Lectures On Discrete Time Filtering
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Lectures On Discrete Time Filtering
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Author : R.S. Bucy
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Lectures On Discrete Time Filtering written by R.S. Bucy and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
The theory of linear discrete time filtering started with a paper by Kol mogorov in 1941. He addressed the problem for stationary random se quences and introduced the idea of the innovations process, which is a useful tool for the more general problems considered here. The reader may object and note that Gauss discovered least squares much earlier; however, I want to distinguish between the problem of parameter estimation, the Gauss problem, and that of Kolmogorov estimation of a process. This sep aration is of more than academic interest as the least squares problem leads to the normal equations, which are numerically ill conditioned, while the process estimation problem in the linear case with appropriate assumptions leads to uniformly asymptotically stable equations for the estimator and the gain. The conditions relate to controlability and observability and will be detailed in this volume. In the present volume, we present a series of lectures on linear and nonlinear sequential filtering theory. The theory is due to Kalman for the linear colored observation noise problem; in the case of white observation noise it is the analog of the continuous-time Kalman-Bucy theory. The discrete time filtering theory requires only modest mathematical tools in counterpoint to the continuous time theory and is aimed at a senior-level undergraduate course. The present book, organized by lectures, is actually based on a course that meets once a week for three hours, with each meeting constituting a lecture.
Lectures On Discrete Time Filtering
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Author : R.S. Bucy
language : en
Publisher: Springer
Release Date : 2011-11-12
Lectures On Discrete Time Filtering written by R.S. Bucy and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-11-12 with Science categories.
The theory of linear discrete time filtering started with a paper by Kol mogorov in 1941. He addressed the problem for stationary random se quences and introduced the idea of the innovations process, which is a useful tool for the more general problems considered here. The reader may object and note that Gauss discovered least squares much earlier; however, I want to distinguish between the problem of parameter estimation, the Gauss problem, and that of Kolmogorov estimation of a process. This sep aration is of more than academic interest as the least squares problem leads to the normal equations, which are numerically ill conditioned, while the process estimation problem in the linear case with appropriate assumptions leads to uniformly asymptotically stable equations for the estimator and the gain. The conditions relate to controlability and observability and will be detailed in this volume. In the present volume, we present a series of lectures on linear and nonlinear sequential filtering theory. The theory is due to Kalman for the linear colored observation noise problem; in the case of white observation noise it is the analog of the continuous-time Kalman-Bucy theory. The discrete time filtering theory requires only modest mathematical tools in counterpoint to the continuous time theory and is aimed at a senior-level undergraduate course. The present book, organized by lectures, is actually based on a course that meets once a week for three hours, with each meeting constituting a lecture.
Sequential Monte Carlo Methods For Nonlinear Discrete Time Filtering
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Author : Marcelo G. S. Bruno
language : en
Publisher: Morgan & Claypool Publishers
Release Date : 2013
Sequential Monte Carlo Methods For Nonlinear Discrete Time Filtering written by Marcelo G. S. Bruno and has been published by Morgan & Claypool Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Computers categories.
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.
Sequential Monte Carlo Methods For Nonlinear Discrete Time Filtering
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Author : Marcelo G. S. Bruno
language : en
Publisher: Springer Nature
Release Date : 2022-06-01
Sequential Monte Carlo Methods For Nonlinear Discrete Time Filtering written by Marcelo G. S. Bruno and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-06-01 with Technology & Engineering categories.
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
Fundamentals Of Signals And Systems
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Author : Mr. Rohit Manglik
language : en
Publisher: EduGorilla Publication
Release Date : 2024-07-04
Fundamentals Of Signals And Systems written by Mr. Rohit Manglik and has been published by EduGorilla Publication this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-07-04 with Technology & Engineering categories.
EduGorilla Publication is a trusted name in the education sector, committed to empowering learners with high-quality study materials and resources. Specializing in competitive exams and academic support, EduGorilla provides comprehensive and well-structured content tailored to meet the needs of students across various streams and levels.
Seminaire De Probabilites Xxxiv
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Author : J. Azema
language : en
Publisher: Springer
Release Date : 2007-05-06
Seminaire De Probabilites Xxxiv written by J. Azema and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-05-06 with Mathematics categories.
This volume contains 19 contributions to various subjects in the theory of (commutative and non-commutative) stochastic processes. It also provides a 145-page graduate course on branching and interacting particle systems, with applications to non-linear filtering, by P. del Moral and L. Miclo.
An Introduction To Stochastic Filtering Theory
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Author : Jie Xiong
language : en
Publisher: OUP Oxford
Release Date : 2008-04-17
An Introduction To Stochastic Filtering Theory written by Jie Xiong and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-04-17 with Mathematics categories.
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.
Digital Signal Processing With Matlab Examples Volume 1
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Author : Jose Maria Giron-Sierra
language : en
Publisher: Springer
Release Date : 2016-11-19
Digital Signal Processing With Matlab Examples Volume 1 written by Jose Maria Giron-Sierra and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-11-19 with Technology & Engineering categories.
This is the first volume in a trilogy on modern Signal Processing. The three books provide a concise exposition of signal processing topics, and a guide to support individual practical exploration based on MATLAB programs. This book includes MATLAB codes to illustrate each of the main steps of the theory, offering a self-contained guide suitable for independent study. The code is embedded in the text, helping readers to put into practice the ideas and methods discussed. The book is divided into three parts, the first of which introduces readers to periodic and non-periodic signals. The second part is devoted to filtering, which is an important and commonly used application. The third part addresses more advanced topics, including the analysis of real-world non-stationary signals and data, e.g. structural fatigue, earthquakes, electro-encephalograms, birdsong, etc. The book’s last chapter focuses on modulation, an example of the intentional use of non-stationary signals.
Lecture Slides For Signals And Systems Edition 6 0
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Author : Michael D. Adams
language : en
Publisher: Michael Adams
Release Date : 2024-12-15
Lecture Slides For Signals And Systems Edition 6 0 written by Michael D. Adams and has been published by Michael Adams this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-12-15 with Technology & Engineering categories.
This document constitutes a detailed set of lecture slides on signals and systems, covering both the continuous-time and discrete-time cases. Some of the topics considered include: signal properties, elementary signals, system properties, linear time-invariant systems, convolution, Fourier series, Fourier transform, Laplace transform, z transform, complex analysis, partial fraction expansions, and MATLAB.
Stochastic Evolution Systems
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Author : Boris L. Rozovsky
language : en
Publisher: Springer
Release Date : 2018-10-03
Stochastic Evolution Systems written by Boris L. Rozovsky and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-03 with Mathematics categories.
This monograph, now in a thoroughly revised second edition, develops the theory of stochastic calculus in Hilbert spaces and applies the results to the study of generalized solutions of stochastic parabolic equations. The emphasis lies on second-order stochastic parabolic equations and their connection to random dynamical systems. The authors further explore applications to the theory of optimal non-linear filtering, prediction, and smoothing of partially observed diffusion processes. The new edition now also includes a chapter on chaos expansion for linear stochastic evolution systems. This book will appeal to anyone working in disciplines that require tools from stochastic analysis and PDEs, including pure mathematics, financial mathematics, engineering and physics.