scholarly journals A generic and efficient Taylor series–based continuation method using a quadratic recast of smooth nonlinear systems

2019 ◽  
Vol 119 (4) ◽  
pp. 261-280 ◽  
Author(s):  
Louis Guillot ◽  
Bruno Cochelin ◽  
Christophe Vergez
Keyword(s):  
Nonlinear Systems ◽  
Taylor Series ◽  
Continuation Method ◽  
Quadratic Recast

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

scholarly journals A Taylor series-based continuation method for solutions of dynamical systems

2019 ◽  
Vol 98 (4) ◽  
pp. 2827-2845 ◽  
Author(s):  
Louis Guillot ◽  
Bruno Cochelin ◽  
Christophe Vergez
Keyword(s):  
Dynamical Systems ◽  
Taylor Series ◽  
Continuation Method

A novel method for computing the vertical gradients of the potential field: Application to downward continuation

2019 ◽  
Author(s):  
Kha Van Tran ◽  
Trung Nhu Nguyen
Keyword(s):  
Series Expansion ◽  
Taylor Series ◽  
Potential Field ◽  
Continuation Method ◽  
Taylor Series Expansion ◽  
Expansion Method ◽  
Downward Continuation ◽  
Source Distribution ◽  
Vertical Derivative ◽  
Series Expansion Method

Summary Downward continuation is a very useful technique in the interpretation of potential field data. It would enhance the short wavelength of the gravity anomalies or accentuate the details of the source distribution. Taylor series expansion method has been proposed to be one of the best downward continued methods. However, the method using high-order vertical derivatives leads to low accuracy and instability results in many cases. In this paper, we propose a new method using a combination of Taylor series expansion and upward continuation for computing vertical derivatives. This method has been tested on the gravitational anomaly of infinite horizontal cylinder in both cases with and without random noise for higher accurate and stable than Hilbert transform method and Laplace equation method, especially in the case of noise input data. This vertical derivative method is applied successfully to calculate the downward continuation according to Taylor series expansion method. The downward continuation is also tested on both complex synthetic models and real data in the East Vietnam Sea (South China Sea). The results reveal that by calculating this new vertical derivative, the downward continuation method gave higher accurate and stable than the previous downward continuation methods.

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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