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ESTIMATIONA 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). C()l'y©r (}� h1)l7 0 hy TIlA(I' C I.\·WHhust'lI.lK·Y Im/illile ,!f Tedmo/u Se'i,1l/lu llolT'illwlll(}Rc O'ls I/aJ/ Pr;lIll'hdOllll/illlIlullII/ U" I /i(,'d SW({'s of AJJJeTi("CI by Th"C %llilll InP(r"e.', .C'-\"lM iUl.lI/·I.JwIeIl,l l/st'lIs Allr iKhlnS' .I·c'NloT edI.' "rt c!f Ihis hook 11/")" hI' I"el'ro",/{","d ill clllyo.rlh "yr m(II II1'<Y'C "I"II".(I"", Irol/ic iolr/ cliIlIiedci/n/g( /nical. 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

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Estimation and Control with Quantized Measurements PDF

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ESTIMATIONA 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). C()l'y©r (}� h1)l7 0 hy TIlA(I' C I.\·WHhust'lI.lK·Y Im/illile ,!f Tedmo/u Se'i,1l/lu llolT'illwlll(}Rc O'ls I/aJ/ Pr;lIll'hdOllll/illlIlullII/ U" I /i(,'d SW({'s of AJJJeTi("CI by Th"C %llilll InP(r"e.', .C'-\"lM iUl.lI/·I.JwIeIl,l l/st'lIs Allr iKhlnS' .I·c'NloT edI.' "rt c!f Ihis hook 11/")" hI' I"el'ro",/{","d ill clllyo.rlh "yr m(II II1'<Y'C "I"II".(I"", Irol/ic iolr/ cliIlIiedci/n/g( /nical. 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

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