Linear and Nonlinear Filtering for Scientists and Engineers (Applied Mathematics)

World Scientific Series in Applicable Analysis (WSSIAA) aims at reporting new developments of high mathematical standard and current interest. Each volume in the series shall be devoted to the mathematical analysis that has been applied or potentially applicable to the solutions of scientific, engineering and social problems. This volume contains 30 research articles on the theory of optimization and its applications by the leading scientists in the field. It is hoped that the material in the present volume will open new vistas in research Introduction to stochastic processes; stochastic differential equations; Kalman filtering for linear systems driven by Weiner process I; Kalman filtering for linear systems driven by Weiner process II; discrete Kalman filtering; linear filtering with correlated noise I; linear filtering with correlated noise II; linear filtering with correlated noise III; linear filtering of jump processes; linear filtering with constraints; filtering for linear systems driven by second order random processes; extended Kalman filtering I,II, and III; nonlinear filtering; numerical techniques for nonlinear filtering; partially observed control; system identification The book combines both rigor and intuition to derive the most from 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 The 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. Combines both rigour and intuition to derive most of the classical results of linear and nonlinear filtering and beyond. The text provides a foundation for theoretical understanding of the subject based on the theory of stochastic differential equations. In all fields of studies including physical and engineering sciences and also economic and social sciences, there are uncertainties which cannot be explained entirely on the basis of exact laws of physics. N.u. Ahmed. Includes Bibliographical References (p. 247-253) And Index.