Maybeck P.S. Stochastic Models. Estimation and Control. Volume 2

Издательство Academic Press, 1982, -307 pp.As was true of Volume 1, the purpose of this book is twofold. First, it attempts to develop a thorough understanding of the fundamental concepts incorporated in stochastic processes, estimation, and control. Second, and of equal importance, it provides experience and insights into applying the theory to realistic practical problems. Basically, it investigates the theory and derives from it the tools required to reach the ultimate objective of systematically generating effective designs for estimators and stochastic controllers for operational implementation.
Perhaps most importantly, the entire text follows the basic principles of Volume 1 and concentrates on presenting material in the most lucid. best motivated, and most easily grasped manner. It is oriented toward an engineer or an engineering student, and it is intended both to be a textbook from which a reader can learn about estimation and stochastic control and to provide a good reference source for those who are deeply immersed in these areas. As a result, considerable effort is expended to provide graphical representations, physical interpretations and justifications, geometrical insights, and practical implications of important concepts, as well as precise and mathematically rigorous development of ideas. With an eye to practicality and eventual implementation of algorithms in a digital computer, emphasis is maintained on the case of continuous-time dynamic systems with sampled-data measurements available; nevertheless, corresponding results for discrete-time dynamics or for continuous-time measurements are also presented. These algorithms are developed in detail, to the point where the various design trade-offs and performance evaluations involved in achieving an efficient, practical configuration can be understood. Many examples and problems are used throughout the text to aid comprehension of important concepts. Furthermore, there is an extensive set of references in each chapter to allow pursuit of ideas in the open literature once an understanding of both theoretical concepts and practical implementation issues has been established through the text.
This volume builds upon the foundations set in Volume 1 . The seven chapters of that volume yielded linear stochastic system models driven by white Gaussian noises and the optimal Kalman filter based upon models of that form. In this volume, Chapters 8-10 extend these ideas to consider optimal smoothing in addition to filtering, compensation of linear model inadequacies while exploiting the basic insights of linear filtering (including an initial study of the important extended Kalman filter algorithm), and adaptive estimation based upon linear models in which uncertain parameters are embedded. Subsequently, Chapter 11 properly develops nonlinear stochastic system models, which then form the basis for the design of practical nonlinear estimation algorithms in Chapter 12.
This book forms a self-contained set with Volume 1, and together with Volume 3 on stochastic control, can provide a fundamental source for studying stochastic models, estimation, and control. In fact, they are an outgrowth of a three-quarter sequence of graduate courses taught at the Air Force Institute of Technology; and thus the text and problems have received thorough class testing. Students had previously taken a basic course in applied probability theory, and many had also taken a first control theory course, linear algebra, and linear system theory; but the required aspects of these disciplines have also been developed in Volume 1 . The reader is assumed to have been exposed to advanced calculus, differential equations, and some vector and matrix analysis on an engineering level. Any more advanced mathematical concepts are developed within the text itself, requiring only a willingness on the part of the reader to deal with new means of conceiving a problem and its solution. Although the mathematics becomes relatively sophisticated at times, efforts are made to motivate the need for, and to stress the underlying basis of, this sophistication.Volume 1 (/file/1744585/, /file/1774240)Deterministic system models
Probability theory and static models
Stochastic processes and linear dynamic system models
Optimal filtering with linear system models
Design and performance analysis of Kalman filters
Square root filtering
Volume 2 (/file/1774232/, /file/1774234)
Optimal smoothing
Compensation of linear model inadequacies
Parameter uncertainties and adaptive estimation
Nonlinear stochastic system models
Nonlinear estimation
Volume 3 (/file/1399064/)
Dynamic programming and stochastic control
Linear stochastic controller design and performance analysis
Nonlinear stochastic controllers