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

Xiaoliang Feng1, Yuxin Feng2, Chenglin Wen3,4

  • 1College of Electrical Engineering, Henan University of Technology, Zhengzhou 450001, China. fxl@haut.edu.cn.

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Summary
This summary is machine-generated.

This study introduces a novel fixed-point iterative filter, enhancing the extended Kalman filter (EKF) for nonlinear systems. The method improves state estimation accuracy by addressing limitations of traditional EKF linearization.

Keywords:
Steffensen’s iterative methodconvergence conditionextended Kalman filterfixed-point filternested iterative method

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Area of Science:

  • Control Systems Engineering
  • Signal Processing
  • Nonlinear Dynamics

Background:

  • Classical extended Kalman filter (EKF) linearizes nonlinear systems, potentially losing accuracy.
  • Higher-order Taylor series terms discarded in EKF can significantly impact state estimation, especially in steady-state conditions.

Purpose of the Study:

  • To develop an improved nonlinear filter based on the EKF.
  • To enhance the accuracy of state estimation for general nonlinear systems.
  • To mitigate the negative effects of discarded higher-order terms in EKF.

Main Methods:

  • A fixed-point iterative filter was developed from the EKF.
  • A nested iterative method was employed to solve a fixed-point function.
  • Steffensen's iterative method was utilized to accelerate the fixed-point function solution.
  • Convergence conditions for the fixed-point function were analyzed.

Main Results:

  • The proposed fixed-point iterative filter demonstrates improved accuracy over the standard EKF.
  • The method effectively reduces the influence of discarded higher-order Taylor series terms.
  • Simulations confirm the feasibility and effectiveness of the nonlinear filtering approach.

Conclusions:

  • The fixed-point iterative filter offers a viable enhancement for nonlinear system state estimation.
  • The method provides better filtering accuracy compared to traditional EKF.
  • The study validates the proposed nonlinear filtering technique through simulations.