An Optimal Approximation for a Certain Class of Nonlinear Filtering Problems PDF Download
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Author: Talal Umar Halawani
Publisher:
ISBN:
Category :
Languages : en
Pages : 43
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Book Description
A new approximation technique to a certain class of nonlinear filtering problems is considered. The method is based on an approximation of nonlinear, partially observable systems by a stochastic control problem with fully observable state. The filter development proceeds from the assumption that the unobservables are conditionally Gaussian with respect to the observations initially. The concepts of both conditionally Gaussian processes and an optimal-control approach to filtering are utilized in the filter development. A two-step, nonlinear, recursive estimation procedure (TNF), compatible with the logical structure of the optimal mean-square estimator, generates a finite-dimensional, nonlinear filter with improved characteristics over most of the traditional methods. Moreover, a close (in the mean-square sense) approximation for the original system will be generated as well. In general the nonlinear filtering problem does not have a finite-dimensional recursive synthesis. Thus, the proposed technique may expand the range of practical problems that can be handled by nonlinear filtering. Application of the derived multi-dimensional filtering algorithm to two low-order, nonlinear tracking problems according to a global criterion and a local-time criterion respectively are presented.
Author: Talal Umar Halawani
Publisher:
ISBN:
Category :
Languages : en
Pages : 43
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Book Description
A new approximation technique to a certain class of nonlinear filtering problems is considered. The method is based on an approximation of nonlinear, partially observable systems by a stochastic control problem with fully observable state. The filter development proceeds from the assumption that the unobservables are conditionally Gaussian with respect to the observations initially. The concepts of both conditionally Gaussian processes and an optimal-control approach to filtering are utilized in the filter development. A two-step, nonlinear, recursive estimation procedure (TNF), compatible with the logical structure of the optimal mean-square estimator, generates a finite-dimensional, nonlinear filter with improved characteristics over most of the traditional methods. Moreover, a close (in the mean-square sense) approximation for the original system will be generated as well. In general the nonlinear filtering problem does not have a finite-dimensional recursive synthesis. Thus, the proposed technique may expand the range of practical problems that can be handled by nonlinear filtering. Application of the derived multi-dimensional filtering algorithm to two low-order, nonlinear tracking problems according to a global criterion and a local-time criterion respectively are presented.
Author: Talal Umar Halawani
Publisher:
ISBN:
Category : Control theory
Languages : en
Pages : 266
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Book Description
A new approximation technique to a certain class of nonlinear filtering problems is considered in this dissertation. The method is based on an approximation of nonlinear, partially-observable systems by a stochastic control problem with fully observable state. The filter development proceeds from the assumption that the unobservables are conditionally Gaussian with respect to the observations initially. The concepts of both conditionally Gaussian processes and an optimal-control approach to filtering are utilized in the filter development. A two-step, nonlinear, recursive estimation procedure (TNF), compatible with the logical structure of the optimal mean-square estimator, generates a finite-dimensional, nonlinear filter with improved characteristics over most of the traditional methods. Moreover, a "close" (in the mean-square sense) approximation model for the original system will be generated as well. In general the nonlinear filtering problem does not have a finite-dimensional recursive synthesis. Thus, the proposed technique may expand the range of practical problems that can be handled by nonlinear filtering. A detailed derivation for the filter with global property is presented. Extension of the results to largescale nonlinear systems is accomplished by incorporating a novel decomposition scheme in the filter design. Application of the developed filter to a scalar nonlinear system which lacks model "smoothness" is presented in [K2]. Application of the derived multi-dimensional filtering algorithm to two low-order, nonlinear tracking problems according to a global criterion and a local-time criterion respectively are presented. Also, a comparison with traditional methods, such as the popular Extended-Kalman Filter (EKE), are given via digital-computer simulation to demonstrate the effectiveness of the obtained results.
Author:
Publisher:
ISBN:
Category : Aeronautics
Languages : en
Pages : 268
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Book Description
Author: Kushner
Publisher: Academic Press
ISBN: 0080956386
Category : Computers
Languages : en
Pages : 263
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Book Description
Probability Methods for Approximations in Stochastic Control and for Elliptic Equations
Author: Wai-Kai Chen
Publisher: CRC Press
ISBN: 9781420041408
Category : Computers
Languages : en
Pages : 3076
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Book Description
A bestseller in its first edition, The Circuits and Filters Handbook has been thoroughly updated to provide the most current, most comprehensive information available in both the classical and emerging fields of circuits and filters, both analog and digital. This edition contains 29 new chapters, with significant additions in the areas of computer-
Author:
Publisher:
ISBN:
Category : Aeronautics
Languages : en
Pages : 1264
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Book Description
Author: Alan Bain
Publisher: Springer Science & Business Media
ISBN: 0387768963
Category : Mathematics
Languages : en
Pages : 395
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Book Description
This book provides a rigorous mathematical treatment of the non-linear stochastic filtering problem using modern methods. Particular emphasis is placed on the theoretical analysis of numerical methods for the solution of the filtering problem via particle methods. The book should provide sufficient background to enable study of the recent literature. While no prior knowledge of stochastic filtering is required, readers are assumed to be familiar with measure theory, probability theory and the basics of stochastic processes. Most of the technical results that are required are stated and proved in the appendices. Exercises and solutions are included.
Author: Sueo Sugimoto
Publisher: Ohmsha, Ltd.
ISBN: 4274805026
Category : Mathematics
Languages : en
Pages : 457
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Book Description
This book covers a broad range of filter theories, algorithms, and numerical examples. The representative linear and nonlinear filters such as the Kalman filter, the steady-state Kalman filter, the H infinity filter, the extended Kalman filter, the Gaussian sum filter, the statistically linearized Kalman filter, the unscented Kalman filter, the Gaussian filter, the cubature Kalman filter are first visited. Then, the non-Gaussian filters such as the ensemble Kalman filter and the particle filters based on the sequential Bayesian filter and the sequential importance resampling are described, together with their recent advances. Moreover, the information matrix in the nonlinear filtering, the nonlinear smoother based on the Markov Chain Monte Carlo, the continuous-discrete filters, factorized filters, and nonlinear filters based on stochastic approximation method are detailed. 1 Review of the Kalman Filter and Related Filters 2 Information Matrix in Nonlinear Filtering 3 Extended Kalman Filter and Gaussian Sum Filter 4 Statistically Linearized Kalman Filter 5 The Unscented Kalman Filter 6 General Gaussian Filters and Applications 7 The Ensemble Kalman Filter 8 Particle Filter 9 Nonlinear Smoother with Markov Chain Monte Carlo 10 Continuous-Discrete Filters 11 Factorized Filters 12 Nonlinear Filters Based on Stochastic Approximation Method
Author:
Publisher:
ISBN:
Category : Mechanics, Applied
Languages : en
Pages : 528
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Book Description
Author: Jitendra R. Raol
Publisher: CRC Press
ISBN: 1498745180
Category : Technology & Engineering
Languages : en
Pages : 581
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Book Description
Nonlinear Filtering covers linear and nonlinear filtering in a comprehensive manner, with appropriate theoretic and practical development. Aspects of modeling, estimation, recursive filtering, linear filtering, and nonlinear filtering are presented with appropriate and sufficient mathematics. A modeling-control-system approach is used when applicable, and detailed practical applications are presented to elucidate the analysis and filtering concepts. MATLAB routines are included, and examples from a wide range of engineering applications - including aerospace, automated manufacturing, robotics, and advanced control systems - are referenced throughout the text.
