Linear Minimum Variance Filters for Measurement Bias Characterization

FOR linear estimation problems, the minimum variance (or Kalman) filter provides unbiased state estimates when sensor measurements contain only zero-mean, random Gaussian errors. When the measurement error statistics are accurately characterized, the Kalman filter covariance matrix is usually consistent with the error statistics of the bias-free estimates. In many real world applications, sensor measurements contain unmodeled static and dynamic measurement biases, or low-frequency systematic errors. Measurement biases cause biases in the Kalman state estimates. The Kalman filter usually under-estimates the error statistics of the biased state estimates, meaning that the filter covariances are smaller than they should be, because the measurement biases are not characterized.