Fundamentals of Kalman Filtering: A Practical Approach Third Edition This page intentionally left blank Fundamentals of Kalman Filtering: A Practical Approach Third Edition Paul Zarchan MIT Lincoln Laboratory Lexington, Massachusetts Howard Musoff Charles Stark Draper Laboratory, Inc. Cambridge, Massachusetts Volume 232 PROGRESSIN ASTRONAUTICSANDAERONAUTICS Frank K. Lu, Editor-in-Chief University of Texas at Arlington Arlington, Texas Publishedbythe AmericanInstituteofAeronauticsandAstronautics,Inc. 1801AlexanderBellDrive,Reston,Virginia20191-4344 MATLAB1andSimulink1areregisteredtrademarksoftheMathWorks,Inc.,3AppleHillDrive,Natick, MA01760-2098USA;www.mathworks.com. Copyright#2009bytheAmericanInstituteofAeronauticsandAstronautics,Inc.PrintedintheUnited States of America. All rights reserved.Reproduction or translation ofany part ofthisworkbeyondthat permittedbySections107and108oftheU.S.CopyrightLawwithoutthepermissionofthecopyrightowner isunlawful.Thecodefollowingthisstatementindicatesthecopyrightowner’sconsentthatcopiesofarticles inthisvolumemaybemadeforpersonalorinternaluse,onconditionthatthecopierpaytheper-copyfee ($2.00)plustheper-pagefee($0.50)throughtheCopyrightClearanceCenter,Inc.,222RosewoodDrive, Danvers,Massachusetts01923.Thisconsentdoesnotextendtootherkindsofcopying,forwhichpermission requests should be addressed to the publisher. Users should employ the following code when reporting copyingfromthevolumetotheCopyrightClearanceCenter: 1-56347-694-0=00$2.50þ.50 Dataandinformationappearinginthisbookareforinformationalpurposesonly.AIAAisnotresponsiblefor anyinjuryordamageresultingfromuseorreliance,nordoesAIAAwarrantthatuseorreliancewillbefree fromprivatelyownedrights. ISBN978-1-60086-718-7 To Maxine, Adina, Ari, and Ronit P.Z. Wally, Sandy, Jay, Stephanie, Charlie, Scott, Cindy, Danielle, and Adam H.M. This page intentionally left blank Progress in Astronautics and Aeronautics Editor-in-Chief FrankK.Lu University of TexasatArlington Editorial Board David A.Bearden Eswar Josyula TheAerospaceCorporation U.S.AirForceResearchLaboratory JohnD.Binder Gail A.Klein viaSolutions Jet Propulsion Laboratory StevenA.Brandt Konstantinos Kontis U.S.AirForceAcademy University ofManchester Jose A.Camberos RichardC. Lind U.S.AirForceResearchLaboratory University of Florida RichardCurran NingQin Delft University of Technology University of Sheffield Sanjay Garg OlegA.Yakimenko NASAGlenn Research Center U.S.Naval PostgraduateSchool Christopher H.Jenkins MontanaState University This page intentionally left blank Foreword The third edition of this volume attests to the contribution of Paul Zarchan and the late Howard Musoff in Kalman filtering. The authors bring with them a rich perspective, having been active in its development over many years if not decades. The volume provides comprehensive coverage of the technique, and the personal involvement of the authors in its development is manifest. For this third edition, Zarchan has brought his expertise to bear on three new chapters covering unusual but practical topics. The utility of this volume is 1 enhanced by codes in Fortran, MATLAB , and Basic, truly an example of dedicationtotheprofession.ThereisnodoubtthatZarchanhasproducedanother bestseller. Frank K. Lu Editor in Chief Progress in Astronautics and Aeronautics