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Technical Brief

Third-Order Continuous-Discrete Filtering for a Nonlinear Dynamical System

[+] Author and Article Information
Hiren G. Patel

Department of Electrical Engineering,
National Institute of Technology,
Surat 395007, India
e-mail: hirenpatel.eed@gmail.com

Shambhu N. Sharma

Department of Electrical Engineering,
National Institute of Technology,
Surat 395007, India
e-mail: snsvolterra@gmail.com

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received March 22, 2013; final manuscript received November 18, 2013; published online February 13, 2014. Assoc. Editor: Eric A. Butcher.

J. Comput. Nonlinear Dynam 9(3), 034502 (Feb 13, 2014) (9 pages) Paper No: CND-13-1068; doi: 10.1115/1.4026064 History: Received March 22, 2013; Revised November 18, 2013

Approximate higher-order filters are more attractive and popular in control and signal processing literature in contrast to the exact filter, since the analytical and numerical solutions of the nonlinear exact filter are not possible. The filtering model of this paper involves stochastic differential equation (SDE) formalism in combination with a nonlinear discrete observation equation. The theory of this paper is developed by adopting a unified systematic approach involving celebrated results of stochastic calculus. The Kolmogorov–Fokker–Planck equation in combination with the Kolmogorov backward equation plays the pivotal role to construct the theory of this paper “between the observations.” The conditional characteristic function is exploited to develop “filtering” at the observation instant. Subsequently, the efficacy of the filtering method of this paper is examined on the basis of its comparison with extended Kalman filtering and true state trajectories. This paper will be of interest to applied mathematicians and research communities in systems and control looking for stochastic filtering methods in theoretical studies as well as their application to real physical systems.

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Topics: Filtration , Filters
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References

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Figures

Grahic Jump Location
Fig. 1

A comparison between three trajectories

Grahic Jump Location
Fig. 2

A comparison between three trajectories

Grahic Jump Location
Fig. 3

A comparison between three trajectories

Grahic Jump Location
Fig. 4

A comparison between three trajectories

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