)