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

1
College of Electrical Engineering, Henan University of Technology, Zhengzhou 450001, China
2
School of Automatic, Hangzhou Dianzi University, Hangzhou 310018, China
*
Author to whom correspondence should be addressed.
Sensors 2019, 19(8), 1893; https://doi.org/10.3390/s19081893
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)
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Abstract

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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