Comparison of Linear Filters in the Presence of Biased Measurements

In addition to the typical random errors that vary between consecutive measurements, the measurements for most all sensors used for target tracking include bias errors that remain fixed during a target tracking episode and are typically characterized by an a priori mean and covariance. Several extensions to the Kalman filter have been developed to consider the bias error statistics when calculating a state error covariance. In this paper, several of these extensions are compared by deriving analytical forms of the steady-state covariance with nearly fixed and nearly constant velocity targets in a scalar coordinate. A novel method for computing the measurement covariance inflation required to contain the bias and random errors at the output of the filter is presented and illustrated.