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An EKF-Based Fixed-Point Iterative Filter for Nonlinear Systems

College of Electrical Engineering, Henan University of Technology, Zhengzhou 450001, China
School of Automatic, Hangzhou Dianzi University, Hangzhou 310018, China
Author to whom correspondence should be addressed.
Sensors 2019, 19(8), 1893;
Received: 13 March 2019 / Revised: 9 April 2019 / Accepted: 15 April 2019 / Published: 21 April 2019
(This article belongs to the Collection Multi-Sensor Information Fusion)
PDF [1489 KB, uploaded 26 April 2019]


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. View Full-Text
Keywords: fixed-point filter; extended Kalman filter; nested iterative method; Steffensen’s iterative method; convergence condition fixed-point filter; extended Kalman filter; nested iterative method; Steffensen’s iterative method; convergence condition

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Feng, X.; Feng, Y.; Wen, C. An EKF-Based Fixed-Point Iterative Filter for Nonlinear Systems. Sensors 2019, 19, 1893.

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