Empirical evidence of bias in extended Kalman filters used for passive target tracking

The bearings-only estimation problem and its application to the intercept of an aircraft target by an air-to-air missile are discussed. That is, how does one estimate the state of a system of a missile and a target (relative position, relative velocity, and target acceleration) in a plane with measurements of the line-of-sight (LOS) or bearing angle only? The ownship-to-target range is unobservable unless the LOS rate is nonzero. The range and range-rate estimates are biased for both the extended Kalman filter (EKF) and the modified gain EKF (MGEKF). Empirical evidence of this biasing is presented using a simple simulation. The bias is shown to be caused by a correlation between the gain and innovations sequences. It is further shown that this bias is not removed (though it is reduced and bounded) when the range is observable