scholarly journals Strong Tracking Filtering Algorithm of Randomly Delayed Measurements for Nonlinear Systems

2015 ◽  
Vol 2015 ◽  
pp. 1-14 ◽  
Author(s):  
Hongtao Yang ◽  
Huibin Gao ◽  
Xin Liu
Keyword(s):  
Nonlinear Systems ◽  
Initial Conditions ◽  
Stochastic Dynamic ◽  
Model Simplification ◽  
Filtering Algorithm ◽  
First Order ◽  
Noise Characteristics ◽  
Delayed Measurements ◽  
Fading Factor ◽  
Stochastic Dynamic Systems

This paper focuses on the filtering problems of nonlinear discrete-time stochastic dynamic systems, such as the model simplification, noise characteristics uncertainty, initial conditions uncertainty, or system parametric variation. Under these circumstances, the measurements of system have one sampling time random delay. A new method, that is, strong tracking filtering algorithm of randomly delayed measurements (STF/RDM) for nonlinear systems based on recursive operating by analytical computation and first-order linear approximations, is proposed; a principle of extended orthogonality is presented as a criterion of designing the STF/RDM, and through the residuals between available and predicted measurements, the formula of fading factor is obtained. Under the premise of using the extended orthogonality principle, STF/RDM proposed in this paper can adjust the fading factor online via calculating the covariance of residuals, and then the gain matrices of the STF/RDM adjust in real time to enhance the performance of the proposed method. Lastly, in order to prove that the performance of STF/RDM precedes existing EKF method, the experiment of tracking maneuvering aircraft is carried out.

scholarly journals Perturbation Solutions to Fifth Order Over-damped Nonlinear Systems

2019 ◽  
pp. 1-11
Author(s):  
Harun-Or- Roshid ◽  
M. Zulfikar Ali ◽  
Pinakee Dey ◽  
M. Ali Akbar
Keyword(s):  
Nonlinear Systems ◽  
Initial Conditions ◽  
Approximate Solutions ◽  
First Order ◽  
Engineering Problems ◽  
Kbm Method ◽  
Fifth Order ◽  
Physical Phenomena ◽  
Good Agreement ◽  
Perturbation Solutions

Fifth order over-damp nonlinear differential systems can be used to describe many engineering problems and physical phenomena occur in the nature. In this article, the Krylov-Bogoliubov-Mitropolskii (KBM) method has been extended to investigate the solution of a certain fifth order over-damp nonlinear systems and desired result has been found. The implementation of the presented method is illustrated by an example. The first order analytical approximate solutions obtained by the method for different initial conditions show a good agreement with those obtains by numerical method.

An Analytical Scheme for Stochastic Dynamic Systems Containing Fractional Derivatives

1999 ◽  
Author(s):  
Om P. Agrawal
Keyword(s):  
White Noise ◽  
Expansion Method ◽  
Stochastic Dynamic ◽  
Stochastic Response ◽  
Analytical Technique ◽  
Analytical Scheme ◽  
Damped System ◽  
Duhamel Integral ◽  
General Response ◽  
Stochastic Dynamic Systems

Abstract This paper presents an analytical technique for the analysis of a stochastic dynamic system whose damping behavior is described by a fractional derivative of order 1/2. In this approach, an eigenvector expansion method proposed by Suarez and Shokooh is used to obtain the response of the system. The properties of Laplace transforms of convolution integrals are used to write a set of general Duhamel integral type expressions. The general response contains two parts, namely zero state and zero input. For a stochastic analysis the input force is treated as a random process with specified mean and correlation functions. An expectation operator is applied on a set of expressions to obtain the stochastic characteristics of the system. Closed form stochastic response expressions are obtained for white noise. Numerical results are presented to show the stochastic response of a fractionally damped system subjected to white noise.

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