Extended Kalman filter modifications based on an optimization view point

The extended Kalman filter (EKF) has been an important tool for state estimation of nonlinear systems since its introduction. However, the EKF does not possess the same optimality properties as the Kalman filter, and may perform poorly. By viewing the EKF as an optimization problem it is possible to, in many cases, improve its performance and robustness. The paper derives three variations of the EKF by applying different optimisation algorithms to the EKF cost function and relate these to the iterated EKF. The derived filters are evaluated in two simulation studies which exemplify the presented filters.