Nonlinear Filtering and Optimal Phase Tracking
Author:
Publisher:
Published: 2011-11-16
Total Pages: 282
ISBN-13: 9781461404880
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Nonlinear Filtering and Optimal Phase Tracking
Author: Zeev Schuss
Publisher: Springer Science & Business Media
Published: 2011-11-16
Total Pages: 276
ISBN-13: 1461404878
DOWNLOAD EBOOKThis book offers an analytical rather than measure-theoretical approach to the derivation of the partial differential equations of nonlinear filtering theory. The basis for this approach is the discrete numerical scheme used in Monte-Carlo simulations of stochastic differential equations and Wiener's associated path integral representation of the transition probability density. Furthermore, it presents analytical methods for constructing asymptotic approximations to their solution and for synthesizing asymptotically optimal filters. It also offers a new approach to the phase tracking problem, based on optimizing the mean time to loss of lock. The book is based on lecture notes from a one-semester special topics course on stochastic processes and their applications that the author taught many times to graduate students of mathematics, applied mathematics, physics, chemistry, computer science, electrical engineering, and other disciplines. The book contains exercises and worked-out examples aimed at illustrating the methods of mathematical modeling and performance analysis of phase trackers.
Nonlinear Filters
Author: Peyman Setoodeh
Publisher: John Wiley & Sons
Published: 2022-03-04
Total Pages: 308
ISBN-13: 1119078156
DOWNLOAD EBOOKNONLINEAR FILTERS Discover the utility of using deep learning and (deep) reinforcement learning in deriving filtering algorithms with this insightful and powerful new resource Nonlinear Filters: Theory and Applications delivers an insightful view on state and parameter estimation by merging ideas from control theory, statistical signal processing, and machine learning. Taking an algorithmic approach, the book covers both classic and machine learning-based filtering algorithms. Readers of Nonlinear Filters will greatly benefit from the wide spectrum of presented topics including stability, robustness, computability, and algorithmic sufficiency. Readers will also enjoy: Organization that allows the book to act as a stand-alone, self-contained reference A thorough exploration of the notion of observability, nonlinear observers, and the theory of optimal nonlinear filtering that bridges the gap between different science and engineering disciplines A profound account of Bayesian filters including Kalman filter and its variants as well as particle filter A rigorous derivation of the smooth variable structure filter as a predictor-corrector estimator formulated based on a stability theorem, used to confine the estimated states within a neighborhood of their true values A concise tutorial on deep learning and reinforcement learning A detailed presentation of the expectation maximization algorithm and its machine learning-based variants, used for joint state and parameter estimation Guidelines for constructing nonparametric Bayesian models from parametric ones Perfect for researchers, professors, and graduate students in engineering, computer science, applied mathematics, and artificial intelligence, Nonlinear Filters: Theory and Applications will also earn a place in the libraries of those studying or practicing in fields involving pandemic diseases, cybersecurity, information fusion, augmented reality, autonomous driving, urban traffic network, navigation and tracking, robotics, power systems, hybrid technologies, and finance.
Fundamentals of Nonlinear Digital Filtering
Author: Jaakko Astola
Publisher: CRC Press
Published: 2020-09-10
Total Pages: 288
ISBN-13: 1000102610
DOWNLOAD EBOOKFundamentals of Nonlinear Digital Filtering is the first book of its kind, presenting and evaluating current methods and applications in nonlinear digital filtering. Written for professors, researchers, and application engineers, as well as for serious students of signal processing, this is the only book available that functions as both a reference handbook and a textbook. Solid introductory material, balanced coverage of theoretical and practical aspects, and dozens of examples provide you with a self-contained, comprehensive information source on nonlinear filtering and its applications.
Nonlinear Filtering
Author: Jitendra R. Raol
Publisher: CRC Press
Published: 2017-07-12
Total Pages: 581
ISBN-13: 1498745180
DOWNLOAD EBOOKNonlinear 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.
Bayesian Bounds for Parameter Estimation and Nonlinear Filtering/Tracking
Author: Harry L. Van Trees
Publisher: Wiley-IEEE Press
Published: 2007-08-31
Total Pages: 951
ISBN-13: 9780470120958
DOWNLOAD EBOOKThe first comprehensive development of Bayesian Bounds for parameter estimation and nonlinear filtering/tracking Bayesian estimation plays a central role in many signal processing problems encountered in radar, sonar, communications, seismology, and medical diagnosis. There are often highly nonlinear problems for which analytic evaluation of the exact performance is intractable. A widely used technique is to find bounds on the performance of any estimator and compare the performance of various estimators to these bounds. This book provides a comprehensive overview of the state of the art in Bayesian Bounds. It addresses two related problems: the estimation of multiple parameters based on noisy measurements and the estimation of random processes, either continuous or discrete, based on noisy measurements. An extensive introductory chapter provides an overview of Bayesian estimation and the interrelationship and applicability of the various Bayesian Bounds for both static parameters and random processes. It provides the context for the collection of papers that are included. This book will serve as a comprehensive reference for engineers and statisticians interested in both theory and application. It is also suitable as a text for a graduate seminar or as a supplementary reference for an estimation theory course.
An Optimal Approximation for a Certain Class of Nonlinear Filtering Problems
Author: Talal Umar Halawani
Publisher:
Published: 1983
Total Pages: 43
ISBN-13:
DOWNLOAD EBOOKA 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.
Nonlinear Filtering Stochastic Analysis and Numerical Methods
Author:
Publisher:
Published: 1998
Total Pages: 31
ISBN-13:
DOWNLOAD EBOOKThe final report contains the outline of the research that was done during the period 1995-98. The main objective was to develop effective numerical algorithms of optimal nonlinear filtering and prediction and (more generally), state and parameter estimation in partially observed stochastic dynamical systems. During the course of the project a number of fundamental results were obtained, such as: development of a Wiener type optimal nonlinear filter (complete solution of "the last Wiener problem"); development of the spectral based approach to nonlinear filtering, which have led to the spectral separating scheme (separation of parameters and observations in optimal nonlinear filter) and other effective numerical approximations for the optimal nonlinear filter that include projection filter and assumed density filters. The results have been applied to specific "difficult" problems in target tracking, particularly, to the angle only tracking in EO and IR search and track systems and track-before-detect of resolved or sub-resolved low SNR targets. Extensive simulation showed that the proposed approach allows us to obtain much better performance as compared to the conventional expended Kalman filter in a number of important practical situations.
Linear And Nonlinear Filtering For Scientists And Engineers
Author: Nasir Uddin Ahmed
Publisher: World Scientific
Published: 1999-01-22
Total Pages: 273
ISBN-13: 9814495646
DOWNLOAD EBOOKThe book combines both rigor and intuition to derive most of the classical results of linear and nonlinear filtering and beyond. Many fundamental results recently discovered by the author are included. Furthermore, many results that have appeared in recent years in the literature are also presented. The most interesting feature of the book is that all the derivations of the linear filter equations given in Chapters 3-11, beginning from the classical Kalman filter presented in Chapters 3 and 5, are based on one basic principle which is fully rigorous but also very intuitive and easily understandable. The second most interesting feature is that the book provides a rigorous theoretical basis for the numerical solution of nonlinear filter equations illustrated by multidimensional examples. The book also provides a strong foundation for theoretical understanding of the subject based on the theory of stochastic differential equations.
Efficient Nonlinear Adaptive Filters
Author: Haiquan Zhao
Publisher: Springer Nature
Published: 2023-02-10
Total Pages: 271
ISBN-13: 3031208188
DOWNLOAD EBOOKThis book presents the design, analysis, and application of nonlinear adaptive filters with the goal of improving efficient performance (ie the convergence speed, steady-state error, and computational complexity). The authors present a nonlinear adaptive filter, which is an important part of nonlinear system and digital signal processing and can be applied to diverse fields such as communications, control power system, radar sonar, etc. The authors also present an efficient nonlinear filter model and robust adaptive filtering algorithm based on the local cost function of optimal criterion to overcome non-Gaussian noise interference. The authors show how these achievements provide new theories and methods for robust adaptive filtering of nonlinear and non-Gaussian systems. The book is written for the scientist and engineer who are not necessarily an expert in the specific nonlinear filtering field but who want to learn about the current research and application. The book is also written to accompany a graduate/PhD course in the area of nonlinear system and adaptive signal processing.
