A New Version of Unscented Kalman Filter

Abstract

Abstract — This paper presents a new algorithm which yields a nonlinear state estimator called iterated unscented Kalman filter. This state estimator makes use of both statistical and analytical linearization techniques in different parts of the filtering process. It outperforms the other three nonlinear state estimators: unscented Kalman filter (UKF), extended Kalman filter (EKF) and iterated extended Kalman filter (IEKF) when there is severe nonlinearity in system equation and less nonlinearity in measurement equation. The algorithm performance has been verified by illustrating some simulation results. Keywords — Extended Kalman Filter, Iterated EKF, Nonlinear state estimator, Unscented Kalman Filter.I. I NTRODUCTION CCURATE estimation of state variables of systems is important for fault detection and control applications. However, estimation in nonlinear systems is not easy to deal with. The optimal (Bayesian) solution to the problem requires propagation of description of full probability density function (pdf) [1]. This solution is general and includes factors such as multimodality, asymmetries, and discontinuities. However, since the form of pdf is not restricted, it cannot, in general, be represented using finite number of parameters. Therefore, any practical estimator must use an approximation of some kinds. Many different types of approximations have been developed; unfortunately, most are either computationally unmanageable or require special assumptions about the form of the process and observation models that cannot be satisfied in practice. For these and other reasons, the KF remains the most widely used estimation algorithm. The most common application of the KF to nonlinear systems is in the form of extended KF (EKF) [2, 3]. EKF was first used by Wu et al. to find the 3D location. Exploiting the assumption that all transformations are quasi-linear, the EKF simply linearizes all nonlinear transformations and substitutes Jacobian matrices for the linear transformations in the KF equations. In addition, EKF is very convenient and fast for real-time processing and quite straightforward to implement if a priori information of the measurement and process noise covariance matrices are available. Linearization in EKF