The Modification Of Second-order Extended Kalman Filter For Non-linear System

Kalman filtering theoryy has been widely used in various fields. The initial Kalman filtering theory is for linear systems. Extended Kalman filter(EKF) is applied to nonlinear system, the nonlinear problem is solved. EKF is widely used.However, this method also has the disadvantages which are ignored the high-order value in the Taylor expansion. The second-order Kalman filter have done to solve this problem. But in the literature the second-order Kalman filter only approximates the non-linear system with addtive-noise. In fact the non-linear system with non-additive noise especially multiplicative noise in the actual situation is very common, optimal state estimates of the system with non-additive noise that has important application value.The main purpose of this paper is to give the second order Kalman filter on nonlinear system with non-additive noise, and for such systems,discussing the estimation effective of EKF and the second order Kalman filter.The first part introduces the history of this subject and the significance, the research of present situation analysis.The second part we give some nature of the Gauss distribution and the minimum variance estimation method. Discussing the general nonlinear system in the sense of minimum variance, and being prepared for the second order Kalman filtering formula of nonlinear system with non-additive noise.The third part reviews the recursive formulation of first order extended Kalman filtering for general systems with non-additive. Then we give the recursive formulation of second order extended Kalman filtering for the system with non-additive noise. This formula are applied to many probability theories.The forth part we give the simulation experiments of the system with non-additive noise, the simulation results are shown the second-order extended Kalman filter is better than EKF.