Fundamentals of Kalman filtering : a practical approach / Paul Zarchan and Howard Musoff.

Format:

Book

Author/Creator:

Zarchan, Paul.

Contributor:

Musoff, Howard.

Series:

Progress in astronautics and aeronautics ; v. 208.

Progress in astronautics and aeronautics ; v. 208

Language:

English

Subjects (All):

Kalman filtering.

Control theory.

Aeronautics--Statistical methods.

Aeronautics.

Physical Description:

1 online resource (790 p.)

Edition:

2nd ed.

Place of Publication:

Reston, Va. : American Institute of Aeronautics and Astronautics, Inc., c2005.

Language Note:

English

Summary:

This text is a practical guide to building Kalman filters and shows how the filtering equations can be applied to real-life problems. Numerous examples are presented in detail, showing the many ways in which Kalman filters can be designed. Computer code written in FORTRAN, MATLAB, and True BASIC accompanies all of the examples so that the interested reader can verify concepts and explore issues beyond the scope of the text. Sometimes mistakes are introduced intentionally to the initial filter designs to show the reader what happens when the filter is not working properly. The text spends a great deal of time setting up a problem before the Kalman filter is actually formulated to give the reader an intuitive feel for the problem being addressed. Real problems are seldom presented in the form of differential equations and they usually do not have unique solutions. Therefore, the authors illustrate several different filtering approaches for tackling a problem. Readers will gain experience in software and performance tradeoffs for determining the best filtering approach for the application at hand. The second edition has two new chapters and an additional appendix. In the first new chapter, a recursive digital filter known as the fading memory filter is introduced and it is shown that for some radar tracking applications the facling memory filter can yield similar performance to a Kalman filter at for less computational cost. A second new chapter presents techniques for improving Kalman filter performance. Included is a practical method for preprocessing measurement data when there are too many measurements for the filter to utilize in a given amount of time. The chapter also containspractical methods for making the Kalman filter adaptive. A new appendix has been added which serves as a central location and summary for the text's most important concepts and formulas.

Contents:

""Cover""; ""Title""; ""Copyright""; ""Table of Contents""; ""Preface""; ""Introduction""; ""Acknowledgments""; ""Chapter 1. Numerical Basics""; ""Introduction""; ""Simple Vector Operations""; ""Simple Matrix Operations""; ""Numerical Integration of Differential Equations""; ""Noise and Random Variables""; ""Gaussian Noise Example""; ""Calculating Standard Deviation""; ""White Noise""; ""Simulating White Noise""; ""State-Space Notation""; ""Fundamental Matrix""; ""Summary""; ""References""; ""Chapter 2. Method of Least Squares""; ""Introduction""; ""Overview""

""Zeroth-Order or One-State Filter""""First-Order or Two-State Filter""; ""Second-Order or Three-State Least-Squares Filter""; ""Third-Order System""; ""Experiments with Zeroth-Order or One-State Filter""; ""Experiments with First-Order or Two-State Filter""; ""Experiments with Second-Order or Three-State Filter""; ""Comparison of Filters""; ""Accelerometer Testing Example""; ""Summary""; ""References""; ""Chapter 3. Recursive Least-Squares Filtering""; ""Introduction""; ""Making Zeroth-Order Least-Squares Filter Recursive""; ""Properties of Zeroth-Order or One-State Filter""

""Properties of First-Order or Two-State Filter""""Properties of Second-Order or Three-State Filter""; ""Summary""; ""References""; ""Chapter 4. Polynomial Kalman Filters""; ""Introduction""; ""General Equations""; ""Derivation of Scalar Riccati Equations""; ""Polynomial Kalman Filter (Zero Process Noise)""; ""Comparing Zeroth-Order Recursive Least-Squares and Kalman Filters""; ""Comparing First-Order Recursive Least-Squares and Kalman Filters""; ""Comparing Second-Order Recursive Least-Squares and Kalman Filters""; ""Comparing Different-Order Filters""; ""Initial Covariance Matrix""

""Riccati Equations with Process Noise""""Example of Kalman Filter Tracking a Falling Object""; ""Revisiting Accelerometer Testing Example""; ""Summary""; ""References""; ""Chapter 5. Kalman Filters in a Nonpolynomial World""; ""Introduction""; ""Polynomial Kalman Filter and Sinusoidal Measurement""; ""Sinusoidal Kalman Filter and Sinusoidal Measurement""; ""Suspension System Example""; ""Kalman Filter for Suspension System""; ""Summary""; ""References""; ""Chapter 6. Continuous Polynomial Kalman Filter""; ""Introduction""; ""Theoretical Equations""

""Zeroth-Order or One-State Continuous Polynomial Kalman Filter""""First-Order or Two-State Continuous Polynomial Kalman Filter""; ""Second-Order or Three-State Continuous Polynomial Kalman Filter""; ""Transfer Function for Zeroth-Order Filter""; ""Transfer Function for First-Order Filter""; ""Transfer Function for Second-Order Filter""; ""Filter Comparison""; ""Summary""; ""References""; ""Chapter 7. Extended Kalman Filtering""; ""Introduction""; ""Theoretical Equations""; ""Drag Acting on Falling Object""; ""First Attempt at Extended Kalman Filters""

""Second Attempt at Extended Kalman Filter""

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

ISBN:

1-60086-677-8

1-60086-458-9

OCLC:

922979103