Lectures on Discrete Time Filtering

1. Front Matter

   Pages i-xv

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2. Review

   • R. S. Bucy

   Pages 1-11

3. Random Noise Generation

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   Pages 13-21

4. Historical Background

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   Pages 23-35

5. Sequential Filtering Theory

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   Pages 37-46

6. Burg Technique

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   Pages 47-54

7. Signal Processing

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   Pages 55-70

8. Classical Approach

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   Pages 71-79

9. A Priori Bounds

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   Pages 81-92

10. Asymptotic Theory

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    Pages 93-105

11. Advanced Topics

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    Pages 107-116

12. Applications

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    Pages 117-125

13. Phase Tracking

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    Pages 127-131

14. Device Synthesis

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    Pages 133-143

15. Random Fields

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    Pages 145-150

16. Back Matter

    Pages 151-156

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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.

• Signal
• electrical engineering
• geophysics
• numerical analysis
• physics

• Department of Aerospace Engineering, University of Southern California, Los Angeles, USA

  R. S. Bucy

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