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Lectures on Discrete Time Filtering

  • R. S. Bucy

Part of the Signal Processing and Digital Filtering book series (SIGNAL PROCESS)

Table of contents

  1. Front Matter
    Pages i-xv
  2. R. S. Bucy
    Pages 1-11
  3. R. S. Bucy
    Pages 13-21
  4. R. S. Bucy
    Pages 23-35
  5. R. S. Bucy
    Pages 37-46
  6. R. S. Bucy
    Pages 47-54
  7. R. S. Bucy
    Pages 55-70
  8. R. S. Bucy
    Pages 71-79
  9. R. S. Bucy
    Pages 81-92
  10. R. S. Bucy
    Pages 93-105
  11. R. S. Bucy
    Pages 107-116
  12. R. S. Bucy
    Pages 117-125
  13. R. S. Bucy
    Pages 127-131
  14. R. S. Bucy
    Pages 133-143
  15. R. S. Bucy
    Pages 145-150
  16. Back Matter
    Pages 151-156

About this book

Introduction

The theory of linear discrete time filtering started with a paper by Kol­ mogorov in 1941. He addressed the problem for stationary random se­ quences and introduced the idea of the innovations process, which is a useful tool for the more general problems considered here. The reader may object and note that Gauss discovered least squares much earlier; however, I want to distinguish between the problem of parameter estimation, the Gauss problem, and that of Kolmogorov estimation of a process. This sep­ aration is of more than academic interest as the least squares problem leads to the normal equations, which are numerically ill conditioned, while the process estimation problem in the linear case with appropriate assumptions leads to uniformly asymptotically stable equations for the estimator and the gain. The conditions relate to controlability and observability and will be detailed in this volume. In the present volume, we present a series of lectures on linear and nonlinear sequential filtering theory. The theory is due to Kalman for the linear colored observation noise problem; in the case of white observation noise it is the analog of the continuous-time Kalman-Bucy theory. The discrete time filtering theory requires only modest mathematical tools in counterpoint to the continuous time theory and is aimed at a senior-level undergraduate course. The present book, organized by lectures, is actually based on a course that meets once a week for three hours, with each meeting constituting a lecture.

Keywords

Signal electrical engineering geophysics numerical analysis physics

Authors and affiliations

  • R. S. Bucy
    • 1
  1. 1.Department of Aerospace EngineeringUniversity of Southern CaliforniaLos AngelesUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4613-8392-5
  • Copyright Information Springer-Verlag New York 1994
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4613-8394-9
  • Online ISBN 978-1-4613-8392-5
  • Series Print ISSN 1431-7893
  • Buy this book on publisher's site