Feng Xiaoliang, Feng Yuxin, Wen Chenglin
College of Electrical Engineering, Henan University of Technology, Zhengzhou 450001, China.
School of Automatic, Hangzhou Dianzi University, Hangzhou 310018, China.
Sensors (Basel). 2019 Apr 21;19(8):1893. doi: 10.3390/s19081893.
In this paper, a fixed-point iterative filter developed from the classical extended Kalman filter (EKF) was proposed for general nonlinear systems. As a nonlinear filter developed from EKF, the state estimate was obtained by applying the Kalman filter to the linearized system by discarding the higher-order Taylor series items of the original nonlinear system. In order to reduce the influence of the discarded higher-order Taylor series items and improve the filtering accuracy of the obtained state estimate of the steady-state EKF, a fixed-point function was solved though a nested iterative method, which resulted in a fixed-point iterative filter. The convergence of the fixed-point function is also discussed, which provided the existing conditions of the fixed-point iterative filter. Then, Steffensen's iterative method is presented to accelerate the solution of the fixed-point function. The final simulation is provided to illustrate the feasibility and the effectiveness of the proposed nonlinear filtering method.
本文针对一般非线性系统，提出了一种基于经典扩展卡尔曼滤波器（EKF）开发的定点迭代滤波器。作为从EKF发展而来的非线性滤波器，通过对原始非线性系统舍弃高阶泰勒级数项后的线性化系统应用卡尔曼滤波器来获得状态估计。为了减少被舍弃的高阶泰勒级数项的影响并提高稳态EKF所获得状态估计的滤波精度，通过嵌套迭代方法求解一个定点函数，从而得到一个定点迭代滤波器。还讨论了定点函数的收敛性，这给出了定点迭代滤波器的存在条件。然后，提出了斯蒂芬森迭代方法来加速定点函数的求解。最后通过仿真说明了所提出的非线性滤波方法的可行性和有效性。
