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Author : Oleg V. Makhnin
Publisher :
ISBN 13 :
Total Pages : 130 pages
Book Rating : 4.3/5 (129 download)
Download or read book Filtering for Some Stochastic Processes with Discrete Observations written by Oleg V. Makhnin and published by . This book was released on 2002 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Andrew H. Jazwinski
Publisher : Courier Corporation
ISBN 13 : 0486318192
Total Pages : 404 pages
Book Rating : 4.4/5 (863 download)
Download or read book Stochastic Processes and Filtering Theory written by Andrew H. Jazwinski and published by Courier Corporation. This book was released on 2013-04-15 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unified treatment of linear and nonlinear filtering theory presents material previously available only in journals, and in terms accessible to engineering students. Its sole prerequisites are advanced calculus, the theory of ordinary differential equations, and matrix analysis. Although theory is emphasized, the text discusses numerous practical applications as well. Taking the state-space approach to filtering, this text models dynamical systems by finite-dimensional Markov processes, outputs of stochastic difference, and differential equations. Starting with background material on probability theory and stochastic processes, the author introduces and defines the problems of filtering, prediction, and smoothing. He presents the mathematical solutions to nonlinear filtering problems, and he specializes the nonlinear theory to linear problems. The final chapters deal with applications, addressing the development of approximate nonlinear filters, and presenting a critical analysis of their performance.
Author : Alan Bain
Publisher : Springer Science & Business Media
ISBN 13 : 0387768963
Total Pages : 395 pages
Book Rating : 4.3/5 (877 download)
Download or read book Fundamentals of Stochastic Filtering written by Alan Bain and published by Springer Science & Business Media. This book was released on 2008-10-08 with total page 395 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : V.N. Fomin
Publisher : Springer Science & Business Media
ISBN 13 : 9401153264
Total Pages : 387 pages
Book Rating : 4.4/5 (11 download)
Download or read book Optimal Filtering written by V.N. Fomin and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 387 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to an investigation of some important problems of mod ern filtering theory concerned with systems of 'any nature being able to per ceive, store and process an information and apply it for control and regulation'. (The above quotation is taken from the preface to [27]). Despite the fact that filtering theory is l'argely worked out (and its major issues such as the Wiener-Kolmogorov theory of optimal filtering of stationary processes and Kalman-Bucy recursive filtering theory have become classical) a development of the theory is far from complete. A great deal of recent activity in this area is observed, researchers are trying consistently to generalize famous results, extend them to more broad classes of processes, realize and justify more simple procedures for processing measurement data in order to obtain more efficient filtering algorithms. As to nonlinear filter ing, it remains much as fragmentary. Here much progress has been made by R. L. Stratonovich and his successors in the area of filtering of Markov processes. In this volume an effort is made to advance in certain of these issues. The monograph has evolved over many years, coming of age by stages. First it was an impressive job of gathering together the bulk of the impor tant contributions to estimation theory, an understanding and moderniza tion of some of its results and methods, with the intention of applying them to recursive filtering problems.
Author : Jean-Claude Bertein
Publisher : John Wiley & Sons
ISBN 13 : 1118600533
Total Pages : 196 pages
Book Rating : 4.1/5 (186 download)
Download or read book Discrete Stochastic Processes and Optimal Filtering written by Jean-Claude Bertein and published by John Wiley & Sons. This book was released on 2012-12-27 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: Optimal filtering applied to stationary and non-stationary signals provides the most efficient means of dealing with problems arising from the extraction of noise signals. Moreover, it is a fundamental feature in a range of applications, such as in navigation in aerospace and aeronautics, filter processing in the telecommunications industry, etc. This book provides a comprehensive overview of this area, discussing random and Gaussian vectors, outlining the results necessary for the creation of Wiener and adaptive filters used for stationary signals, as well as examining Kalman filters which are used in relation to non-stationary signals. Exercises with solutions feature in each chapter to demonstrate the practical application of these ideas using MATLAB.
Author : Richard S. Bucy
Publisher : American Mathematical Soc.
ISBN 13 : 0821837826
Total Pages : 238 pages
Book Rating : 4.8/5 (218 download)
Download or read book Filtering for Stochastic Processes with Applications to Guidance written by Richard S. Bucy and published by American Mathematical Soc.. This book was released on 2005 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: This second edition preserves the original text of 1968, with clarification and added references. From the Preface to the Second Edition: ``Since the First Edition of this book, numerous important results have appeared--in particular stochastic integrals with respect to martingales, random fields, Riccati equation theory and realization of nonlinear filters, to name a few. In Appendix D, an attempt is made to provide some of the references that the authors have found useful and tocomment on the relation of the cited references to the field ... [W]e hope that this new edition will have the effect of hastening the day when the nonlinear filter will enjoy the same popularity in applications as the linear filter does now.''
Author : V. Solo
Publisher :
ISBN 13 :
Total Pages : 25 pages
Book Rating : 4.:/5 (227 download)
Download or read book Smoothing Estimation of Stochastic Processes. Part II. Two Filter Formulae written by V. Solo and published by . This book was released on 1980 with total page 25 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this article these two-filter results and some new ones are derived in a simple way in a very general setting (for arbitrary nonstationary processes). It turns out however that only if a wide-sense (i.e. second order) Markovian assumption is added can one of the filters be viewed as a backwards filter. The remainder of the paper is organized as follows. Section 2 recalls some smoothing formulae that apply to both continuous and discrete observations. Section 3 discusses two types of two-filter-like formulae for general nonstationary processes. In Section 4 one of the filters is shown to be a backwards least squares estimate provided a wide sense Markovian assumption is satisfied. Section 5 contains a derivation of some backwards filters. In Section 6 some additional two-filter-like formulae are given. The final section is a conlusion.
Author : Bert Fristedt
Publisher : American Mathematical Soc.
ISBN 13 : 0821843338
Total Pages : 266 pages
Book Rating : 4.8/5 (218 download)
Download or read book Filtering and Prediction: A Primer written by Bert Fristedt and published by American Mathematical Soc.. This book was released on 2007 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: Filtering and prediction is about observing moving objects when the observations are corrupted by random errors. The main focus is then on filtering out the errors and extracting from the observations the most precise information about the object, which itself may or may not be moving in a somewhat random fashion. Next comes the prediction step where, using information about the past behavior of the object, one tries to predict its future path. The first three chapters of the book deal with discrete probability spaces, random variables, conditioning, Markov chains, and filtering of discrete Markov chains. The next three chapters deal with the more sophisticated notions of conditioning in nondiscrete situations, filtering of continuous-space Markov chains, and of Wiener process. Filtering and prediction of stationary sequences is discussed in the last two chapters. The authors believe that they have succeeded in presenting necessary ideas in an elementary manner without sacrificing the rigor too much. Such rigorous treatment is lacking at this level in the literature. in the past few years the material in the book was offered as a one-semester undergraduate/beginning graduate course at the University of Minnesota. Some of the many problems suggested in the text were used in homework assignments.
Author : G. Kallianpur
Publisher : Springer Science & Business Media
ISBN 13 : 1475765924
Total Pages : 326 pages
Book Rating : 4.4/5 (757 download)
Download or read book Stochastic Filtering Theory written by G. Kallianpur and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is based on a seminar given at the University of California at Los Angeles in the Spring of 1975. The choice of topics reflects my interests at the time and the needs of the students taking the course. Initially the lectures were written up for publication in the Lecture Notes series. How ever, when I accepted Professor A. V. Balakrishnan's invitation to publish them in the Springer series on Applications of Mathematics it became necessary to alter the informal and often abridged style of the notes and to rewrite or expand much of the original manuscript so as to make the book as self-contained as possible. Even so, no attempt has been made to write a comprehensive treatise on filtering theory, and the book still follows the original plan of the lectures. While this book was in preparation, the two-volume English translation of the work by R. S. Liptser and A. N. Shiryaev has appeared in this series. The first volume and the present book have the same approach to the sub ject, viz. that of martingale theory. Liptser and Shiryaev go into greater detail in the discussion of statistical applications and also consider inter polation and extrapolation as well as filtering.
Author : Vladimir Nikolaevič Fomin
Publisher :
ISBN 13 : 9789401153270
Total Pages : 396 pages
Book Rating : 4.1/5 (532 download)
Download or read book Optimal Filtering written by Vladimir Nikolaevič Fomin and published by . This book was released on 1998-11-30 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Marcelo G.
Publisher : Springer Nature
ISBN 13 : 3031025350
Total Pages : 87 pages
Book Rating : 4.0/5 (31 download)
Download or read book Sequential Monte Carlo Methods for Nonlinear Discrete-Time Filtering written by Marcelo G. and published by Springer Nature. This book was released on 2022-06-01 with total page 87 pages. Available in PDF, EPUB and Kindle. Book excerpt: In these notes, we introduce particle filtering as a recursive importance sampling method that approximates the minimum-mean-square-error (MMSE) estimate of a sequence of hidden state vectors in scenarios where the joint probability distribution of the states and the observations is non-Gaussian and, therefore, closed-form analytical expressions for the MMSE estimate are generally unavailable. We begin the notes with a review of Bayesian approaches to static (i.e., time-invariant) parameter estimation. In the sequel, we describe the solution to the problem of sequential state estimation in linear, Gaussian dynamic models, which corresponds to the well-known Kalman (or Kalman-Bucy) filter. Finally, we move to the general nonlinear, non-Gaussian stochastic filtering problem and present particle filtering as a sequential Monte Carlo approach to solve that problem in a statistically optimal way. We review several techniques to improve the performance of particle filters, including importance function optimization, particle resampling, Markov Chain Monte Carlo move steps, auxiliary particle filtering, and regularized particle filtering. We also discuss Rao-Blackwellized particle filtering as a technique that is particularly well-suited for many relevant applications such as fault detection and inertial navigation. Finally, we conclude the notes with a discussion on the emerging topic of distributed particle filtering using multiple processors located at remote nodes in a sensor network. Throughout the notes, we often assume a more general framework than in most introductory textbooks by allowing either the observation model or the hidden state dynamic model to include unknown parameters. In a fully Bayesian fashion, we treat those unknown parameters also as random variables. Using suitable dynamic conjugate priors, that approach can be applied then to perform joint state and parameter estimation. Table of Contents: Introduction / Bayesian Estimation of Static Vectors / The Stochastic Filtering Problem / Sequential Monte Carlo Methods / Sampling/Importance Resampling (SIR) Filter / Importance Function Selection / Markov Chain Monte Carlo Move Step / Rao-Blackwellized Particle Filters / Auxiliary Particle Filter / Regularized Particle Filters / Cooperative Filtering with Multiple Observers / Application Examples / Summary
Author : Jie Xiong
Publisher : OUP Oxford
ISBN 13 : 0191551392
Total Pages : 288 pages
Book Rating : 4.1/5 (915 download)
Download or read book An Introduction to Stochastic Filtering Theory written by Jie Xiong and published by OUP Oxford. This book was released on 2008-04-17 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic Filtering Theory uses probability tools to estimate unobservable stochastic processes that arise in many applied fields including communication, target-tracking, and mathematical finance. As a topic, Stochastic Filtering Theory has progressed rapidly in recent years. For example, the (branching) particle system representation of the optimal filter has been extensively studied to seek more effective numerical approximations of the optimal filter; the stability of the filter with "incorrect" initial state, as well as the long-term behavior of the optimal filter, has attracted the attention of many researchers; and although still in its infancy, the study of singular filtering models has yielded exciting results. In this text, Jie Xiong introduces the reader to the basics of Stochastic Filtering Theory before covering these key recent advances. The text is written in a style suitable for graduates in mathematics and engineering with a background in basic probability.
Author : Maksym Luz
Publisher : John Wiley & Sons
ISBN 13 : 1786305038
Total Pages : 308 pages
Book Rating : 4.7/5 (863 download)
Download or read book Estimation of Stochastic Processes with Stationary Increments and Cointegrated Sequences written by Maksym Luz and published by John Wiley & Sons. This book was released on 2019-12-12 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: Estimation of Stochastic Processes is intended for researchers in the field of econometrics, financial mathematics, statistics or signal processing. This book gives a deep understanding of spectral theory and estimation techniques for stochastic processes with stationary increments. It focuses on the estimation of functionals of unobserved values for stochastic processes with stationary increments, including ARIMA processes, seasonal time series and a class of cointegrated sequences. Furthermore, this book presents solutions to extrapolation (forecast), interpolation (missed values estimation) and filtering (smoothing) problems based on observations with and without noise, in discrete and continuous time domains. Extending the classical approach applied when the spectral densities of the processes are known, the minimax method of estimation is developed for a case where the spectral information is incomplete and the relations that determine the least favorable spectral densities for the optimal estimations are found.
Download or read book Research Reports written by and published by . This book was released on 1993 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Richard S. Bucy
Publisher : American Mathematical Soc.
ISBN 13 : 9780821837825
Total Pages : 240 pages
Book Rating : 4.8/5 (378 download)
Download or read book Filtering for Stochastic Processes with Applications to Guidance written by Richard S. Bucy and published by American Mathematical Soc.. This book was released on 2005 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: This second edition preserves the original text of 1968, with clarification and added references. From the Preface to the Second Edition: ``Since the First Edition of this book, numerous important results have appeared--in particular stochastic integrals with respect to martingales, random fields, Riccati equation theory and realization of nonlinear filters, to name a few. In Appendix D, an attempt is made to provide some of the references that the authors have found useful and tocomment on the relation of the cited references to the field ... [W]e hope that this new edition will have the effect of hastening the day when the nonlinear filter will enjoy the same popularity in applications as the linear filter does now.''
Author : Asger Roer Pedersen
Publisher :
ISBN 13 :
Total Pages : 20 pages
Book Rating : 4.:/5 (488 download)
Download or read book Maximum Likelihood Estimation Based on Imcomplete Observations for a Class of Discrete Time Stochastic Processes by Means of the Kalman Filter written by Asger Roer Pedersen and published by . This book was released on 1993 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Venkatarama Krishnan
Publisher : Courier Corporation
ISBN 13 : 0486781836
Total Pages : 353 pages
Book Rating : 4.4/5 (867 download)
Download or read book Nonlinear Filtering and Smoothing written by Venkatarama Krishnan and published by Courier Corporation. This book was released on 2013-10-17 with total page 353 pages. Available in PDF, EPUB and Kindle. Book excerpt: Most useful for graduate students in engineering and finance who have a basic knowledge of probability theory, this volume is designed to give a concise understanding of martingales, stochastic integrals, and estimation. It emphasizes applications. Many theorems feature heuristic proofs; others include rigorous proofs to reinforce physical understanding. Numerous end-of-chapter problems enhance the book's practical value. After introducing the basic measure-theoretic concepts of probability and stochastic processes, the text examines martingales, square integrable martingales, and stopping times. Considerations of white noise and white-noise integrals are followed by examinations of stochastic integrals and stochastic differential equations, as well as the associated Ito calculus and its extensions. After defining the Stratonovich integral, the text derives the correction terms needed for computational purposes to convert the Ito stochastic differential equation to the Stratonovich form. Additional chapters contain the derivation of the optimal nonlinear filtering representation, discuss how the Kalman filter stands as a special case of the general nonlinear filtering representation, apply the nonlinear filtering representations to a class of fault-detection problems, and discuss several optimal smoothing representations.
