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. 190.

Progress in astronautics and aeronautics ; v. 190

Language:

English

Subjects (All):

Kalman filtering.

Control theory.

Physical Description:

xx, 664 pages : illustrations ; 24 cm + 1 computer optical disc (4 3/4 in.)

4 3/4 in.

Other Title:

CD-ROM title: Kalman-filtering software

Place of Publication:

Reston, Va. : American Institute of Aeronautics and Astronautics, Inc., [2000]

System Details:

System requirements: IBM PC or Macintosh computer; Absoft FORTRAN compiler version 4.3 for IBM PCs, or Absoft Power Macintosh Pro FORTRAN compiler version 6.0; MATLAB version 5.0 for IBM PCs, or MATLAB 5.2 for Macintosh; True BASIC Silver edition for IBM PCs, or True BASIC Bronze edition for Macintosh.

text file

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.

Contents:

Chapter 1. Numerical Basics 1

Simple Vector Operations 1

Simple Matrix Operations 3

Numerical Integration of Differential Equations 13

Noise and Random Variables 19

Gaussian Noise Example 23

Calculating Standard Deviation 26

White Noise 28

Simulating White Noise 30

State-Space Notation 33

Fundamental Matrix 34

Chapter 2. Method of Least Squares 41

Zeroth-Order or One-State Filter 42

First-Order or Two-State Filter 46

Second-Order or Three-State Least-Squares Filter 50

Third-Order System 56

Experiments with Zeroth-Order or One-State Filter 59

Experiments with First-Order or Two-State Filter 64

Experiments with Second-Order or Three-State Filter 71

Comparison of Filters 78

Accelerometer Testing Example 80

Chapter 3. Recursive Least-Squares Filtering 91

Making Zeroth-Order Least-Squares Filter Recursive 91

Properties of Zeroth-Order or One-State Filter 93

Properties of First-Order or Two-State Filter 103

Properties of Second-Order or Three-State Filter 112

Chapter 4. Polynomial Kalman Filters 129

General Equations 129

Derivation of Scalar Riccati Equations 131

Polynomial Kalman Filter (Zero Process Noise) 134

Comparing Zeroth-Order Recursive Least-Squares and Kalman Filters 136

Comparing First-Order Recursive Least-Squares and Kalman Filters 139

Comparing Second-Order Recursive Least-Squares and Kalman Filters 142

Comparing Different-Order Filters 148

Initial Covariance Matrix 151

Riccati Equations with Process Noise 155

Example of Kalman Filter Tracking a Falling Object 159

Revisiting Accelerometer Testing Example 171

Chapter 5. Kalman Filters in a Nonpolynomial World 183

Polynomial Kalman Filter and Sinusoidal Measurement 183

Sinusoidal Kalman Filter and Sinusoidal Measurement 194

Suspension System Example 203

Kalman Filter for Suspension System 207

Chapter 6. Continuous Polynomial Kalman Filter 219

Theoretical Equations 219

Zeroth-Order or One-State Continuous Polynomial Kalman Filter 221

First-Order or Two-State Continuous Polynomial Kalman Filter 227

Second-Order or Three-State Continuous Polynomial Kalman Filter 232

Transfer Function for Zeroth-Order Filter 238

Transfer Function for First-Order Filter 243

Transfer Function for Second-Order Filter 248

Filter Comparison 251

Chapter 7. Extended Kalman Filtering 257

Theoretical Equations 257

Drag Acting on Falling Object 259

First Attempt at Extended Kalman Filter 261

Second Attempt at Extended Kalman Filter 274

Third Attempt at Extended Kalman Filter 284

Chapter 8. Drag and Falling Object 293

Problem Setup 293

Changing Filter States 309

Why Process Noise Is Required 311

Linear Polynomial Kalman Filter 320

Chapter 9. Cannon-Launched Projectile Tracking Problem 331

Problem Statement 331

Extended Cartesian Kalman Filter 334

Polar Coordinate System 349

Extended Polar Kalman Filter 354

Using Linear Decoupled Polynomial Kalman Filters 367

Using Linear Coupled Polynomial Kalman Filters 376

Robustness Comparison of Extended and Linear Coupled Kalman Filters 385

Chapter 10. Tracking a Sine Wave 395

Extended Kalman Filter 395

Two-State Extended Kalman Filter with a Priori Information 408

Alternate Extended Kalman Filter for Sinusoidal Signal 417

Another Extended Kalman Filter for Sinusoidal Model 431

Chapter 11. Satellite Navigation 443

Problem with Perfect Range Measurements 443

Estimation Without Filtering 447

Linear Filtering of Range 453

Using Extended Kalman Filtering 455

Using Extended Kalman Filtering with One Satellite 465

Using Extended Kalman Filtering with Constant Velocity Receiver 474

Single Satellite with Constant Velocity Receiver 479

Using Extended Kalman Filtering with Variable Velocity Receiver 493

Variable Velocity Receiver and Single Satellite 505

Chapter 12. Biases 515

Influence of Bias 515

Estimating Satellite Bias with Known Receiver Location 519

Estimating Receiver Bias with Unknown Receiver Location and Two Satellites 525

Estimating Receiver Bias with Unknown Receiver Location and Three Satellites 533

Chapter 13. Linearized Kalman Filtering 549

Theoretical Equations 549

Falling Object Revisited 552

Developing a Linearized Kalman Filter 556

Cannon-Launched Projectile Revisited 569

Linearized Cartesian Kalman Filter 570

Chapter 14. Miscellaneous Topics 587

Sinusoidal Kalman Filter and Signal-to-Noise Ratio 587

When Only a Few Measurements Are Available 595

Detecting Filter Divergence in the Real World 606

Observability Example 618

Aiding 629

Appendix Fundamentals of Kalman-Filtering Software 647

Software Details 647

MATLAB 648

True BASIC 654.

Notes:

Includes bibliographical references and index.

ISBN:

1563474557

OCLC:

45665763