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Kalman Filtering with Real-Time Applications

  • Textbook
  • © 1987

Overview

Authors:
  1. Charles K. Chui

    1. Department of Mathematics and Department of Electrical Engineering, Texas A & M University, College Station, USA

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    You can also search for this author in PubMed   Google Scholar

  2. Guanrong Chen

    1. Department of Electrical and Computer Engineering, Rice University, Houston, USA

    View author publications

    You can also search for this author in PubMed   Google Scholar

Part of the book series: Springer Series in Information Sciences (SSINF, volume 17)

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Table of contents (10 chapters)

  1. Front Matter

    Pages i-xv
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  2. Preliminaries

    • Charles K. Chui, Guanrong Chen
    Pages 1-19

  3. Kalman Filter: An Elementary Approach

    • Charles K. Chui, Guanrong Chen
    Pages 20-32

  4. Orthogonal Projection and Kalman Filter

    • Charles K. Chui, Guanrong Chen
    Pages 33-49

  5. Correlated System and Measurement Noise Processes

    • Charles K. Chui, Guanrong Chen
    Pages 50-67

  6. Colored Noise

    • Charles K. Chui, Guanrong Chen
    Pages 68-77

  7. Limiting Kalman Filter

    • Charles K. Chui, Guanrong Chen
    Pages 78-98

  8. Sequential and Square-Root Algorithms

    • Charles K. Chui, Guanrong Chen
    Pages 99-110

  9. Extended Kalman Filter and System Identification

    • Charles K. Chui, Guanrong Chen
    Pages 111-124

  10. Decoupling of Filtering Equations

    • Charles K. Chui, Guanrong Chen
    Pages 125-136

  11. Notes

    • Charles K. Chui, Guanrong Chen
    Pages 137-151

  12. Back Matter

    Pages 153-191
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Keywords

About this book

Kalman filtering is an optimal state estimation process applied to a dynamic system that involves random perturbations. More precisely, the Kalman filter gives a linear, unbiased, and min­ imum error variance recursive algorithm to optimally estimate the unknown state of a dynamic system from noisy data taken at discrete real-time intervals. It has been widely used in many areas of industrial and government applications such as video and laser tracking systems, satellite navigation, ballistic missile trajectory estimation, radar, and fue control. With the recent development of high-speed computers, the Kalman filter has become more use­ ful even for very complicated real-time applications. lnspite of its importance, the mathematical theory of Kalman filtering and its implications are not well understood even among many applied mathematicians and engineers. In fact, most prac­ titioners are just told what the filtering algorithms are without knowing why they work so well. One of the main objectives of this text is to disclose this mystery by presenting a fairly thor­ ough discussion of its mathematical theory and applications to various elementary real-time problems. A very elementary derivation of the filtering equations is fust presented. By assuming that certain matrices are nonsingular, the advantage of this approach is that the optimality of the Kalman filter can be easily understood. Of course these assump­ tions can be dropped by using the more well known method of orthogonal projection usually known as the innovations approach.

Authors and Affiliations

  • Department of Mathematics and Department of Electrical Engineering, Texas A & M University, College Station, USA

    Charles K. Chui

  • Department of Electrical and Computer Engineering, Rice University, Houston, USA

    Guanrong Chen

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