
asthiramaaya vipuleekritha kalman filter

samamithikal (allengil "invarians") ulla nonleeniyar systengalkkaayi extended kalman filterinte (iii. keey. eph) oru pathippayi invariyant extended kalman filter (aii. iii. keey. eph) (aavarthichulla extended kalman filterumaayi thettidharikkaruthu) aadyam avatharippichu, thudarnnu leanier kalman filtering sidhaanthathinte lye grouppukalilekkulla oru poruthappedutthalaayi saamanyavalkkarikkukayum punarnirmmikkukayum cheythu. oru leanier outtputtu erarine adisthaanamaakkiyulla oru leanier karakshan padam upayogikkunathinupakaram, oru inveyarant outtputtu erarine adisthaanamaakkiyulla jyamitheeyamaayi poruthappetta thiruthal padam iekf upayogikkunnu; athupole thanne geyin matricks oru leanier stettu eraril ninnu update cheiyunnilla, marichu oru inveyarant stettu eraril ninnaan. nettavum covarians samavaakyangalum samsthaanathinte kanakkakkiya moolyathe aashrayikkunnath kurachirikkunnu ennathaanu pradhana nettam. chila sandarbhangalil avaa iii. keey. eph.-nekkaal valare valia sanjaarapathangalil sthiramaaya moolyangalilekku othucherunnu, ithu esttimettinte mikacha samyojanathinu kaaranamaakunnu.
filter derivation.
vyathirikthamaya samaya chattakkood.
lye group formula _ 3-nte oru ghadakam formula _ 2 vazhi time steppu formula _ 1-ll encode cheythirikkunna oru sisttam pariganikkuka, koodaathe dynamicsinu inipparayunna aakruthiyunda
formula _ 5 ennathu formula _ 3-nte oru group automorphisamaanu, formula _ 7 ennathu group pravartthanavum formula _ 8 formula _ 3-nte oru gadakavumaanu. thaazhepparayunna aakruthiyilulla oru alaveduppu formula _ 10-loode sisttam nireekshikkendathundu
formula _ 12 oru vekttar space formula _ 13-ll ulppedunnu, formula _ 7 kondu veendum soochippikkunna formula _ 3-nte gadakangalude idathu pravartthanam (ithu group pravartthanavumaayi ashayakkuzhappam srishtikkaan kazhiyilla, kaaranam pravartthanatthinte randaamathe amgam formula _ 13-nte oru gadakamaanu, formula _ 3-nte allah). pakaramaayi, sariyaaya pravartthanam nirvachichirikkunna alavinu ithe sidhaantham baadhakamaanu
filter samavaakyangal.
alaveduppu pravartthanam oru idathu pravartthanamaanenkil inipparayunna samavakyangalaal nirvachikkapetta oru nireekshaka soothravaakyamaanu _ 19.
ivide formula _ 22 ennathu formula _ 3-nte exponential maappaan, formula _ 24 ennathu oru ricati samavaakyathiloode tyoon cheyyenda oru gaine maatriksaanu.
alaveduppu pravartthanam sariyaaya pravartthanamaanenkil update avasthaye ingane nirvachikkunnu
thudarchayaaya samaya chattakkood.
aakruthiyude thudarchayaaya samaya chalanaathmakathaykkaayi mukalilulla vyathiriktha-samaya chattakkood aadyamaayi avatharippichu
vekttar feeld formula _ 27 eathu samayathum formula _ 28 bandham parishodhikkunnu
grouppinte aidantitti gadakathe formula _ 30 kondu soochippikkukayum short-hand notteshan formula _ 31 (rep. idathu vivarthana soothravaakyam _ 33 (rep. sariyaaya vivarthana soothravaakyam _ 34) ivide soothravaakyam _ 35 taanjant spacine soothravaakyam _ 37-ll soothravaakyam _ 3 aayi soochippikkunnu. ithu vyathiriktha-samaya chattakkoodinekkaal kooduthal ulppetta kanakkukoottalukalilekku nayikkunnu, pakshe gunangal samaanamaan.
pradhana swathukkal.
alavinte tharatthe aashrayichirikkunna nirvachanamulla invariyant error veriyabilinte swabhaavamaanu invariyant extended kalman filteringinte pradhana nettam. idathu pravarthanangalkkaayi njangal oru idathu-invariyant error variable ingane nirvachikkunnu
sariyaaya pravarthanangalkkaayi nammal oru raitt-invariyant error variable ingane nirvachikkunnu
vaasthavathil, formula _ 2, formula _ 43, formula _ 44 ennivaykku pakaram avayude moolyangal upayogichu chila beejaganithathinu sesham idathu pravarthanangalkku namukk labikkum
sariyaaya pravarthanangalkkaayi
airer variable pinthudarunna samavaakyathil samsthaanathinte kanakkakkiya moolyam ulppedunnillennu nammal kaanunnu, classical extended kalman filter filter cheiyunna leanier kalmaante oru property pankidunnilla, pakshe leanier kesumaayulla saamyam yadhaarthathil valare kooduthalaanu. formula _ 49 aidantitti nirvachicha error veriyabilinte oru leanier pathippayirikkatte
appol, tailor vipuleekarana soothravaakyam _ 53 nirvachicha formula _ 52 upayogichu namukk yadhaarthathil undu 
mattoru vidhathil paranjaal, uyarnna kramatthilulla padangalonnumilla error variable formula _ 55-nuu chalanathmakatha rekheeyamaanu. eee phalavum error dynamics swaathanthryavum iekfinte saidhaanthika gunangaludeyum praayogika prakadanatthinteyum kaathalaan.
samamiti samrakshikkunna nireekshakarumaayulla bandham.
mikka bhauthika samvidaanangalkkum swaabhaavika samamiti (allengil invarians) undu, i.iii. parivartthanangal nilavilundu (udha.jii. systethe maattamillathe nirthunna bhramanagal, vivarthanangal, scalingukal). ganithashaasthra, enchiniyaring kazhchappadil, pariganikkunna systethinaayi nannayi roopakalppana cheytha oru filter athe invarians propertykal samrakshikkanamennu ardhamundu. sisttathinte samamiti prayojanappeduthunnathi ikf samavaakyangalude parishkkaranamaan ikf enna ashayam.
nirvachanam.
samvidaanathe pariganikkuka
ivide formula _ 58 swatantra velutha gausiyan shabdangalaanu.
formula 59-neey aidantitti formula 60 ulla oru nuna groupaayi kanakkaakkuka, koodaathe
(praadeshika) parivartthana grouppukalude formula _ 61 (formula _ 62) athaayath formula _ 63. shabdamullah muun sisttam parivartthana grouppukalude formula _ 61 enna pravarthanatthaal maattamillathe avasheshikkukayaanenkil "invariyant" ennu parayappedunnu; athaayath,
filter samavaakyangalum pradhana phalavum.
ithu oru samamiti samrakshikkunna filter aayathinal, oru iekfinte pothuvaaya roopam vaayikkunnu.
evide
pishak samyojanam vishakalanam cheiyunnathinu, oru invariyant stettu error formula _ 73 nirvachikkappedunnu, ithu staanderd outtputtu error formula _ 74 ll ninnu vyathyasthamaan, kaaranam staanderd outtputtu error saadhaaranayaayi sisttathinte samamiti samrakshikkunnilla.
pariganikkunna samvidaanavum anubandha parivartthana group kanakkiledukkumbol, chalikkunna frame reethiye adisthaanamaakki formula _ 75 nirnnayikkaan oru kriyaathmaka reethi nilavilundu.
ekfinu samaanamaayi, geyin matricks formula _ 72 nirnnayikkunnath samavakyangalil ninnaan.
ivide matricks formula _ 79 staanderd ekephile formula _ 81 nekkaal ariyappedunna invariyant vekttar formula _ 71 neey maathram aasrayichirikkunnu. valare lalithamaaya eee aashrithathvavum athinte anantharafalangalumaanu iekfinte pradhana thalpparyangal. vaasthavathil, metriksukalude formula _ 79 appol ekfilennapole santulita pooyintukalekkaal valare valia sanjaarapathangalil ("sthiramaaya sanjaarapathangal" ennu vilikkappedunnava) sthiramaayirikkum. atharam paathakalodu chernnu, nammal "sharee" yilek madangunnu, athaayath.iii. kanverjans urappunalkunna leanier, kalman filter. anoupachaarikamaayi, ithinartham iii. keey. eph.-nte eathenkilum saavadhaanam maarunna santulita binduvinu chuttum allathe, kuranjathu pathukke maarunna eathenkilum sthiramaaya paathaykk chuttum iii. iii. keey. eph pothuve othucherunnu ennaanu.
aaplikkeshan udaaharanagal.
manobhaavavum thalakkett reference samvidaanangalum.
udaaharanathinu, maattamillaatha vipuleekritha kalman filterukal manobhaavathilum thalakkettilum reference sisttangalil upayogikkunnu. atharam samvidaanangalil chalikkunna oru karkkashamaaya vasthuvinte ooriyanteshan, vegatha koodaathe/allengil sthaanam,
iii.jii. jadatwa censorukal, magnettometerukal, gps allengil sonarukal polulla vividha ulchertha censorukalil ninnaan oru vimanam kanakkaakkunnath. oru iekfinte upayogam swaabhaavikamaayum kwaternian pishak formula _ 83 pariganikkunnathilekku nayikkunnu, ithu kwaternian grouppinte parimithikal samrakshikkunnathinulla oru "adhock" thanthramaayi palappozhum upayogikkunnu. oru valia koottam sanjaarapathangalkkaayi iii. keey. efumaayi thaarathamyappeduthumbol iii. iii. keey. ephinte gunangal pareekshanaathmakamaayi kaanikkunnu.
inertial naavigeshan.
group ooppareshan nirvachicha lye group formula 87-lake avastha (attidute matricks formula _ 84, velosity vekttar formula _ 85, position vekttar formula _ 37 enniva ulkkollunnu) ulcherthathinu sesham chattakodinodu yojikkunna inertial naavigeshanaanu invariyant extended kalman filterinte oru pradhana prayogam
oresamayam praadeshikavalkkaranavum mapping.
oresamayam praadeshikavalkkaranathinu mappinginteyum prashnam group ooppareshan nirvachicha lye group formula _ 92 (allengil planner sistangalkkulla formula _ 93)-lake avastha (manobhaava matricks formula _ 84, position vekttar formula _ 37, staatik feature pooyint formula _ 91 ennivayude oru shreni enniva ulkkollunnu) ulcherthathinu sesham inavariyant extended kalman filteringinte chattakkoodumaayi poruthappedunnu
eee saahacharyathil invariyant extended kalman filterinte pradhana nettam thettaaya nireekshanakshamathayude prashnam pariharikkuka ennathaanu.