Table Of ContentA Now Technique for Inercasing the
Fleaibility of Reeursive Least
Squares Data Smoothing
By >. LEVINE,
tng rvarne fet apuniee de somthing te
ams lh gina sip on beep Je
‘lara. The ava rercton of ¢ convent dz ier cen Be re
‘nove tne ting the option weipting a Pours Sots. he
‘math aso prone a 2 {Ee vate) eimai he eet
at sy the ems jor ns ote ena ino
Gotinem esse eticims eon be deans, Ths
festawe gent soe
fg, 200 ern 9
rose Tet ast da ae
Dag sk fee ja veal Ie cm Fr attain a
viqes which can be apd, na tne trader obras of Sdios
raveliag alam Mgie webriahle (ajeetnie, The besvatinay an
sieually proces liga sep, a7 tea. match ft haw be
ces dese toeaniyses vite 9 the anaes inion
‘of conatess Pieper eee te ne ae tonic, mene
Test ysis soothing, was theort x) oumdacon say seabed
serena pure ge Hg tr pep se ha ls ele se er
tle ticery ayer Mesilla In encore vice va of
Dieta tutions mile macnt ning ite euebtity “or eompuse a
Tytler nr vu rnd comes adsl lo
sw rn yresicesiy emule ave vey at le Cone. mebe
‘nd anew user acou, Tha the alcrage teenies ace fadepec
fe toe ramber of bkervatrce and ars aetuall quite modest. ‘We wi
sks use the term “cps-mua smnnthin," which ste aaterperted 21 -be
Tense snsice seuss 2, le weuhting of daca mresoly ptepersieal
thsi ovr yarn: Th cacy ta peor eynicnm amoorbing i ra
tina phere ie vurathi fet neeseirly Hiv magitie' in bere
tional ror are detenaiagble (ese Puen Aeperdent cute i um
OF the seeuagee of sho oethod Aske heres Onor lene pets of
bserration, «sgl et inereae fn Ube ara of che sescothe oo
tds nny Hrsskceved by propel wcging thease he we
derivation, honrser, so Testes unre anche weighting fae,
th sllowing an arsilrezysequete ef sights lr be placed on the data,
‘ovions Hod {Il eee devote a the seizes oh position one
svlneiteeemmiag-bo lo er sfner vain elie lone rag
Tine ita nn aotelotalin, In fet LL wo eaider Qe vote of soueant
tea intra» phors ene spas te eva lace an the ably 1
ompensite propre iv aising obscene Wr baum lk “nels
ens for Getermiing nptisnite gaze ea for pera bseneations,
tahish aw of wonnrad rte nov og ater. Ln Soc
an ILD Cie sorbic iy exornded 20 ale Hi en uf arbitrary da
Interv
‘hu hu eptieion to eas igloo it “he appleby
his a br my onuenl veneheon Section LV, bere ch
Ini Torhang the eis” eno aceleacieze ar dsr wT Ap
Dpendig AUsee shew tins te ea ajuae diate fre Uae bea
Dares line of res wnay be wblzaned neve, Thi wal sy
vet aoa meunsoF real Hine ene detent way ef ong
fn instaneanuons swine Sarthe rea olvercl oee rae dats
teaching ApponlisP wesrtns tar shame reoeseury i pei eas
ques roe eve inning aes a ae Toe f pr obervatione
votes br Te aoetEod iy te woke be, whee Las smoocbing
ofenlive iver al. chaevetins, Favs ia Appedis C, the eeensin of
the meted ta include wlio uf aroolraon ie eure.
"Tn evisetion and csr ow of UN stn ot de aco we
ovenied iv il onciest of rida obarsvalioas & mown hedies. Hw
{het oh teebnigue er heaping] oa aerate quit hi ea
Ieesprexed se lircr somliveton of smactnns wate he wean
sitsients are to be estimated
"Ve divans of this estou af yevormicg course lense ones
sisannleng bese on tetas expla iy Kaos.” Foe sions,
‘eect conde Us cae of eagle ostenio High A 0.
(iene ueeracione fd — 1,2," yw, eeceonds parts re made by
tr roianeks whe rmeascrenen rues ae sake Uy he neers
WeENEITR DKA? st oh ata sETIEN sa
suv ty itn cb sw wea at yaraine 4 We wah eo
bla ve hea eatin the poston (iy? ata ity Gy
to Ue at wove inn® by iM earing the atest ey aio
#.) sits Tear oneal ec thet — 1 pave ebseration, Lhd
Uv aoe il Bed ie some 7 ped Geto fron che eet
aque eo! sgpeadon, A amtaniag unre ians Taser ae
‘We may vote this sam as dolon
ae- Sin in wane bs
here =a and wan arty wig fst iteatting
this Foust wits spect 20, a, tl elling ner ting eg
tio Sq. vote Hes Henne eutine
a Sma Daw sie
nEw tne Biante Bhan cow,
seth pai) hake te
the Vii Shin bm in
he Sinolsnoass elucon of 1 ae 184 viele he stondand eos
quarse erinatos nf pasion aad eloily: homer the expiry
anv he perneetal ae estivis Tae ie rec oc,
Tsien enemy bor an pr ea bw ne 9 by
82 an nag seem mactstead aun RAYE
swe repo the avwoas af 11 eheough ve ning the lst obsreua:
Bhs viders nates ofthe Ge Tie sein al vols
aot Doucet a wa
Deeerticting wit neq bs fa and faa gil takin uae a doin
i 2, ee resulta ea be westan the Gort
Bike dd peal
EIR Ht | Mytnaa = Ey tae sh a
Sbteting (7) fen £1 a(R) Rowe (32, we bn
Bis Ry EB Bly
ee
6d =, a
whe mis ae
oat 19
ao tt an
8 I, asi
J a: un
gnetiony (> ate (1.5 aypleity iota ha ame cee
dinate een vambénction of “OP de ith vee uboewvetions
tec and oy zw the yetion and rebvity senting suena and ae
‘elected orca savers ro 121 (0 Ung dette
Bye (UE
“The wlio Bey | a 8M oy re owely be peed th
cto ua Mune 2a ana 25
poss and veleity frmes che data inser Mased et ® — 1 ebverie
ions ao as we ey dice
onthe hte a8)
The snarting gations nye tke the rm
ht A) ety = ad i)
B= MG = 2) = 194 Aaa) | Baby UT)
which show thatthe predited wth postion aad veloity may be sd
Ye repent all ast its
‘The ily to optimize the sswothing for varying, measurement
errr. aries tram the Hack that he anttioe I Soy td
fan theres be simmered
FoeRyee
6-0
Uy Mya + Bor Ps,
te ety
us)
‘Ths, coc now oben ees I subir sight Bye an
courte show by stotnial enalyds ptiasin’y we'ghtea ky hsieg
wwe = ye! Sine Jy fede by 114), te latexes elon aoe
roy fe cond ava consiteney choc, Note chet = mised bseration
rag be promis keemunted for by ching ite wright fart val
vero aml wen th use wel Equariees (10) though 1) thew at
Tuestnatheel rorites eq 20 thei pected values, athe futur
sweating ofboth ld nd ee dat eno aezed to coment fr le
rmising observation, Tw Mast his, Talis Pan 1 has boo =
structed to shan how the weighting a cys fr the nse or
liygseund soi observations, Meze we ave eoeen wy — 1 fo sim
plies, Not thot the effet of te missing obserstons om the varias
Patios ogc? ad esting (woe Tab 11 eines rp with the
tition of tw observations romped to the valet of these ratios
‘shew all absarvtione ane pose
Tho cetal weighting cnet appli! to dhe observations v0 sel
the smote potion ad veloiey eaosenates cam be determined br
solving (2) and (3) sineltomssoae, Ie deine
Ben aeEan, om
‘Dawin T— Aes, Oaeuawanions Pensrer 6) —
a
aud 8 ye
e= Luk = t= 0h, on
ah = AG, = ln — AE bw, (ay
"Thus vecens ar tbat! "alls Tan IE forthe special enses
conidesed
Th digital computer applicainss this mele would requiee storage
Obs lag Pony fon y Hoy ttl Jy gy eve) Upon eesipt
oc, teria the cams ae asi, IB ay and 2. ace on
uted, (12) and (U9; fy gd dy are derives, C104 ane (5 wd
peta qe formed. (18), gna raed with the uri) vale at
Titeuies “Fae antou't of storge aoe eptacon per eye ile
Denes uf i inte af uber
Tn siitione where “his “ye of faeathicg can oe cmplayel rhe
rvethsd witli hese effers seve slvactages over eoasta anal
conv Les? Syl sles MAL sor 07
Yasue ML Ossuuvarions 2 Avo 6 Misoeo
rnet2od. Yr ex he wlan fators oun e abit chosen
tritsoul afin. the Stness sete, Le i the hace of eon,
true steht stan sna ered yah soothing pres. hus,
thew ft he wow ta ple rater Zor lssst empha oa be dat.
by inensusng Cor soenns qt bel elive eight with expert ole
fhe. The neseanmyat sees to) vary th a Kin way wih pe
tion, velr3, wr in thew ean be shosts eq to Loy ab ott
Tinie Isang for ss tors. It inporcant o ote ere that
tin et ores oni feed of dhe rab of fhe eeu
bet thei giles ee he sgn Be Rn oak
finevalusce te station savy of the snate eonrinates,
‘The press ofthe ts es pei diene a aia
rls at ae Hine assign
Inted Gauss mets rene) fora nortan caw
fa) the righting fasts nes sual Ka ene Kin
Ib) ae ma a nt oh and = La
8 oom nm, sven TarmNEAE HoULLNAL, MAY 1001
Tooth ease, we may write
hich, yal wo of (ah (14, eb aad
sath ;
newts, co
bon (oa, oR
wn (on, EB) os
fiw cas (), sd K repeal ih Tor case ih
‘he wextuey of ae aclieary peeic-iou ofp unite (pr acande} inve
ho puss or fl ns tay Be oeenined ors
uation (2515 re: ea in wee wing pss wha he
fe tyat observation's pla" iy walking a pict, bof
dye aad surrogate ie vaio ase
She opin ws sae ix abe yen the varices of she
fink Ties observation ant the poetnn, ue, using (25) with p= 1
sve
agin ‘i
pot GH, cas cai,
timate Liga gxie = en)
Loqfel ease
“The gate size deerme Tae (28) 4 irae awraged when
servations ate ised, le aplinny Tory rgane abee
tins and ice
Tor eompletenes, we pre the expe value al quate aftr
observations for he ese ofall =
USI MRASH AUER a amore ew
SH
et,
tie 2)
arent)
Bin = 1) = aol
Pie Tee
a agg 8 1H
sgana gate oy go LETS
Iv rey oan of intone, che tne sntsvle beta nor
tage suey seers Hele tose af tho previous seein. at sy
sete Te iat ade Devas aliknary bert ties by
eploing the spuscity EES fhe hs ail easing oy He 6
‘Tren Gad 06 tadeid
-Ee-
=D tits,
830m nue erst coe-SIOAT ouuNal HEY IB
swbere Pe mncbangl thsi Tas seein aos ream
Bea awe
Gb
ant ik tos 2
Mo bl Fe Ns Be
Soot = th
‘ke soothing eftatinas agin he eae turn, wes Tah te
mesthing evel arn inpliiiy conte the ive dependence
Tho proiets G | List ober fut a compat Foun
hae an
eho, obeinasy, om rites know Leas awit he (| Th
Slnervatin evesforsounpcatn 2 tafe hee} stakes
‘en yaad, Fo ie teres mE ue polit the Ge Dist ob
sevsticn ay ote to "evi if, me must etinate 1 te of le
oveation “fyi nal apply a appeepine yale about fy?
The = tolfe, lege stright sever forall acinecs St exmor. No
Aleeedatio ye aality of the BU 2 made only a peor elie ts uf
caer he obtened, ess This mgs a devi for mpi, ary
i enn oe Sonn woenved, ae as De wE Into vil
fle
BaF Rage hasan a
Th cho preven sean, 96 doseribecl Tat wisi bervarion
ro be ervey aesunted fs In he ease of varia dete tees,
Suly the ins Miferencs bereech swerve obserratins enters he
Suncor. Thus, an sbsreution Mat ueeas iepaced (2a ,) ut
over mule Qees = 02 hava sire on te equacon. hoes narren
ign pesca tre yoy bs
fer Faun = thn hangs ows
fd Me coig pant erceving He pt ms se BS
“Tae atesaintion of "ve npc ace lee Faw suns
