
projection filterukal

nonleeniyar stettu-space sistangalkkulla filtering prashnangalkk ekadesha pariharam kandethaan upayogikkunna yaadruchika vishakalanatheyum vivara jyamithiyeyum adisthaanamaakkiyulla algorithangalude oru koottamaanu projection filterukal.
signalinte bhagika shabda nireekshanangalil ninnu kramarahithamaya chalanathmaka samvidaanathinte nireekshikkaatha signal kanakkaakkunnath filtering prashnatthil ulppedunnu. shabda-thadassa nireekshanangalude charithratthil vyavasthaapithamaaya signalinte probability vitharanam kanakkaakkuka ennathaanu lakshyam. nireekshanangalude charithram kanakkiledukkumbol signalinte ellah sthithivivarakkanakukalum kanakkukoottalukalkk eee vitharanam anuvadikkunnu. eee vitharanathinu saandrathayundengil, saandrata kushner-stratonovichu samavaakyam allengil sakaay samavaakyam ennu vilikkunna (spdes) thripthippeduthunnu. 
nonleeniyar filter saandrata ananthamaaya dimensional function speysilaanu vikasikkunnathennu ariyappedunnu.
oraalkk probability saandrathayude oru parimitha dimensional kudumbam thiranjedukkaam, udaaharanathinu gausiyan saandrata, gausiyanmaarude mishrithangal, allengil exponential kudumbangal, athil ananthamaaya dimensional filter saandrata ekadeshamaayi kanakkakkaam. thiranjeduttha parimithamaaya dimensional kudumbatthilekku opttimal filterinte ananthamaaya dimensional ezz. pii. dii. yeei project cheiyunnathinu saandrathayude thiranjeduttha edangalil oru jyaamitheeya ghadana upayogikkuka ennathaanu projection filterinte adisthaana ashayam, poornna filter parinaamatthe ekadeshamaayi kanakkaakkunna parimithamaaya dimensional kudumbatthile saandrathayude paaraameettarin oru parimitha dimensional stokkaastik deferential samavaakyam (ezz. dii. iii) neduka. ithu cheiyunnathinu, thiranjeduttha parimitha dimensional kudumbatthil vivara jyaamithiyilennapole oru manifold ghadana sajjeekarichirikkunnu. 
cubic sensor prashnathinu opttimal filterinethire projection filter pareekshichu. extended kalman filter polulla staanderd algorithangal upayogichu ekadeshamaayi kanakkakkaan prayaasamulla opttimal filterinte bimodal saandrata phalapradamaayi tracuchaian projection filterinu kazhiyum.
projection filterukal inn-line esttimeshanu anuyojyamaanu, kaaranam avaa krithyasamayathu kaaryakshamamaayi nadappilakkaanum pravarthippikkaanum vegamullathinaal kaaryakshamamaayi nadappilakkaan kazhiyunna paaraameettarin oru parimithamaaya alavilulla sde nalkunnu. 
projection filterukalum vazhakkamullathaan, kaaranam avaa sambannamaaya ekadesha kudumbangal thiranjedutthu ekadesharekhayude krithyatha nannayi tyoon cheyyaan anuvadikkunnu, koodaathe chila exponential kudumbangal projection filtering algorithathil thiruthal ghattam krithyamaayi cheiyunnu. chila formulationukal huristic adisthaanamaakkiyulla anumaanikkappedunna saandrata filterukalumaayo gallerkin reethikalumaayo poruthappedunnu. sharashari square minimisation polulla krithyamaaya maanadandangalkkanusarichu, sped kofifishyantukalude maathram opttimal ekadesha kanakkinappuram, poornnamaaya ananthamaaya alavilulla filterine opttimal reethiyil projection filterukalkku ekadeshamaayi kanakkakkaanum kazhiyum. naavigeshan, ooshyan dynamics, kwaandam optiks, kwaandam sisttangal, fiber vyaasathinte kanakk, araajakathva samaya shreniyude kanakk, chenchu-pooyint dittakshan, mattu mekhalakal ennivayulppede vividha mekhalakalil projection filterukal vijayakaramaayi prayogichittundu.
charithravum vikasanavum.
projection filter" enna padam aadyamaayi 1987 ll bernard haanson aanu upayogichathu, anubandha sidhaanthavum samkhyaaparamaaya udaaharanangalum piechu samayat poornnamaayum vikasippikkukayum vipuleekarikkukayum karshanamaakkukayum cheythu.dii. bernard haansan, francois legland ennivarumaayi sahakarichu damiano brigoyude pravartthanam.
thiranjeduttha exponential kudumbatthil opttimal filter ananthamaaya-dimensional ezz. pii. dii. iii project cheyyaan upayogichirunna hellinger doorathilum fisher information metrikkilum projection filterukal kaikaaryam cheiyunnavayaanu eee kruthikal. filtering algorithathinte pravachana ghattam krithyamaayi cheiyunnathinu exponential kudumbam thiranjedukkaam. 
mattoru tharatthilulla projection filterukal, oru badal projection metrik adisthaanamaakki, direct formula _ 1 metrik, amstrong, brigo (2016) ennivayil avatharippichu. eee metrik upayogichu, misritham vitharanam cheiyunna kudumbangalile projection filterukal gallerkin reethikale adisthaanamaakkiyulla filterukalumaayi poruthappedunnu. pinneedu, amstrong, brigo, rossie feroochi (2021) enniva ananthamaaya alavilulla opttimal filter ekadeshamaayi kanakkaakkunnathil nirddishta optimaalitti maanadandangal thripthippeduthunna opttimal projection filterukal nedunnu. vaasthavathil, stratonovichu adisthaanamaakkiyulla projection filterukal thiranjeduttha manifoldil speddy verthirikkunna gunakangalude ekadesha kanakk opttimais cheythu, pakshe mothatthil speddy pariharam allah. opttimal projection filterukal avatharippichaanu ithu kaikaaryam cheythath. filter samavaakyathinte stratonovichu calculus pathipp avalambikkunathinupakaram ittoo calculusumaayi nerittu pravartthikkuka ennathaanu ivideyulla puthuma. ithu jettu bundle adisthaanamaakkiyulla maanifoldukalile ittoo stokkaastik deferential samavaakyangalude jyaamithiyekkurichulla gaveshanathe adisthaanamaakkiyullathaanu, maanifoldukalile ittoo stokkaastik deferential samavaakyangalude 2-jettu vyaakhyaanam ennu vilikkappedunnu.
projection filter derivation.
ivide vyathyastha projection filterukalude derivation varachirikkunnu.
stratonovichu adisthaanamaakkiyulla projection filterukal.
haanson varachathum brigo, haanson, legland enniva poornnamaayum vikasippicheduthathumaa hellinger/fisher metrik adisthaana filterinteyum, amstrong, brigo (2016) ennivar nerittulla ell2 metrik adisthaanamaakkiyulla pilkkala projection filterinteyum oru vyathiyaanamaanith.
nireekshikkaatha kramarahithamaya signal formula _ 2 aitto stokkaastik deferential samavaakyathinte maathrkayilaanennu anumaanikkappedunnu
ivide "f" umm formula 4 umm formula 5 moolyamullathum formula 6 oru brouniyan chalanavumaan. referenceukalil nalkiyirikkunna vishadaamshangalkkoppam phalangal nilanirthunnathinu aavashyamaaya ellah sthiratha vyavasthakaludeyum saadhuta anumanikkum. anubandha shabda nireekshana prakriya formula _ 7 maathrkayaakkunnu 
formula 9 formula 10 moolyamullathum formula 11 formula 6 ll ninnu swathanthramaaya oru brouniyan chalanavumaan. mukalil soochippichathupole, poornna filter vyavasthaapithamaanu.
formula _ 14-nuu munkootty nalkia formula _ 13-nte vitharanam
eee vitharanathinu anoupachaarikamaayi vivaricha saandrata undengil, formula _ 15-nte time formula _ 16 vareyulla charithram 
shabdabharithamaaya nireekshanangalude formula 15 muthal time formula 16 vareyulla charithram srishtikkunna sigma feeldaanu formula 18, anuyojyamaaya saankethika saahacharyangalil saandrata formula 21 kushner-stratonovichu spde-neey thripthippeduthunnu
ivide formula _ 23 pratheekshayaan 
formula _ 24 
forwade defusion oopparettar formula _ 25 aanu 
ivide formula _ 27 umm formula _ 28 umm transpositione soochippikkunnu.
projection filterukalude aadya pathipp labhikkunnathin, oraal _ 21 spde enna soothravaakyam stratonovichu roopathil idanam. oraalkk labikkum 
cheyin niyamathiloode, formula _ 31-nulla spde udan thanne labikkum. 
notteshan cheruthakkaan oraalkk eee avasaanathe spde ingane mattiyezhuthaam
soothravaakyam _ 32
oopparettarmaarude formula _ 33 umm formula _ 34 umm ingane nirvachikkappedunnu
square root pathipp 
soothravaakyam _ 37
ananthamaaya dimensional function speysukalil parinamikkunna pariharangalulla stratonovichu spdekalaanu iva. udaaharanathinu formula _ 21 formula _ 1 (direct metrik formula _ 40) ll parinamichekkaam. 
allengil formula _ 42 formula _ 1 (hellinger metrik formula _ 44) ll parinamichekkaam.
ivide formula _ 46 ennathu hilbert space formula _ 1-nte maanadandamaanu.
enthaayaalum, formula _ 21 (allengil formula _ 42) saandrathayude oru parimitha dimensional kudumbatthilum parinamikkilla. 
projection filter ashayam oru parimitha dimensional density formula 53 (allengil formula 54) vazhi formula 51 (allengil formula 52) kanakkakkunnu.
filter ezz. pii. dii. iii. stratonovichu roopathilaanenna vastutha inipparayunnava anuvadikkunnu. stratonovichu spdes shringhala niyamam thripthippeduthumbol, soothravaakyam _ 55 umm soothravaakyam _ 56 umm vekttar feeldukalaayi pravartthikkunnu. athinaal, eee samavaakyathinte savisheshatha oru soothravaakyam _ 57 vekttar feeld formula _ 55 umm oru soothravaakyam _ 59 vekttar feeld formula _ 56 umm aanu. projection filterinte eee pathippin rund vekttar feeldukalum vevvere kaikaaryam cheiyunnathil oraal samthrupthanaanu. 
formula 63 (direct metrik) allengil avayude square roottukalil (hellinger metrik) saandrathayude taanjant spacil oraalkk formula 55 umm formula 56 umm project cheyyaam. nerittulla metrik cases varumanam 
ivide formula _ 65 ennathu manifold formula _ 63-nte pooyint formula _ 66-leeii taanjant space projakshanaanu, koodaathe formula _ 68 polulla oru vektaril prayogikkumbol, formula _ 68-nte oro gadakangalum project cheythukondu ghadakam thirichulla pravartthanamaanennu anumaanikkappedunnu. eee sparshanasthaanathinte adisthaanam 
formula _ 1-nte aantharika uthppannathe formula _ 72 upayogichu soochippikkunnathiloode oraal metrik nirvachikkunnu.
projection ingane
ivide soothravaakyam _ 75 ennathu soothravaakyam _ 76-nte vipareethamaanu. 
project cheytha samavaakyam ingane vaayikkunnu
ingane ezhuthaam
avide stratonovichu calculus cheyin ruul anusarikkunnath nirnaayakamaan. melpparanja samavaakyathil ninnu, anthima projection filter ezz. dii. iii.
soothravaakyam _ 79
prarambha vyavasthayil oru thiranjeduttha formula _ 80.
oopparettarmaaraaya f, g ennivayude nirvachanam mattisthaapikkunnathiloo nerittulla metrik bhashayil poornnamaayum vyakthamaaya projection filter samavaakyam namukk labikkum
oraal metrik nirvachikkunnu
metrik formula _ 83 aanu fisher information metrik. oraal direct metrik kesinu poornnamaayum samanamaaya gattangal pinthudarunnu, koodaathe hellinger/fisher metrik filter samavaakyam
veendum prarambha vyavasthayil thiranjeduttha formula _ 80.
eph, jii ennivaykku pakaram vaykkunnathu labikkum
<kanakk> d\heta _ i (t) 
 \left [\sum _ {j = 1} ^ m g ^ {ij} (\heta _ t)\; 
 \int\frac

