I. Introduction
In the domain of state estimation for nonlinear system, the extended Kalman filter (EKF) is the commonly used state estimator. The EKF is based on linearizing state transition and observation equations about the estimated state trajectory under the Gaussian assumption [1]. So the EKF may introduce large error and even diverge when the nonlinearities become severe. To improve the performance of the EKF, the iterated Extended Kalman filter (IEKF) proposed involves the use of an iterative measurement update [1]. The IEKF is more accurate on the condition the state estimate is close enough to the true value. The sequence of iterates generated by the IEKF has the property of globally convergence; however, the sequence generated does not go up the likelihood surface [2]. Whether EKF or IEKF, calculation of Jacobians required often introduces numerical instability and limits their applications.