Iterative system modeling using multigrid techniques.

144 Pages·1.4 MB·en_US

by  Richter, Dean A.;Tummala, Murali.

I4AV/ 3 IADUATE SCHOOt
MONTtflEY. CALIFORNIA93943-5002

NAVAL POSTGRADUATE SCHOOL
Monterey, California
THESIS
ITERATIVE SYSTEM MODELING
USING
MULTIGRID TECHNIQUES
by
Dean A. Richter
December, 1991
ThesisAdvisor: Murali Tummala
Approved for public release; distribution is unlimited
T258484

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11 TITLE (IncludeSecurityClassification)
ITERATIVESYSTEMMODELINGUSINGMULTIGRIDMETHODS
12.PERSONALAUTHOR(S) RICHTER,DeanAnthony
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Master'sThesis From To 1991 December 135
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17 COSATICODES 18 SUBJECTTERMS(continueonreverseifnecessaryandidentifybyblocknumber)
FIELD GROUP SUBGROUP finiteimpulseresponsemodeling;autoregressivemodeling;infiniteimpulseresponse
modeling;2-1)autoregressivemodeling;spectralestimation;iterativemethods;Toeplitz;
multigridtechniques
19 ABSTRACT(continueonreverseifnecessaryandidentifybyblocknumber)
Oneandtwo-dimensionalsystemidentificationandmodelingalgorithmsutilizingmultigridtechniquesarepresented. Finiteimpulseresponse
(FIR),autoregressive(AR),infiniteimpulseresponse(11Ri,and2Dblockmatrixiterativesystemmodelingalgorithmsareenhancedandmade
moreefficientusingthemultigridmethods. Theconvergenceperformanceofthesealgorithmsisimprovedwiththemultigridtechniques. The
reductioninthenumberofiterationsrequiredtoconvergetoasolutionisrealizedbyforcingthelowfrequencyerrorcomponentstoappeartobeat
ahigherfrequencybytransferringtoacoarsersamplingperiod. PerformancecomparisonsarepresentedforFIR,AR,IIR,and2-Dblockmatrix
modelingsimulationswithandwithoutthemultigridtechniquesemployed.
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Iterative System Modeling
Using
Multigrid Techniques
by
Dean A. Richter
Lieutenant, United States Navy
B.S.M.E., University ofMissouri - Rolla 1983
,
Submitted in partial fulfillment
ofthe requirements for the degree of
MASTER OF SCIENCE IN ELECTRICAL ENGINEERING
from the
NAVALPOSTGRADUATE SCHOOL
December 1991
ABSTRACT
One and two-dimensional system identification and modeling algorithms utilizing
multigrid techniques are presented. Finite impulse response (FIR), autoregressive (AR),
infinite impulse response (IIR), and 2-D block matrix iterative system modeling
algorithms are enhanced and made more efficient using the multigrid methods. The
convergence performance ofthese algorithms is improved with the multigrid techniques.
The reduction in the number of iterations required to converge to a solution is realized
by forcing the low frequency error components to appear to be at a higher frequency by
transferring to a coarser sampling period. Performance comparisons are presented for
FIR, AR, IIR, and 2-D block matrix modeling simulations with and without the multigrid
techniques employed.
in
MO'O
/
6,1
TABLE OF CONTENTS
INTRODUCTION
I. 1
A. PARAMETER ESTIMATION METHODS 1
B. THESIS OUTLINE 2
ELEMENTS OF THE MULTIGRID TECHNIQUE
II. 3
A. THE THEORY OF MULTIGRID 3
1. Toeplitz Approximation Algorithm 7
MULTIGRID V CYCLE
B. 8
FULL MULTIGRID V CYCLE
C. 10
D. PERFORMANCE COMPARISONS 12
SYSTEM MODELING
III. 16
A. THE FINITE IMPULSE RESPONSE (FIR) MODEL 16
B. THE AUTOREGRESSIVE (AR) MODEL 18
C. THE INFINITE IMPULSE RESPONSE (IIR) MODEL 22
D. THE 2-D AUTOREGRESSIVE (AR) MODEL 23
1. Quarter-Plane Support 24
2. 2-D AR Spectral Estimation 25
IV