Table Of ContentESTIMATIONA ND CONTROL WITH
QUANTIZEMDE ASUREMENTS
ESTIMATIONA ND CONTROL
WITH QUANTIZED
MEASUREMENTS
RENWICKE . CURRY
ReseaMrocnho graNpoh.6 0
1111TH1E M1.LT.P 1RESS
CambridMgaes,s achusetts,
andL ondoEnn,g land
I woullidkt eot hantkh e InsotfEi ktcuttreia cnadEl k ctronic
EnginefeMrp se rmistsoi roenp rmiantte rfiraoltm h feo llowairntgi cks:
R.E .C urr.y,,1\/\ e w/\ IgnriftohSrmu boptimal SCtooncthraoslt:i'c
IEEET riIS.l AlI I/liCmOal//il(ro"l , AC-1(4O,c t5o3hI3%a ·l) 5)�3 6
R.L Curr"y;\,S eparaTthieoonr efmoN ro nlinear Measurements,"
IEEET I"lIAIIII.LI (JC/OIl//ullr;ocl , AC-U, 561-5�6 4 (Oct()her 19(9)
R. E. uCunrWdr. yE .V andeVre ld".:A,n E XlcndCr"idt erfioonSr t atistical
Line'lrizaItiEoEnET, "J "(II/s. A,/I((FleIbIryIu <1al9rI7;0()"; Conlrol
R. E. CWu.rE r.Vy a,n deVre ldaen,dJ .E .P oller, "NEosntliimnaetairo n
witQhu antMiezaseudr cmcntsP:r ePdCiMcQ,tu ainvtei zatainond,
O"tC"o mpression," IhE�E/E; mTTlhmlem.o.( r Mya rc1h9 70).
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I'hOIOcol'yillgo,rh ylI i'leilI'y�c /o;rJ/d'i.''\"I'/m'"g·t,ai golli' (llld
'·,'t"-';.1'(.1"'/1"<a"l"' , lI'iliil"ll..i,o tli"lgl/l'itt·h,'Ie1I'1 "1Im/I iMsis.iloi"l l'r.
ISBN0 262030(3I7U3/ /"dnJl"'/")
LihraroyfC Ollgr("."\'.>< Imtna//l"l!!.l 17m1b-(J'1I/3"S:1) 4
ISB0N- 262-53(pap2e1r6b-6a ck)
To Sue
Katie
Smith
Susan
Contents
1.I ntroduction
1.113 ackground
1.2O bjecatndi vSecso pe 3
1.3E stim.wniitoQhnu antMieals.ucrdcm c3n ts
1.4O ptimCaoln twritoQhl u antMic. z. esldlr cme5n ts
1.5N otation 6
2.N onlineEasrt imatwiiotnQh u antizMeeda suremen7t s
2.1I ntroduction 7
2.2 Maximum-Likelihood Estimate� of Parameters 7
2.3B ayesiEasn timaotfPe asr 'll11ctcrs 9
2.4G allsPsairaanm et1e2r s
2.5 Extension Dytnoa imc L inSeyasrtF eimlst:e rPirnegd.i catnidn g
Smoothing 14
2.6C ond.i1.tM ciaonan n dCo varianocrte h Mee asuremVeenct1t 7o r
2.7 ApproNxoinmlaitneEe satri mat2i1o n
2.8S ummary 30
3. ThDriegei tCaolm munication S3y1s tems
3.1 Intro3d1u ction
3.2P ulCsoed eM odulat(iPoCnM )3 1
3.3P redicQtuiavne ti3z2a tion
3.4 PredictiveD-aCto'Im-pCaormiprseos3ns5 i on
3.5 System Simulations 37
3.6 Summ4a0r y
vii
VII! CONTENTS
4.O ptimaLli naer EstimatfoorrQs u antizSedt ationary
Process4e2s
4.1 Introduction 41
4.2A utocorrelaotfti hoQne u antiOzuctr p4u2t
4.3 A INnetwe rpreotfta htDeie osncr ibfinugn cti4o7n
4.4 OptimaFli lLteifrnosQer ua arn tizcd McaslIfl'mcnts 51
4.5J oinOtp timizatoifon the aQnuda Fnit5li6l zere r
4.6S ummar6y1
5.O ptimSatlo chasCtoinct rwoilt Qhu antized
Measureme6n2t s
5.1I ntroduct6io1n
5.2O ptimSatloc hasCtoicn tr6o3l
5.3 SoErxnael l1opfkO sp timalS tochaCsotnitcr ol with Quantizcd
Mt';P"llf()RC Il'h'nr...
5.4 A SeparationNo nTlhieneoMarcreu ms ufroetrls l7 l5c n
5.5S ummary7 8
6.S uboptimal and LineaQr uCaonnttirzoel dw ith
Measureme7n9t s
6.1I ntroduc7t9i on
6.2O pen-Loop-OFpcteidmbaaClco kn trol Xl)
6.3A NewA lgoritfhomS ru hoptimSatlo cha,tic 1i�C Orltrol
6.4 The Ikst Linear Controlkr: Discus,ion 91
6,5S Ulllmar')y7
7.S ummarya ndR ecommendatfioorFn usr thSetru dy9 8
7.1I ntroulIl,tion 9�
7.2S ummary Caonndc lus9iXo ns
7.3R C<:Olllmcndatiom fOf9 9 Further Study
AppendAi.xP ower-SeArpiperso ximattoi otnh eC on
ditiMoenaanal n dC ovariaonfac Qeu antized
GaussiVane cto1r0 1
AppendBi.xP erformaEnsctei maftoers Gtaheu ssFiiatn
Algorithm 104
AppendCi.xS ensitivoift Mieeasn S quarEes timation
Error Rweistphe tcoQt uantPiazrearm eters 109
AppendDi.x A Proao Sfe poafr atTihoeno refmo rN on�
lineMaera suremen1t1s4
AppendEi.x DerivatioOnn eo-fM eatshuer emCeonstt
Functio1n1 7
Foreword
Thiiss t hes ixtivoeltuhm ei nt heM .LRTe.s earMocnho graph
Seripeubsl ishbeydt he .I.TM. PresTsh.eo bjecoftt hiivssee r iiset os
contritbotu htepe r ofessilointael raa ntuumrbeeor f s ignifipciaecnets
ofr esealracrhg.ie nrs copte hajno urnaalr ticbluestn ormalllye ss
ambititohuafisnn ishboeodk sW.e believseu ethsh tautd dieesse ar ve
widecri rculatthiaoncna nb ea ccomplibsyinh foermda lc hannaenlds ,
we hopteh att hifso romfp ublicwaitlmilao knet hemr eadialcyc essible
tor eseaorrcgahn izatliiobnrsa.r ainedsi ,n depenndte workers.
HowardW .J ohnson
ix
Preface
Thede mando nd igiftaacli lsiutciahe ssc ommunicatsiyosnt eamnsd
data-stosryasgtee imscs o nstanitnlcyr easIinnt gh.pe a stth ep rsesurse
haveb eenr eliebvyue pdg raditnhge icra pacitpireism;a ritlhyr ough
thea dvancbeesi nmga dein d igihtaarld waraett,en tion hatsu rnetdo
thper oblme ofu sintgh esfea cilimtoireees ffi cientMlayn.y o ft hee fforts
ared escribienad g eneralw aya s" data-compr"ersesdiuondna,n"c y
reductioann,d"" b andwidth-compreasnsdim oons,to" f t hemr eloyn
theq uantizaatinodsnu bsequernetc onstruocftdi aotna .
Thimso nograpprhe setnst here sultso fs omer esearpcehr taintion g
thed istbiuntcr te lattaesdok fse fficieenstt imatainondco ntrolb ased
on quantzied measuremenItths a.s b eenp ublisihnt ehdhe o pet hat
bothr esearchaenrdes n gineewrislfi ln ds omeu seulfi deatso e xpand
anda daptto t heiorw n needsT.h e readeirs a ssumetdo h avea
familiwairthip rtoyb abitlheiotryya ndra ndom proces(seatsth el evel
ofL anninagn dB attiRna, ndoPmr ocesislAelWs o l1lCaotnitcr oorl ,
PapoulPiros,h ahilRiatlyl,dV oamr iaballelSsdt, o chaPsrotciecs ses),
anda basiucn derstaonfed sitnigma ttihoeno ry.
Discrete-ptroibmleem s arc considearneddt hee mphasisip sla ced
onc oarsqeualnyt izmeeda suremeanntsdo n l inaenadrw, h enp ertinent,
time-vasryystienmTgsh .e h earotf t hem ateriiasal new interpretation
ando utlooonk t hper obleomf g eneratnionngl ineeasrt imfarotme s
quantimzeeads uremenTthsed. e velopmoefnt th mei nimumv ariance,
orc onditimoenaanle stimiasqt uei tfeu ndamentsianlc,ie tl a yts he
groundworfko ro thetry peosf e stimates. Approximaatned m ore
xi
fREt-ACE XII
easimlpyel meinted nonlinefialrt earrese xaminiensd o med etail,
especiiancl olny junwcittthih roecneo mmunicatsiyosnt emsso,t hat
thes ubjemcatt teirsn o tl imitteodt heoarlyon Te.h e deosroi pgtni mal
lineeastria tmors isr e-examined,p earfnodr mtainhcscee oi mrp ;.J[ed
witthh aotf n onlinear filterNso.t s urprisincgolnys,i deraoftt ihoen
controolfs tochasstyisct etmsh ahta vqeu antimezaesdu remelntesa ds
toi nsigihnttso a,n dc ontsrtorla tefgioerssy, s temwsi toht hteyrp oefs
nonlinearities.
Them ajorp ortion, no bmuetan sa blyol f,t hirse seawracss hu b
mitteadsa Ph.Dt.h estoit sh Dee partmoefA netro nautaincdsA stro
nautiactts h eM assachuIsnsettittosufT t eec hnoloTghyi. s monograph
isa n extensrievvei siooftn hoer iginwaolr ka,n di ti ncorponrewa tes
analytiacnadnl u mericraels ulatnsd t hew elcomceo mmentosf m any
anonymourse vIewers.
I wistho t hankt hem embeorfsm y thesciso mmitPtreoef.e ssor
WallacEe.V andVeerl dcch,a irmParno.f eAsrstohrEu .rB rysoJrn.,,
andP rofeJsasmoerEs .P ottefro trh eiprer tinqeunets tioannsdf ruitful
suggestiMoyn sa.s sociatwiiotnth h emh as beexetnr emveallyu able,
fonro to nlayr ct heoyu tstandtinega chbeurtst ,h eaiprp roactho
tcchnipcarlo bleimsons e t haIt p articualdamrilrMyer. .C harles F.
Pricaec teads sao undbionagrf odrm a nyi deaasn dp rovicdoemmde nts
ands uggestaiobnosut th ieni tiald rafth;ihs elipsg reaatplpyr eciated.
1 shouallds loi tkoea cknowledthgeep rofitabdlies cussiwointsh
ProfessToerr renFcien eD,r .H erbeGrits ahn dD r.D onaldF raser.
Finalwloyu lIld i kteot hankm y wifSeu,s afno,tr y pitnhgie n itial
draaftn di trse visainodfn osrh epra tienacnede n couragement.
Thisr eseawracss hu pportbeydG rantN GR 22-009f-r0o1mt0 h e
NatioAnearlo nautaincdsS pacAedm inistratmioonni,t orbeyd M r.
JuleIs.K antoefrN ASA HeadquarteWrass,h ingtoDn.,C. • and sw a
carroiuetda tt heMe asuremeSnyts temLsa borat(foorrym ertlhye
ExperimenAtsatlrn oomy LaboratoartyM ) . I.T.
R.E .C urry
Ithaca, New York
June1,9 69
ESTIMATIONA ND CONTROL WITH
QUANTIZEMDE ASUREMENTS
