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LINEAR AND NONLINEAR FILTERING FOR SCIENTISTS AND ENGINEERS
by N U Ahmed (University of Ottawa)
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.
Contents:
- Introduction to Stochastic Processes
- Stochastic
Differential Equations
- Kalman Filtering for Linear Systems Driven by Wiener Process I
- Kalman Filtering for Linear Systems Driven by Wiener 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
Readership: Researchers in analysis & differential equations, applied
mathematics, probability & statistics, numerical & computational methods, statistical physics, engineering, chaos/dynamical systems and economics/finance.
"... many new results, especially on nonlinear filtering problems and their numerical techniques, are included in book form for the first time ... it will serve as a useful reference book on the recent progress in this field. The book can be used for teaching graduate courses to students in mathematics, probability, statistics, and engineering. And finally, doctoral students and young researchers in the area of filtering theory and its applications can find inspiring ideas and techniques."
| Journal of Applied Mathematics and Stochastic Analysis |
| 272pp |
Pub. date: Jan 1999 |
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