A Note on the Limiting Properties of the Extended Kalman Filter’s Estimates : Invited Presentation

In this paper, I focus on the estimates produced by the extended Kalman filter (EKF) and their corresponding predicted error covariance matrices. The EKF is often used in place of the standard Kalman filter when the functional relationship between consecutive states and/or the functional relationship between the states and their measurements is not linear. In these cases, the state estimates and their predicted error covariances are biased. In this paper, I mathematically show that as the nonlinear relationship between the states and the measurements approaches linearity, these biases go to 0.