Allan Variance

A statistical method for how sensor noise changes with averaging time, commonly used to calibrate IMU noise parameters.

Allan variance is the “two-sample variance” that David W. Allan proposed in 1966 to measure the frequency stability of atomic clocks and crystal oscillators; it later became the standard method for calibrating noise in gyroscopes and accelerometers, and IEEE Std 952-1997 (the fiber-optic gyroscope test standard) documents how to read noise parameters off it. In practice, an IMU sits still and records a long stretch of data; the data is divided into segments of different averaging times τ, the mean of each segment is computed, and the variance of the differences between neighboring segment means is plotted on a log-log curve. A segment of the curve with slope −1/2 corresponds to white noise (noise density), while a slope of +1/2 corresponds to bias random walk. Kalibr’s IMU noise model documentation recommends recording 15 to 24 hours while stationary, reading white noise at τ = 1 second and the random-walk line at τ = 3 seconds. These readings feed into the configuration of visual-inertial odometry, camera-IMU joint calibration, and Kalman filters; getting them wrong makes the fusion algorithm trust the IMU too much or too little.

ExampleBefore doing camera-IMU joint calibration, the IMU is left recording overnight while stationary; allan_variance_ros plots the curve, and the gyroscope’s and accelerometer’s noise density and random walk are read off it and written into Kalibr’s IMU configuration file.

Also called

Allan Deviation, Two-Sample Variance, AVAR

Related

Inertial Measurement Unit · Sensor Drift · Camera-IMU Calibration · Kalibr · Visual-Inertial Odometry · Kalman Filter

Sources

Kalibr Wiki: IMU Noise Model
Wikipedia: Allan variance