The second order Central Divided-difference Kalman Filter

In the paper the second order Central Divided-difference Interpolation Formula (CDIF) was proposed and applied to improve the estimation performance of the Extended Kalman Filter (EKF), which makes use of the first order Taylor series linearization. Firstly the comparison between the second order CDIF and the second order Taylor series showed that the former has higher approximation accuracy than that of the latter. Then the second order CDIF was used to reconstruct the prediction steps in the ordinary Extended Kalman Filter (EKF) by deriving the estimated mean and estimated covariance of a random variable through nonlinear function transformation. Numerical experiment showed that the Kalman Filter improved by the second order CDIF, or CDKF, can not only lead to more accurate state estimations than those using ordinary EKF, but also has a very limited growth in calculation workload.