Table Of ContentNPS-CS-09-002
NAVAL
POSTGRADUATE
SCHOOL
MONTEREY, CALIFORNIA
Center for Joint Services Electronic Warfare
Technical Report
A COMPARISON OF NONLINEAR FILTERS AND MULTI-
SENSOR FUSION FOR TRACKING BOOST-PHASE
BALLISTIC MISSILES
by
Kyungsu Kim
Phillip E. Pace
Robert G. Hutchins
James B. Michael
January 2009
Approved for public release; distribution unlimited.
Prepared for: U.S. Missile Defense Agency
1
FEDDOCS
D 208.14/2:
NPS-CS-09-002
FEDDOCS
V
«^*G*xCP D 208.14/2:
y$^?r \& NPS-CS-09-002
s>
THIS PAGE INTENTIONALLY LEFT BLANK
DUDLEYKNOXLIBRARY
NAVALPOSTGRADUATESCHOOL
MONTEREY CA
93843-5101
NAVAL POSTGRADUATE SCHOOL
Monterey, California 93943-5000
Daniel T. Oliver Leonard A. Ferrari
President Executive Vice President and
Provost
This report was funded in part by U.S. Missile Defense Agency and the Agency for
Defense Development (ADD), South Korea.
Reproduction ofall or part ofthis report is authorized.
THIS PAGE INTENTIONALLY LEFT BLANK
REPORT DOCUMENTATION PAGE
FormiAApppp,rovedOMB,Vo. 0704-0188
Public reporting burden for this collection ofinformation is estimated to average 1 hour per response, including
thetime forreviewing instruction, searchingexistingdatasources, gathering and maintainingthedataneeded, and
completing and reviewing the collection of information. Send comments regarding this burden estimate or any
other aspect of this collection of information, including suggestions for reducing this burden, to Washington
headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson Davis Highway, Suite
1204, Arlington, VA 22202-4302, and to the Office of Management and Budget, Paperwork Reduction Project
(0704-0188)Washington DC 20503
I.AGENCY USEONLY(Leaveblank) 2. REPORTDATE 3.REPORTTYPEAND DATESCOVERED
January2009 Technical report
». TITLE AND SUBTITLE: A COMPARISON OF NONLINEAR FILTERS 5.FUNDING NUMBERS
\ND MULTI-SENSOR FUSION FOR TRACKING BOOST-PHASE
MD7080101P0630
BALLISTICMISSILES
6.AUTHOR(S) Kyungsu Kim, Phillip E. Pace, RobertG. Hutchins,
JamesB. Michael
7. PERFORMINGORGANIZATION NAME(S)ANDADDRESS(ES) 8. PERFORMING
CenterforJoint Services ElectronicWarfare ORGANIZATION REPORT
NUMBER
Naval Postgraduate School
Monterey,CA 93943-5000 NPS-CS-09-002
9.SPONSORING/MONITORING AGENCY NAME(S)ANDADDRESS(ES) 10.SPONSORING/MONITORING
MISSILE DEFENSE AGENCY AGENCY REPORTNUMBER
Washington,DC
11. SUPPLEMENTARY NOTES The views expressed in this report are those ofthe author and do not reflect the official
policyorpositionofthe DepartmentofDefenseortheU.S. Government.
12a. DISTRIBUTION/AVAILABILITYSTATEMENT 12b. DISTRIBUTIONCODE
Approved forpublic release; distribution isunlimited. A
13.ABSTRACT(maximum 200words)
This reportstudiestwoaspectsoftrackingballistic missilesduringboost phase. The firstpartcompares
theperformance ofseveral nonlinear filteringalgorithms intrackingasingletarget: theextendedKalman filter
(EKF);the unscentedKalman filter(UKF);theparticle filter(PF); and,the particle filterwith UKF update(UPF).
Measurementsare range, azimuth and elevation. Intheabsenceofmeasurementerror, all algorithmsworkwell
except forthe PF, whichdoes notconverge. With measurementnoise (standard deviationsof 10 meters and 1 de-
gree)the EFK also performs poorly,whiletheUPF isthetopperformer(although it isalsothe most computation-
ally intensive).
The second partcomparestheextended information filter(E1F)withearlierworkon track scoringtoper-
formsensor/data fusion inamulti-hypothesis framework. Herewe findthatthe ELFhandilyoutperformedother
fusion algorithmsbasedon track scoringthatwetested.
14. SUBJECT TERMS Boost-phase Missile Defense, Impulse Modeling, IMPULSE, RF 15.NUMBEROF
sensors, Multiple Hypotheses Tracking, Extended Kalman Filtering, Unscented Kalman PAGES
Filtering, Particle Filtering, Unscented Particle Filtering, Multi-sensor fusion, Extended 93
Information Filter 16. PRICECODE
17.SECURITY 18.SECURITY 19.SECURITY 20. LIMITATION
CLASSIFICATIONOF CLASSIFICATIONOFTHIS CLASSIFICATIONOF OFABSTRACT
REPORT PAGE ABSTRACT
Unclassified Unclassified Unclassified Unlimited
NSN7540-01-280-5500 StandardForm298(Rev 2-89)
PrescribedbyANSIStd 239-18
THIS PAGE INTENTIONALLY LEFT BLANK
Approved for public release; distribution is unlimited.
A COMPARISON OF NONLINEAR FILTERS AND MULTI-SENSOR FUSION
FOR TRACKING BOOST-PHASE BALLISTIC MISSILES
Kyungsu Kim
Phillip E. Pace
Robert G. Hutchins
James B. Michael
Center for Joint Services Electronic Warfare and the Department ofElectrical and
Computer Engineering
at the
NAVAL POSTGRADUATE SCHOOL
January 2009
in
ABSTRACT
This reportstudies two aspects oftrackingballistic missiles duringboostphase.
Thefirstpartcompares theperformance ofseveral nonlinearfilteringalgorithms in
trackingasingle target: the extendedKalmanfilter (EKF); the unscentedKalmanfilter
(UKF); theparticlefilter (PF); and, theparticlefilterwith UKFupdate (UPF). Meas-
urements are range, azimuth andelevation. In the absence ofmeasurementerror, all al-
gorithms workwell exceptfor the PF, which does not converge. With measurement noise
(standarddeviations of10 meters and 1 degree) the EFKalsoperformspoorly, while the
UPFis the topperformer (although it is also the most computationally intensive).
The secondpart compares the extended informationfilter (EIF) with earlier work
on trackscoring toperform sensor/datafusion in a multi-hypothesisframework. Here we
find that the EIF handily outperformed otherfusion algorithms based on track scoring
that we tested.
IV
TABLE OF CONTENTS
INTRODUCTION
I. 1
II. SENSOR MODELS AND MULTIPLE HYPOTHESES TRACKING 4
A. GENERATING BALLISTIC MISSILE PROFILE 4
SENSOR MODELS
B. 4
MULTIPLE HYPOTHESES TRACKING
C. 11
1. Contacts, Targets, Scans and Associations 11
MHT
2. Implementation 14
III. NON-LINEAR FILTERS FOR TRACKING 19
A. EXTENDED KALMAN FILTER (EKF) 19
B. UNSCENTED KALMAN FILTER (UKF) 19
C. PARTICLE FILTER (PF) 24
D. UNSCENTED PARTICLE FILTER (UPF) 25
IV. SENSOR DATA FUSION 29
A. INTRODUCTION TO INFORMATION FILTER 30
B. LINEAR INFORMATION FILTER 31
C. EXTENDED INFORMATION FILTER 33
D. DISTRIBUTED AND DECENTRALIZED DATA FUSION SYSTEMS 35
1. Data Fusion Architecture 36
2. Proposed Fusion Architecture 43
V. SIMULATION RESULTS 44
A. MODELS OF TARGET MOTION AND RADAR MEASUREMENTS 46
B. COMPARISON OF PERFORMANCE OF NONLINEAR FILTERS 50
C. MULTI-SENSOR FUSION 58
VI. CONCLUSION 75
VII. FUTURE WORKS 76
.. 1
LIST OF FIGURES
Figure 1. Main functional area implemented in this study to include the
IMPULSE@ threat profile, the RF sensor models, and the multiple
hypothesis tracking algorithm 5
Figure 2. Multiple missile attack directed toward the American continent 5
Figure 3. Radar Sensor 1 SNR versus time while observing BM1 8
Figure 4. Calculation ofthe incident angle 9 9
Figure 5. Calculated the incident angle 9 10
Figure 6. Polar plot ofthe Ballistic Missile RCSG 10
Figure 7. Linear plot ofthe Ballistic Missile RCS 1
Figure 8. BSingle target tracking (in 2-D) illustrating measurement-to-target state
prediction pairing, and next-state prediction correectin 12
Figure 9. Multiple-target tracking (2-D) scenario 14
Figure 10. Schematic diagram ofthe Unscented Transformations 20
Figure 1 1 Single Level Hierarchical Sensor Tracking System 37
Figure 12. Multiple Level Hierarchical Multiple Sensor Tracking System 38
Figure 13. Blackboard Architecture in Data Fusion 39
Figure 14. Decentralized data fusion system implemented with a point-to-point
communication architecture 41
Figure 15. A decentralzed data fusion system implemented with a broadcast, fully
connected, communication architecture 42
Figure 16. GA decentralized data fusion system implented with a hybrid, broadcast
and point-to-point, communication architecture 42
Figure 17. A Proposed simple hierarchical fusion architecture 43
Figure 18. Sx near-simultaneous launches ofballistic missiles (viewed looking north) ..44
Figure 19. Same profile as in in Figure 23: Six, near simultaneous, ballistic missile
launches (looking East-to-West) and 7 RF sensors 44
Figure 20. Average distance error ofseven sensors for 1st upper stage trajectory
v range azimuth elevation '
Figure 21 Average distance error ofseven sensors for 1st lower stage trajectory
^ range azimuth elevation /*
Figure 22. Average distance error ofseven sensors for 2nd upper stage trajectory
V range azimuth elevation /
Figure 23. Average distance error ofseven sensors for 2nd lower stage trajectory
^ range azimuth elevation J
Figure 24. Average distance error ofseven sensors for st lower stage trajectory
1
=^meters,a =\\cT ^\ 55
(Grange a:inwlh c„evalHm )
Figure 25. Average distance error ofseven sensors for 1st lower stage trajectory
(vUKFv.s. UPF- amrannig,e,=\0meters,'(Tazimut,h =\°,'a,elevat,ion =1°)' 55
Figure 26. Average distance error ofseven sensors for 1st upper stage trajectory
Grange =Wmeters,(Ta:imulh =\ ,(TclcYaliim =} ) 56
VI
