Overview
- Maximizes reader insights into stochastic modeling, estimation, system identification, and time series analysis
- Reveals the concepts of stochastic state space and state space modeling to unify the idea
- Supports further exploration through a unified and logically consistent view of the subject
Part of the book series: Series in Contemporary Mathematics (SCMA, volume 1)
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About this book
This book presents a treatise on the theory and modeling of second-order stationary processes, including an exposition on selected application areas that are important in the engineering and applied sciences. The foundational issues regarding stationary processes dealt with in the beginning of the book have a long history, starting in the 1940s with the work of Kolmogorov, Wiener, Cramér and his students, in particular Wold, and have since been refined and complemented by many others. Problems concerning the filtering and modeling of stationary random signals and systems have also been addressed and studied, fostered by the advent of modern digital computers, since the fundamental work of R.E. Kalman in the early 1960s. The book offers a unified and logically consistent view of the subject based on simple ideas from Hilbert space geometry and coordinate-free thinking. In this framework, the concepts of stochastic state space and state space modeling, based on the notionof the conditional independence of past and future flows of the relevant signals, are revealed to be fundamentally unifying ideas. The book, based on over 30 years of original research, represents a valuable contribution that will inform the fields of stochastic modeling, estimation, system identification, and time series analysis for decades to come. It also provides the mathematical tools needed to grasp and analyze the structures of algorithms in stochastic systems theory.
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Keywords
Table of contents (17 chapters)
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Front Matter
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Back Matter
Reviews
“The purpose of this book is to present the mathematical background necessary for understanding the linear state-space modeling of second-order random processes and its applications to estimation and identification theory. … this monograph is an excellent reference for researchers interested in geometric theory of stochastic realization and its applications.” (Viorica M. Ungureanu, Mathematical Reviews, January, 2016)
Authors and Affiliations
Bibliographic Information
Book Title: Linear Stochastic Systems
Book Subtitle: A Geometric Approach to Modeling, Estimation and Identification
Authors: Anders Lindquist, Giorgio Picci
Series Title: Series in Contemporary Mathematics
DOI: https://doi.org/10.1007/978-3-662-45750-4
Publisher: Springer Berlin, Heidelberg
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag Berlin Heidelberg 2015
Hardcover ISBN: 978-3-662-45749-8Published: 11 May 2015
Softcover ISBN: 978-3-662-52618-7Published: 29 October 2016
eBook ISBN: 978-3-662-45750-4Published: 24 April 2015
Series ISSN: 2364-009X
Series E-ISSN: 2364-0103
Edition Number: 1
Number of Pages: XV, 781
Number of Illustrations: 37 b/w illustrations
Topics: Systems Theory, Control, Probability Theory and Stochastic Processes, Control and Systems Theory