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.
Highlights
Interesting but unavailable signal variables can be estimated using a proper filter
The Kalman filter is designed for linear systems with noise-satisfying Gaussian distribution, and is an optimal filter due to the minimum mean square error (MMSE) [6]
For the filtering problem of nonlinear systems, a large number of effective filters have been developed on the basis of the classical Kalman filter
Summary
Interesting but unavailable signal variables can be estimated using a proper filter. In recent decades, filter design for various theoretical and applied systems has been a popular research topic in the fields of automatic control, target tracking, fault diagnosis, etc. [1,2,3,4,5]. The EKF can estimate the state of a nonlinear system, the estimation accuracy of the EKF is always limited, due to the discarded second and higher order Taylor series terms of the process function and the measurement function in their linearization processes In this context, a few nonlinear filters have been developed from the EKF. The discarded higher-order terms of the Taylor series in the linearization processes still inevitably affect the estimation accuracy of the nonlinear filters developed from the EKF. Motivated by the discussion above, in this paper, a novel fixed-point nonlinear filtering method is studied to update the state estimate obtained by the EKF. (1) A fixed-point function was utilized to reduce the influence of discarded second- and higher-order Taylor series terms of nonlinear systems and to improve the filtering accuracy of the steady-state EKF.
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