Discretization of nonlinear systems with delayed multi-input via Taylor series and scaling and squaring technique

2005 ◽  
Vol 19 (11) ◽  
pp. 1975-1987 ◽  
Author(s):  
Zhang Yuanliang ◽  
Kil To Chong
Keyword(s):  
Nonlinear Systems ◽  
Taylor Series ◽  
Scaling And Squaring Technique

scholarly journals Weighted Measurement Fusion Particle Filter for Nonlinear Systems with Correlated Noises

Sensors ◽  
2018 ◽  
Vol 18 (10) ◽  
pp. 3242 ◽  
Author(s):  
Ke Wei Zhang ◽  
Gang Hao ◽  
Shu Li Sun
Keyword(s):  
Nonlinear Systems ◽  
Particle Filter ◽  
Series Expansion ◽  
Taylor Series ◽  
Asymptotic Optimality ◽  
Taylor Series Expansion ◽  
Full Rank ◽  
Expansion Method ◽  
Least Square ◽  
Correlated Noises

The multi-sensor information fusion particle filter (PF) has been put forward for nonlinear systems with correlated noises. The proposed algorithm uses the Taylor series expansion method, which makes the nonlinear measurement functions have a linear relationship by the intermediary function. A weighted measurement fusion PF (WMF-PF) was put forward for systems with correlated noises by applying the full rank decomposition and the weighted least square theory. Compared with the augmented optimal centralized fusion particle filter (CF-PF), it could greatly reduce the amount of calculation. Moreover, it showed asymptotic optimality as the Taylor series expansion increased. The simulation examples illustrate the effectiveness and correctness of the proposed algorithm.

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

Sensors ◽  
2019 ◽  
Vol 19 (8) ◽  
pp. 1893
Author(s):  
Feng ◽  
Feng ◽  
Wen
Keyword(s):  
Fixed Point ◽  
Kalman Filter ◽  
Nonlinear Systems ◽  
Iterative Method ◽  
Taylor Series ◽  
Nonlinear Filtering ◽  
Higher Order ◽  
Point Function ◽  
State Estimate ◽  
Linearized System

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.

Time-discretization of nonlinear systems with delayed multi-input using Taylor series

2004 ◽  
Vol 18 (7) ◽  
pp. 1107-1120 ◽  
Author(s):  
Ji Hyang Park ◽  
Kil To Chong ◽  
Nikolaos Kazantzis ◽  
Alexander G. Parlos
Keyword(s):  
Nonlinear Systems ◽  
Taylor Series ◽  
Time Discretization

A Novel Adaptive UKF and its Application in the SINS/GPS Integrated Navigation

2014 ◽  
Vol 597 ◽  
pp. 521-524
Author(s):  
Yong Li ◽  
She Sheng Gao ◽  
Yi Yang
Keyword(s):  
Nonlinear Systems ◽  
State Estimation ◽  
Kalman Filtering ◽  
Taylor Series ◽  
Navigation System ◽  
Statistical Characteristics ◽  
Integrated Navigation ◽  
Integrated Navigation System ◽  
Taylor Series Approximation ◽  
Improve Accuracy

This paper reports the solution of the state estimation problem of nonlinear systems without knowing prior noise statistical characteristics. An adaptive UKF algorithm is proposed. This novel UKF algorithm is constructed by traditional UKF and EM algorithm, also it improve accuracy through Taylor series approximation. By applying the proposed algorithm into SINS/GPS integrated navigation system and comparing with the unscented Kalman filtering (UKF) algorithm, the adaptive UKF algorithm we proposed can effectively improve the filtering performance , also it outperforms UKF in terms of accuracy.

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