Kalman Filter Covariance Tuning Using Allan Variance Bias Metrics
Allan Variance bias stability metrics directly determine discrete Kalman process noise matrix entries to prevent filter divergence under non-stationary drift.
Measurement Noise Matrix
Matrix Composition
Mathematical representation of the uncertainty in sensor readings uses a diagonal or dense array to specify the variance of individual signals and the covariance between them. Kalman filtering algorithms rely on the measurement noise matrix to determine how much weight to give to incoming sensor data compared to the state predictions of the system model. This matrix holds the expected variance of each sensor, with larger values causing the filter to rely more on its internal predictions.
The stability of these noise parameters across different temperatures dictates how well the filter performs in harsh environments.
Covariance Calculation
Off-diagonal elements in the matrix describe the correlation between noise sources across different channels of a multi-axis sensor. In many applications, these terms are assumed to be zero because the sensor axes are physically decoupled, which simplifies the calculations and reduces the processing time of the correction loop.
Calibration Procedure
Characterizing the values in the matrix requires logging the output of the sensor under static conditions in a temperature-controlled, vibration-free laboratory environment. This characterization is performed during factory testing to ensure that the noise statistics represent the actual hardware performance under nominal operating conditions.
Estimation Impact
If the noise variance is set too low, the filter will over-respond to noise, leading to jittery and inaccurate state estimates. Conversely, setting the values too high causes the filter to respond slowly to real physical changes, which can degrade the tracking performance of the system.