Discrete Kalman Process Noise Covariance Derivation from Inertial Bench Test Metrics
Bench Allan variance parameters convert to discrete Kalman process noise matrices by integrating state transition matrices over the sampling interval.
Vibration Rectification
Bias Induction
Error mechanisms in inertial sensors occur when high-frequency oscillatory motion is converted into a steady-state dc offset. Usually, vibration rectification happens when non-linearities in the sensor or the associated electronics process an input vibration, resulting in an apparent constant acceleration or rotation. This effect is particularly problematic in environments with heavy mechanical noise, such as on a moving vehicle or near heavy machinery.
Non-linear Origin
Non-linear origins of this error are often found in the asymmetry of the sensor response or the clipping of the signal in the amplifier stage. Even if the vibration itself has a zero mean, the rectified output of the sensor will show a non-zero average.
Qualification Standard
Qualification standards define the vibration rectification coefficient, which measures the sensitivity of the sensor to this specific type of error. During testing, the device is subjected to a random vibration profile, and the resulting change in the output bias is recorded. A low coefficient indicates that the sensor is well-designed and capable of maintaining accuracy in harsh environments.
Manufacturers specify this value in units of acceleration per gravity squared to allow users to predict the error based on the expected vibration levels.
Mitigation Strategy
Mitigation strategies focus on mechanical isolation and the selection of high-linearity components. Soft mounts can filter out the high-frequency vibrations before they reach the sensor. In the digital domain, high sampling rates and sophisticated filtering can help reduce the impact of the rectified signal on the final measurement.