discrete stochastic processes and optimal filtering

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Discrete Stochastic Processes And Optimal Filtering

Author : Jean-Claude Bertein
ISBN : 9781118615492
Genre : Technology & Engineering
File Size : 32. 31 MB
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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.

Optimal Filtering

Author : V.N. Fomin
ISBN : 9789401146913
Genre : Mathematics
File Size : 25. 47 MB
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In this volume the investigations of filtering problems, a start on which has been made in [55], are being continued and are devoted to theoretical problems of processing stochastic fields. The derivation of the theory of processing stochastic fields is similar to that of the theory extensively developed for stochastic processes ('stochastic fields with a one-dimensional domain'). Nevertheless there exist essential distinctions between these cases making a construction of the theory for the multi-dimensional case in such a way difficult. Among these are the absence of the notion of the 'past-future' in the case of fields, which plays a fundamental role in constructing stochastic processes theory. So attempts to introduce naturally the notion of the causality (non-anticipativity) when synthesising stable filters designed for processing fields have not met with success. Mathematically, principal distinctions between multi-dimensional and one-dimensional cases imply that the set of roots of a multi-variable polyno mial does not necessary consist of a finite number of isolated points. From the main theorem of algebra it follows that in the one-dimensional case every poly nomial of degree n has just n roots (considering their multiplicity) in the com plex plane. As a consequence, in particular, an arbitrary rational function ¢(.

Stochastic Processes And Filtering Theory

Author : Andrew H. Jazwinski
ISBN : 9780486318196
Genre : Science
File Size : 80. 7 MB
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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.

Stochastic Processes Estimation And Control

Author : Jason L. Speyer
ISBN : 9780898716559
Genre : Mathematics
File Size : 35. 35 MB
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The authors provide a comprehensive treatment of stochastic systems from the foundations of probability to stochastic optimal control. The book covers discrete- and continuous-time stochastic dynamic systems leading to the derivation of the Kalman filter, its properties, and its relation to the frequency domain Wiener filter aswell as the dynamic programming derivation of the linear quadratic Gaussian (LQG) and the linear exponential Gaussian (LEG) controllers and their relation to HÝsubscript 2¨ and HÝsubscript Ýinfinity¨¨ controllers and system robustness. This book is suitable for first-year graduate students in electrical, mechanical, chemical, and aerospace engineering specializing in systems and control. Students in computer science, economics, and possibly business will also find it useful.

Nonlinear Filtering And Optimal Phase Tracking

Author : Zeev Schuss
ISBN : 1461404878
Genre : Mathematics
File Size : 26. 70 MB
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This 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.

Discrete Time Stochastic Systems

Author : Torsten Söderström
ISBN : 9781447101017
Genre : Mathematics
File Size : 34. 98 MB
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This comprehensive introduction to the estimation and control of dynamic stochastic systems provides complete derivations of key results. The second edition includes improved and updated material, and a new presentation of polynomial control and new derivation of linear-quadratic-Gaussian control.

Adaptive Filtering Prediction And Control

Author : Graham C Goodwin
ISBN : 9780486137728
Genre : Technology & Engineering
File Size : 70. 2 MB
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This unified survey focuses on linear discrete-time systems and explores natural extensions to nonlinear systems. It emphasizes discrete-time systems, summarizing theoretical and practical aspects of a large class of adaptive algorithms. 1984 edition.

Statistics Of Random Processes

Author : Robert Liptser
ISBN : 9783662130438
Genre : Mathematics
File Size : 52. 23 MB
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These volumes cover non-linear filtering (prediction and smoothing) theory and its applications to the problem of optimal estimation, control with incomplete data, information theory, and sequential testing of hypothesis. Also presented is the theory of martingales, of interest to those who deal with problems in financial mathematics. These editions include new material, expanded chapters, and comments on recent progress in the field.

Fundamentals Of Adaptive Signal Processing

Author : Aurelio Uncini
ISBN : 9783319028071
Genre : Technology & Engineering
File Size : 28. 87 MB
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This book is an accessible guide to adaptive signal processing methods that equips the reader with advanced theoretical and practical tools for the study and development of circuit structures and provides robust algorithms relevant to a wide variety of application scenarios. Examples include multimodal and multimedia communications, the biological and biomedical fields, economic models, environmental sciences, acoustics, telecommunications, remote sensing, monitoring and in general, the modeling and prediction of complex physical phenomena. The reader will learn not only how to design and implement the algorithms but also how to evaluate their performance for specific applications utilizing the tools provided. While using a simple mathematical language, the employed approach is very rigorous. The text will be of value both for research purposes and for courses of study.

Introduction To Random Signals And Noise

Author : Wim C. Van Etten
ISBN : 9780470024126
Genre : Science
File Size : 73. 71 MB
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Random signals and noise are present in many engineering systems and networks. Signal processing techniques allow engineers to distinguish between useful signals in audio, video or communication equipment, and interference, which disturbs the desired signal. With a strong mathematical grounding, this text provides a clear introduction to the fundamentals of stochastic processes and their practical applications to random signals and noise. With worked examples, problems, and detailed appendices, Introduction to Random Signals and Noise gives the reader the knowledge to design optimum systems for effectively coping with unwanted signals. Key features: Considers a wide range of signals and noise, including analogue, discrete-time and bandpass signals in both time and frequency domains. Analyses the basics of digital signal detection using matched filtering, signal space representation and correlation receiver. Examines optimal filtering methods and their consequences. Presents a detailed discussion of the topic of Poisson processes and shot noise. An excellent resource for professional engineers developing communication systems, semiconductor devices, and audio and video equipment, this book is also ideal for senior undergraduate and graduate students in Electronic and Electrical Engineering.

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