Holdings: Fundamentals of Kalman filtering

Fundamentals of Kalman filtering: a practical approach

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Bibliographic Details
Main Authors:	Zarchan, Paul (Author), Musoff, Howard (Author)
Format:	Book
Language:	English
Published:	Reston, Va. American Inst. of Aeronautics and Astronautics 2005
Edition:	2. ed.
Series:	Progress in astronautics and aeronautics 208
Subjects:	Aéronautique - Méthodes statistiques Commande, Théorie de la Kalman, Filtrage de Aeronautics > Statistical methods Control theory Kalman filtering Kalman-Filter
Online Access:	Inhaltsverzeichnis Klappentext
Physical Description:	XXV, 765 S. graph. Darst.
ISBN:	1563476940

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adam_text	Table of Contents Preface ............................................ xv Introduction ........................................ xvii Acknowledgments .................................... xxv Chapter 1. Numerical Basics ........................... 1 Introduction ................................ 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 Summary .................................. 38 References .................................. 38 Chapter 2. Method of Least Squares ..................... 41 Introduction ................................ 41 Overview .................................. 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 Summan .................................. 89 References ................................. 90 Chapter 3. Recursive Least-Squares Filtering ............... 91 Introduction ................................ 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 Summary .................................. 124 References ................................. 128 ix χ TABLE OF CONTENTS Chapter 4. Polynomial Kalman Filters .................... 129 Introduction ................................ 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 Summary .................................. 179 References ................................. 182 Chapter 5. Kalman Filters in a Nonpolynomial World ......... 183 Introduction ................................ 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 Summary .................................. 218 References ................................. 218 Chapter 6. Continuous Polynomial Kalman Filter ............ 219 Introduction ................................ 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 Summary .................................. 255 References ................................. 255 Chapter 7. Extended Kalman Filtering .................... 257 Introduction ................................ 257 Theoretical Equations .......................... 257 TABLE OF CONTENTS χι 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 Summary .................................. 291 References ................................. 291 Chapter 8. Drag and Falling Object ...................... 293 Introduction ................................ 293 Problem Setup .............................. 293 Changing Filter States .......................... 309 Why Process Noise Is Required .................... 311 Linear Polynomial Kalman Filter ................... 320 Summary .................................. 329 References ................................. 329 Chapter 9. Cannon-Launched Projectile Tracking Problem ..... 331 Introduction ................................ 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 Summary .................................. 393 Reference ................................. 394 Chapter 10. Tracking a Sine Wave ........................ 395 Introduction ................................ 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 Summary .................................. 441 References ................................. 441 Chapter 11. Satellite Navigation .......................... 443 Introduction ................................ 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 XII TABLE OF CONTENTS Single Satellite with Constant Velocity Receiver .......... 479 Using Extended Kalman Filtering with Variable Velocity Receiver ................................ 493 Variable Velocity Receiver and Single Satellite ........... 505 Summary .................................. 513 References ................................. 513 Chapter 12. Biases ................................... 515 Introduction ................................ 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 Summary .................................. 544 Reference ................................. 547 Chapter 13. Linearized Kalman Filtering ................... 549 Introduction ................................ 549 Theoretical Equations .......................... 549 Falling Object Revisited ......................... 552 Developing a Linearized Kalman Filter ................ 556 Cannon-Launched Projectile Revisited ................ 569 Linearized Cartesian Kalman Filter .................. 570 Summary .................................. 583 References ................................. 585 Chapter 14. Miscellaneous Topics ........................ 587 Introduction ................................ 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 Summary .................................. 642 References ................................. 646 Chapter 15. Fading-Memory Filter ........................ 647 Introduction ................................ 647 Fading-Memory-Filter Structure and Properties ........... 647 Radar Tracking Problem ........................ 662 Summary .................................. 673 References ................................. 675 Chapter 16. Assorted Techniques for Improving Kalman-Filter Performance .............................. 677 TABLE OF CONTENTS XIII Introduction ................................ 677 Increasing Data Rate ........................... 677 Adding a Second Measurement .................... 682 Batch Processing ............................. 690 Adaptive Filtering — Multiple Filters ................. 701 Adaptive Filtering — Single Filter with Variable Process Noise . . 710 Summary .................................. 720 Appendix A Fundamentals of Kalman-Filtering Software ........ 723 Software Details ............................. 723 MATLAB* ................................ 724 True BASIC ................................ 730 Reference ................................. 738 Appendix В Key Formula and Concept Summary ............. 739 Overview of Kalman-Filter Operation Principles .......... 739 Kalman-Filter Gains and the Riccati Equations ........... 739 Kalman-Filter Gain Logic ........................ 740 Matrix Inverse ............................... 740 Numerical Integration .......................... 741 Postprocessing Formulas ........................ 741 Simulating Pseudo White Noise .................... 742 Fundamental Matrix ........................... 742 Method of Least-Squares Summary .................. 742 Fading-Memory Filter Summary .................... 745 Index .............................................. 747 Supporting Materials ................................... 765 LEARN ABOUT ONE OF THE MOST IMPORTANT ALGORITHMIC TECHNIQUES EVER DEVISED · A PRACTICAL GUIDE WITH APPLICATIONS TO REAL-WORLD PROBLEMS ABOUT THE AUTHORS Paul Zarchan has a BSEE degree from the City College of New York and an MSEE degree from Columbia University. He has more than 35 years of experience in the missile guidance and control field, has worked as Principal Engineer for Raytheon, served as Senior Research Engineer with the Israeli Ministry of Defense, and as a Principal Member of the Technical Staff at the Charles Stark Draper Laboratory. He is currently a member of the technical staff at MIT Lincoln Laboratory and is working on problems related to missile defense. Howard Musoff had a BSEE degree from the City College of New York, an MSEE degree from Northeastern University and an Sc.D. degree from MIT. He was a Principal Member of the Technical Staff at the Charles Stark Draper Laboratory, where he had been employed for more than 40 years where he designed Kalman filters for applications in the Held of inerţial navigation. Dr. Musoff was also a co-holder of two patents in that field. He died suddenly in April 2004. ABOUT THE BOOK This text is a practical guide to building Kalman fil¬ ters 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 inter¬ ested 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 formu¬ lated 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 fading- memory filter can yield similar performance to a Kalman filter at far less computational cost. A second new chapter presents techniques for improving Kalman filter performance. Included is a practical method for preprocessing measure¬ ment data when there are too many measure¬ ments for the filter to utilize in a given amount of time. The chapter also contains practical 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. American Institute of Aeronautics and Astronautics 1801 Alexander Bell Drive. Suite 500 Reston, VA 20191—4344 USA Web site: www.aiaa.org ISBN 1563476940
adam_txt	Table of Contents Preface . xv Introduction . xvii Acknowledgments . xxv Chapter 1. Numerical Basics . 1 Introduction . 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 Summary . 38 References . 38 Chapter 2. Method of Least Squares . 41 Introduction . 41 Overview . 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 Summan' . 89 References . 90 Chapter 3. Recursive Least-Squares Filtering . 91 Introduction . 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 Summary . 124 References . 128 ix χ TABLE OF CONTENTS Chapter 4. Polynomial Kalman Filters . 129 Introduction . 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 Summary . 179 References . 182 Chapter 5. Kalman Filters in a Nonpolynomial World . 183 Introduction . 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 Summary . 218 References . 218 Chapter 6. Continuous Polynomial Kalman Filter . 219 Introduction . 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 Summary . 255 References . 255 Chapter 7. Extended Kalman Filtering . 257 Introduction . 257 Theoretical Equations . 257 TABLE OF CONTENTS χι 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 Summary . 291 References . 291 Chapter 8. Drag and Falling Object . 293 Introduction . 293 Problem Setup . 293 Changing Filter States . 309 Why Process Noise Is Required . 311 Linear Polynomial Kalman Filter . 320 Summary . 329 References . 329 Chapter 9. Cannon-Launched Projectile Tracking Problem . 331 Introduction . 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 Summary . 393 Reference . 394 Chapter 10. Tracking a Sine Wave . 395 Introduction . 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 Summary . 441 References . 441 Chapter 11. Satellite Navigation . 443 Introduction . 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 XII TABLE OF CONTENTS Single Satellite with Constant Velocity Receiver . 479 Using Extended Kalman Filtering with Variable Velocity Receiver . 493 Variable Velocity Receiver and Single Satellite . 505 Summary . 513 References . 513 Chapter 12. Biases . 515 Introduction . 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 Summary . 544 Reference . 547 Chapter 13. Linearized Kalman Filtering . 549 Introduction . 549 Theoretical Equations . 549 Falling Object Revisited . 552 Developing a Linearized Kalman Filter . 556 Cannon-Launched Projectile Revisited . 569 Linearized Cartesian Kalman Filter . 570 Summary . 583 References . 585 Chapter 14. Miscellaneous Topics . 587 Introduction . 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 Summary . 642 References . 646 Chapter 15. Fading-Memory Filter . 647 Introduction . 647 Fading-Memory-Filter Structure and Properties . 647 Radar Tracking Problem . 662 Summary . 673 References . 675 Chapter 16. Assorted Techniques for Improving Kalman-Filter Performance . 677 TABLE OF CONTENTS XIII Introduction . 677 Increasing Data Rate . 677 Adding a Second Measurement . 682 Batch Processing . 690 Adaptive Filtering — Multiple Filters . 701 Adaptive Filtering — Single Filter with Variable Process Noise . . 710 Summary . 720 Appendix A Fundamentals of Kalman-Filtering Software . 723 Software Details . 723 MATLAB* . 724 True BASIC . 730 Reference . 738 Appendix В Key Formula and Concept Summary . 739 Overview of Kalman-Filter Operation Principles . 739 Kalman-Filter Gains and the Riccati Equations . 739 Kalman-Filter Gain Logic . 740 Matrix Inverse . 740 Numerical Integration . 741 Postprocessing Formulas . 741 Simulating Pseudo White Noise . 742 Fundamental Matrix . 742 Method of Least-Squares Summary . 742 Fading-Memory Filter Summary . 745 Index . 747 Supporting Materials . 765 LEARN ABOUT ONE OF THE MOST IMPORTANT ALGORITHMIC TECHNIQUES EVER DEVISED · A PRACTICAL GUIDE WITH APPLICATIONS TO REAL-WORLD PROBLEMS ABOUT THE AUTHORS Paul Zarchan has a BSEE degree from the City College of New York and an MSEE degree from Columbia University. He has more than 35 years of experience in the missile guidance and control field, has worked as Principal Engineer for Raytheon, served as Senior Research Engineer with the Israeli Ministry of Defense, and as a Principal Member of the Technical Staff at the Charles Stark Draper Laboratory. He is currently a member of the technical staff at MIT Lincoln Laboratory and is working on problems related to missile defense. Howard Musoff had a BSEE degree from the City College of New York, an MSEE degree from Northeastern University and an Sc.D. degree from MIT. He was a Principal Member of the Technical Staff at the Charles Stark Draper Laboratory, where he had been employed for more than 40 years where he designed Kalman filters for applications in the Held of inerţial navigation. Dr. Musoff was also a co-holder of two patents in that field. He died suddenly in April 2004. ABOUT THE BOOK This text is a practical guide to building Kalman fil¬ ters 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 inter¬ ested 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 formu¬ lated 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 fading- memory filter can yield similar performance to a Kalman filter at far less computational cost. A second new chapter presents techniques for improving Kalman filter performance. Included is a practical method for preprocessing measure¬ ment data when there are too many measure¬ ments for the filter to utilize in a given amount of time. The chapter also contains practical 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. American Institute of Aeronautics and Astronautics 1801 Alexander Bell Drive. Suite 500 Reston, VA 20191—4344 USA Web site: www.aiaa.org ISBN 1563476940
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id	DE-604.BV023167135
illustrated	Illustrated
index_date	2024-07-02T19:56:31Z
indexdate	2024-07-09T21:12:05Z
institution	BVB
isbn	1563476940
language	English
oai_aleph_id	oai:aleph.bib-bvb.de:BVB01-016349420
oclc_num	60334628
open_access_boolean
owner	DE-92 DE-703 DE-83
owner_facet	DE-92 DE-703 DE-83
physical	XXV, 765 S. graph. Darst.
publishDate	2005
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publisher	American Inst. of Aeronautics and Astronautics
record_format	marc
series	Progress in astronautics and aeronautics
series2	Progress in astronautics and aeronautics
spelling	Zarchan, Paul Verfasser aut Fundamentals of Kalman filtering a practical approach 2. ed. Reston, Va. American Inst. of Aeronautics and Astronautics 2005 XXV, 765 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Progress in astronautics and aeronautics 208 Aéronautique - Méthodes statistiques Commande, Théorie de la Kalman, Filtrage de Aeronautics Statistical methods Control theory Kalman filtering Kalman-Filter (DE-588)4130759-8 gnd rswk-swf Kalman-Filter (DE-588)4130759-8 s DE-604 Musoff, Howard Verfasser aut Progress in astronautics and aeronautics 208 (DE-604)BV001890233 208 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016349420&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016349420&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext
spellingShingle	Zarchan, Paul Musoff, Howard Fundamentals of Kalman filtering a practical approach Progress in astronautics and aeronautics Aéronautique - Méthodes statistiques Commande, Théorie de la Kalman, Filtrage de Aeronautics Statistical methods Control theory Kalman filtering Kalman-Filter (DE-588)4130759-8 gnd
subject_GND	(DE-588)4130759-8
title	Fundamentals of Kalman filtering a practical approach
title_auth	Fundamentals of Kalman filtering a practical approach
title_exact_search	Fundamentals of Kalman filtering a practical approach
title_exact_search_txtP	Fundamentals of Kalman filtering a practical approach
title_full	Fundamentals of Kalman filtering a practical approach
title_fullStr	Fundamentals of Kalman filtering a practical approach
title_full_unstemmed	Fundamentals of Kalman filtering a practical approach
title_short	Fundamentals of Kalman filtering
title_sort	fundamentals of kalman filtering a practical approach
title_sub	a practical approach
topic	Aéronautique - Méthodes statistiques Commande, Théorie de la Kalman, Filtrage de Aeronautics Statistical methods Control theory Kalman filtering Kalman-Filter (DE-588)4130759-8 gnd
topic_facet	Aéronautique - Méthodes statistiques Commande, Théorie de la Kalman, Filtrage de Aeronautics Statistical methods Control theory Kalman filtering Kalman-Filter
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016349420&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016349420&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA
volume_link	(DE-604)BV001890233
work_keys_str_mv	AT zarchanpaul fundamentalsofkalmanfilteringapracticalapproach AT musoffhoward fundamentalsofkalmanfilteringapracticalapproach

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