Journal ArticleDOI
Third-Order Continuous-Discrete Filtering for a Nonlinear Dynamical System
Hiren G. Patel,Shambhu N. Sharma +1 more
TLDR
In this paper, a stochastic differential equation (SDE) formalism in combination with a nonlinear discrete observation equation is developed by adopting a unified systematic approach involving celebrated results of stochastically calculus, where the conditional characteristic function is exploited to develop filtering at the observation instant.Abstract:
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.read more
Citations
More filters
Journal Article
A high order Method for estimation of dynamic systems
TL;DR: An analytical approach is presented for developing an estimation framework to study the interplay of major issues in nonlinear estimation such as model nonlinearity, measurement sparsity and initial condition uncertainty in the presence of low process noise.
Journal ArticleDOI
Parameter Estimation Algorithms for Hammerstein–Wiener Systems With Autoregressive Moving Average Noise
Yanjiao Wang,Feng Ding +1 more
Journal ArticleDOI
Variational Integrators for Structure-Preserving Filtering
TL;DR: It is shown how the optimality of the Kalman filter can be preserved through discretization by means of modified discrete-time Riccati equations for the covariance updates, which leads to further improvement in filter accuracy.
Proceedings ArticleDOI
Wiener meets Kolmogorov
TL;DR: In this article, a connection between the stochastic differential rules of the Wiener process and the Kolmogorov forward and backward equations is made, and the authors demonstrate the application of these equations to achieve the nonlinear filtering of a non-linear dynamic circuit with embedded stochiasticity.
Journal ArticleDOI
An Analysis of a Wind Turbine-Generator System in the Presence of Stochasticity and Fokker-Planck Equations
TL;DR: The articleutilizes the Fokker-Planck method and is attributed to the Markov process, and the Stochasticity of the Wind TurbineGenerator System.
References
More filters
Journal ArticleDOI
An Introduction to Probability Theory and Its Applications
David A. Freedman,William Feller +1 more
Book
Ordinary differential equations
TL;DR: The fourth volume in a series of volumes devoted to self-contained and up-to-date surveys in the theory of ODEs was published by as discussed by the authors, with an additional effort to achieve readability for mathematicians and scientists from other related fields so that the chapters have been made accessible to a wider audience.
Book
Stochastic Processes and Filtering Theory
TL;DR: In this paper, a unified treatment of linear and nonlinear filtering theory for engineers is presented, with sufficient emphasis on applications to enable the reader to use the theory for engineering problems.
Book
Applied Optimal Estimation
TL;DR: This is the first book on the optimal estimation that places its major emphasis on practical applications, treating the subject more from an engineering than a mathematical orientation, and the theory and practice of optimal estimation is presented.
Related Papers (5)
Nonlinear Stochastic Differential-Algebraic Equations with Application to Particle Filtering
Markus Gerdin,Johan Sjöberg +1 more
Estimating the State in Stiff Continuous-Time Stochastic Systems within Extended Kalman Filtering
G. Yu. Kulikov,Maria V. Kulikova +1 more