XAY DUNG THANG THOI GIAN VIET NAM UrC(VMI)
NguyJn Bdng, Le Vdn Ninh, Ngiiylm Thi Hdng, Trien Viet Phucmg, Ngiiy§n Dde Trung Phong Do I iron g 7'hdi gian vd Tdn sd, Vien Do liiviig Viet Nam
Tdm tdt:
Moi cpmc gia ddu ed tinmg thcyi gicm rieng UTC(k) tren ccr .sa he thong ddiighojigiiyen tit.
Viec thirc hi^n thiicit todn thang thcyi gian tren co- .scr he thdng dc'mg ho nguyen tir .se tgc) ra mot tliang then gian he thdng cd dd dn dinh tdt han bdt kv mdt dchig hd iic'io trcmg hg thong. Bai hdo m)y gi&i thieu vice .u?y dung tlumg thai gian Viet Nam UTC(VMI) .sir dung .so lieu aia ba ddng hd iiguven lir Ceassium thircrng mgi. Cluing ten dd dp dung thudt todn thang thai gian ATI cda NIST cimg vc'ri phucmg phdp rieng cle xdv (hi-n,^ nen UTC(VMI) tren ca .sd he thdng thiet hi hien cd ted phcmg do Iirang tlic'ri gian vd tdn .sd Vien do ludrng Vict Nam.
Abstract:
The national metrology institutes always establish their time scale UTC(k) (UTC of k lahoratoiy ) based on the atomic clocks. .Monde clocks and a time scale algorithm provides an en.semble time which is better than any component clock in the .system. This paper introduces establishing of Vietnam time scale UTC(VMI) (UTC of Vietnam Metrology Institute) using the comparison data of commercicd Ceasiitm atomic clocks. We applied the time scale cdgorithm named ATI and an own our method and present instrument at the time and frequency laboratory - Vietnam Metrology Institute.
I. Gidi thieu
Thdi gian la mdt trong bdy dai lugng co bdn ndn vide xay dung va duy tri thang thdri gian la mdt trong nhirng nhiem vu ciia mdi vien do ludrng qudc gia. De xdy dung va duy tri thang thai gian, phdng thf nghiem thai gian va tdn sd a cac vien do ludng qudc gia ludn van hanh mdt he thdng gdm nhidu ddng bd nguydn tir ceasium (loai thuong mai hodc tu che tao). Ben canh vide van hanh lien tuc cac ddng hd nguyen tir, mgt thudt toan thang thdri oian cung phdi duoc nghidn cuu thue hidn trdn co sd dir lieu thu dugc tir phep so sdnh cac ddng hd rieng le. Ket qud so sanh ciia cac ddng hd nguyen tir ciing vai thudt toan xir ly sd lieu se tao ra mdt thang thdi gian co do dn dinh, ciing cd nghTa la kha ndng tidn doan, tdt ban bat ky ddng ho thanh vien nao trong he thdng. Hien nay cdng ddng thdi gian thd giai da vd dang sir dung cdc thuat toan ALGOS(BIPM) va'ATI(NIST). Thudt toan ALGOS(BIPM) dd xay dung TAI co do 6n djnh dai rdt tdt va thudt toan ATI de xay dung thang thdi gian ciia NIST (National Institute of Standards and Technology) vd la thang thdi gian thue. Theo khuydn nghi ciia BIPM rdng cac vien do ludng qudc gia ndn duy tri thang thai gian rieng voi sai lech ndn nhd hon 100 ns so vdi UTC, cac vien do ludng qudc gia thudng dp dung thudt toan ATI dd xay dung thang thoi gian ciia minh. Tuy nhidn, moi phong- thf nghiem thdi gian vd tdn sd so hii-u sd ddng h6 nguyen tir khac nhau, sir dyng cac. phuang phap so sanh thai gian va cac phuang tien do luong khac nhau, do do moi pho.ng thf nghiem ddu phai nghien ciru thirc hien thuat toan thang thdi gian bdng phuang phap ridng ciia minh.
Bai bao nay phan tfch thudt toan ATI ciia NIST.va^denghi phuang phdp xay dung rieng biet trdn co sd ciia 03 ddng hd nguyen tir Ceasium cua Vien do ludng Viet Nam. Thdng thudng, de xay dung thang thai gian thue, kdt qud so sdnh dong hd phdi co dugc tir ft nhat 03 ddng hd va TA dugc thue hi?n trdn mdt ddng hd rieng Id. Tuy nhien, VMI chi'co 03 ddng h6 ndn Chung tdi phdi vira thue hien so sanh cdc ddng hd, ddng thdi thue hien TA bdng each sii dung mdt trong cac ddng hd.nay ma van phdi ddm bdo sir khdng tuong quan cua s6 lieu so
sanh, mdi dieu kien tidn quyet trong vide thirc hien thudt toan thang thdi gian. Vide xay dung thanh cdng thang thdi gian trung binh TA(VMI), ngoai viec tdng hgp 03 ddng hd de cd do dn dinh tdt han cdn dat ndn mons cho viec xay dung thang thdi sian vdi sd ddns hd Idn han, cd dd chfnh xac cao hon trong lirono; lai.
Bai bao dugc td chirc nhu sau : phdn II md ta viec duy tri he thdng ddng hd nguyen tir ciia vien do ludng Viet Nam, thual loan tdng quat xay dung thang thdi gian dugc ndu Irong phan III. Trong phan IV. thuat loan cu the va vide xay dung thang thdi gian trung binh TA(VMI) trong didu kien ciia Viet Nam vai 03 ddng hd nguyen tii' dugc md ta chi tiel va cudi cung kdl luan la phdn V
II. Thuat toan xay dung thang thoi gian
Mdt sd dinh nghTa : khi ndi den thai gian ("time") la ta dang noi ddn thai gian thue sai lech so vdi thdi gian ly tudng ("ideal time") la thang thdi gian deu dan tuyet doi. Thdi gian ly tudng chi la khai niem, khdng the cd dugc tir do dac hodc tfnh toan.
Ve ly thuyet mdt thang thdi gian trung binh dugc dinh nghTa nhu sau :
rA0(/) = XI, '*•'. W ( 0 Zl ^''(^) = 1 (1)
O day, / la chi sd gan cho mdi ddng hd /i,. Id thdi giaacua ddng hd /
w. la trgng sd cua ddng hd i A^ la sd ddng hd
Khi cdc ddng hd dgc lap vdi nhau, viec Idy trung binh trgng sd (vdi trgng sd tdi uu) se cho ta mdt thang thdi gian dn dinh hon bdt ky mdt ddng hd thanh phdn nao trong he thdng.
Trong phuang trinh (1), ndu ddng hd 1 bi loai bd vdo thdi khdc t^thi thdi gian /z,(r) ciing dugc loai bd ra khdi qua trinh tfnh toan gdy ra mdt do lech dang kd a kdt qud tdng trgng sd cudi ciing. Muc dfch ciia (1) la lam gidm sir thang giang ciia thang thdi gian. Vi le do, chung ta phdi trfch ra cac thdng gidng va Idy trung binh ciia chung. Tren co sd yeu cdu nay, thang thdi gian trung binh phai dugc tfnh theo bidu thirc sau:
TA(t) = XI, w,(0(/x,(0 -/UO), XM ^'(0 = 1 (2)
Noi each khdc, ta phdi lay thai gian thue ciia ddng bd / tm di gia tri tidn doan ciia no rdi lay trung binh tdt cd cdc thang gidng vai trgng sd. Trgng sd w,.(f) va tien doan ddng hd /i.(r)dugc xdc djnh bdng nhirng thii tuc khac nhau phu thudc vao cac phong thf nghiem do ludng qudc gia.
Tuy nhien ta ciing khdng the tfnh TA{t) tir (2) dugc vi li.(t) la khdng the do dugc do thdri gian ly tuang la khdng the biet. Cdi ma ta co the tfnh dugc la sai khdc thdi gian x^ giiia ddng hd / va thang thdi gian trung binh :
x.(t) = TA{t)-h^(t) (sy Gia tri duy nhdt ma ta co the do dugc la sai khac thdi.gian giiia cac ddng hd x^j. Ta tfnh x.
ixx cac gia tri sai khac do nhu sau.
Ta biet rang
X;ji.t) = x.{t)-x^{t), i = i...N,i ^ j (4) Cac phuang trinh (2), (3) vd (4) cho ta mdt he phuang trinh de xdc dinh cac gid tri A-,(r)
duy nhat nhu sau :
[XM^n^o^/(o=X,>,ww ^3^
X;j(r) = A-,.(0 -XJ(t), / = 1,..., A^;/ ^ j
Tir he phuang trinh trdn la tfnh dugc cac .v,.(/) nhu sau :
.v,(/)=x';;,M<ofc (/)-.%(/)} (6)
/;.(/)dugc lien doan vdi bieu ihirc luyen tfnh nhu sau :
//,(/)=.v,(/„)+v, (/)(/-/„) , , (7) d day /, ki chu ky Imdc ma lai do .v,dugc linh, .v,(/„) la sai khac thdi gian giua ddng hd / va TA lai thdi khfic t^ va \, (/) la tdn sd tidn doan ciia ddng hd /.
Tdm lai, vice ifnh TA lidn quan ddn viec tfnh sai khac thai gian A,(Ogiua ddng hd / va thang Ihdi gian trung binh. .v (r)lhi lai dugc ifnh lir gia In sai khac thai gian X,^{t) giua cac dong hd, thdi khdc t^mix vide tfnh loan dugc thue hidn, gid tri A, (/o)dugc tfnh tai r^, trgng so
u',(/) va tan so lien doan v,.(Ocua mdi ddng bd. Vi khdng thd biet //,(/) nen ta cung khdng the tfnh dugc TA{t) nhung la co the tfnh dugc su thay ddi ciia no.
HI. Xay dung thang thdi gian UTC(VMl)
D8 xay dung thang thdi gian trung binh vdi sd lugng ddng hd ban che, chung ta cdn phai lua chgn thuat toan thfch hgp. Ndi chung, mdt thudt toan thang thai gian se Idy cdc kdt qua so sanh cua cac ddng hd trong he thdng va tdng hgp chimg bdng toan bgc dd tao ra thang thai gian trung binh. Thuat toan chung tdi sir dung dh tao ra TA(VMI) cd cac budc gidng vai thuat toan ATI da dugc sir dung thanh cdng a NIST, se dugc md td sau day.
Nhirng dieu kidn tidn quyet khi thue hidn thudt toan thang thdi gian la :
Ldi do sai khac thdi gian giira cac ddng hd x.j{t) phdi rdt nhd so vdri dn ciia cac ddng hd.
Cac ddng hd phai dgc lap va khdng co su tuong quan nao giira cac sai khac thdri gian do dugc giiia cdc ddng hd.
Neu cac dieu kidn trdn khdng dugc thda man, phuang phap tfnh thang thdri gian trung binh ndu tren se khdng dung nua.
Ngoai ra cdn phdi chii y mdt sd didu kien khac nira nhu phdi lira chgn phuong phdp tien doan tan sd cho phu hgp vai ddng hd va khoang thdi gian tien dodn.
Ddu vao ciia thudt toan la cdc sd do sai khdc thdi gian v giira tdt ca cac cap dong hd, voi khoang thai gian giira cdc Idn do la mdt ngay. Khoang thdi gian nay la dii lorn dt loai triranli hudng ciia dn cd trong cdc phep do.
Tien dodn thii: nhdt cua do lech thai gian ciia moi dong hd so vdri thdri gian he thong duoc cho bdi cdng thue sau :
.v,(/-hr) = A-,(0 + y;(Or {%
Uac lugng tot nhdt do lech thai gian ciia moi ddng hd / tai thdri khdc {t + t) vai cac phep do da c6 x.j{t + z) dugc tfnh nhu sau:
^•, (^+r) = X ^ (^)[-^'y (^+^) - Xii ('+^)i ^ Khi da biet x.{t + r ) , tdn sd trung binh cua mdi ddng hd trong khodng thai gian r trudc^o
CO the dugc udc lugng nhu sau:
T
Mdt gia tri udc lugng dugc Igc ham mu cua tdn sd trung binh hien thdi cua ddng hd i, duoc sir dung cho vide tidn doan d khodng thdi gian tidp tlieo, dugc tfnh nhu sau:
.v,(/ + r) •[v,a + r) + ///,.v,(/) (11) d day m^ la hang sd Ihdi gian ciia ham loc mii dugc xac dinh lir mire luong ddi ciia while noise va random u'alk FM, cd nghTa la:
/", = —s 1 +
I 4r,;
- +
- l l / :
3 3r^ (12)
la chu ky dn dinh nhat ciia ddng hd
Cac trgng sd ddng hd w. trong (2) dugc ifnh lir cac phirong sai ciia cac loi ihdi gian ciia cac ddng hd ef nhu sau:
w. =
(e-irf)
(13) 1^(fr(^))
Ldi tien doan ciia ddng hd / qua khoang thdi gian / + r dugc udc lugng bdi:
f- = l.x,{t + T)-.x,{t-tT)fK^ (14) Vi thdi gian he thdng la trung binh ciia thdi gian ciia cac ddng bd, uac lugng ldi tien doan
(7) la Chech vi mdi ddng hd la thanh vien cua he thdng, can phdi hieu chinh do chdch nay bang he sd:
A:. = I ( l - n v )
Do cac dac tmng dn cua mdt ddng hd ceasium cd the khdng dimg, ldi tien doan hidn thai ciia mdi ddng hd dugc Igc mii, d day ldi tien doan trong qua khir dugc giam trgng sd, nhu sau:
£iit + T) = -^[£rit + T) + N,e'rit)] (16) vdi hang sd thai gian cua bd Igc z dugc chgn bang 20 ngay va gia tri khdi tao cho sf bang
^ o-,.(r)
Hien nay, thang thdi gian qudc gia Viet nam UTC(VMl) dang dugc xay dung trdn co sd he thdng dugc md td trdn hinh 1. Cac phep do ddng bd dugc thue hidn timg giay bang ngay lidn tuc. Tir tap dir lieu nay, cac sd lieu irng vdi cac Tau bdng 1 s, 10 s, 100 s, 1000 s, 10000 s va 100000 s dugc lua chgn de phuc vu cho vide danh gia kiem tra chdt lugng ddng hd (ndu cd).
Ci day chiing tdi dang sir dung khodng thdi gian do bdng 1 ngay (86400 s) nen cdc sd do tai thdi khdc 00:00:00 UTC cp y nghTa quan trgng vi nd dugc sir dung de tfnh TA(VMI)
Tir phuong trinh (3) thdy rdng ta eg the co dugc thdi gian trung binh rA(r)bdng each sira ddu ra cua dong hd /z,(/)mgt lugng bdng A-.(r) ma ta da tfnh dugc. Tuy nhien chung ta khdng the didu chinh tan sd ciia cdc ddng hd nguyen tii' ceasium vi chung la co sd cho viec tfnh toan thang thdi gian trung binh. Thay vao dd, chung ta phai sira ddu ra cua mdt bd didu chinh tdn sd ung vdi mdt ddng ho va tfn hidu lir ddu ra bddidu chinh nay dugc xem nhu TA(t). Tidp theo, sau khi didu chinh tfn hieu nay theo UTC. ta se cd UTC(VMI). Ky hidu ddu ra ciia bd didu chinh tdn sd nay la /;^(/)(nhu da noi a trdn, day chfnh la UTC(VMI)), ky hidu sai khac thdi gian tuong doi ciia ddu ra bd didu chinh so vdi ddng hd tham chieu s la A,;,(/) thi
TA(t) CO the diwc bidu didn ribu sau :
rA(/) = /;,(/) + {A,(/)-A,,(0} (17)
105
D6 duv Iri ihang thdi gian, la phai ifnh loan va hieu chmh hang ngay sao cho g.a tn hiei ihdi cua //Ja khdng ddi cho dc-n ngay lidp Iheo. Ta biet rang bg didu chinh tan so luon cnii do dich lAn cua cua ddnu hd iham chicui (ddng hd cung cap tan sd cho nd). Nhu vay, neu m\i ca lirgn. d.Gu chinh y,„„(t) cua ho di6u chinh pha/lan sd thi dau ra cua bd didu chinh pha/tan .so ongay licp thco hi :
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liv dicii cliinli ph;i/l:'in so
Hv plijn phoi .lunf
b i i ph.'ni phi t."in so
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Di^u chmh i:tn s6 (Thue hi^n thai gian hg ihong) 5 MHz
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Hinh 1. Sa do khoi he thong chuan thoi gian quoc gia UTC(VMI).
//,(/ + 7) = /i,(0 + y,(r)r + y,,,(r)r |
d day y],(Ola tdc dg cua ddng hd a dugc lay tir v^ebsite cua BIPM. Do do gia trie y,,,/^dugc xac dinh sao cho gia tn//^(/+ 7) trong ( I I ) bdng vdri 7A(r)trong phuangtiij (10). Sau mdt vai phep bidn ddi don gidn, gia tri cdn phai c6 cua y,,,,^ (T) dugc xac dinhnj sau:
Vw,(0 = _ 2SA '^'sA(0-.t,(0
T
-v.(/)
Tuy nhidn, de duy tri UTC(VMl) trong giai ban dugc khuyen nghi bdi BIPM, chiinS thye hidn nhirng lugng dieu chinh bd xung them nii-a d bg dieu chinh pha/tSn so. M didu chinh nay dugc tfnh toan dua trdn so lieu cua UTC(VMI) dugc cong bd hang'l' trdn website ciia BIPM.
Hien nay, Trung tam do ludng Viet Nam duy tri viec so sanh 03 ddng hd nguyen tir ceasium. Cac sd lieu so sanh ddng hd dugc gui di BIPM tham gia xay dung thang thdi gian nguyen lu' qiudc te TAI, vi vay khdng thd danh rieng mdi dong hd lam ngudn tan sd chudn cho viec thd hidn TA(VMI) va UTC(VMI). Chimg tdi da su dung tfn hieu lii' mdt ddng hd nguydn tir co chat lugng cao nhdt cho muc dfch nay. Ddng hd nay phuc vu cho ca muc dfch so Scinh xay dung TA(VMI) va cung dugc sir dung cho viec thd hidn TA(VMI), UTC(VMI) thdng qua bg dieu chinh pha/tdn sd chdt lugng cao. Vice thue hien TA(VMI) bdng bd didu chinh pha/tan sd hang ngay dugc thue hidn bdng chuong trinh dieu khidn he thdng theo cac budc nhu sau :
1. Lua chgn cac tham sd de lay dii' lieu sai khac thdi gian cac ddng ho nhu MJD, thai gian, sd hidu ddng hd v.v.
2. Kdt noi vdi co sd dir lieu SQL
3.Ldy dCr lieu so sanh cac ddng hd vdi nhau va so sanh vai UTC(VMI) 4.TvnhTA(VMI)
5. Tmh UTC(VMI)-TA(VMI)
6. Tfnh lugng dieu chinh tdn sd cdn thidt theo ly thuydt (cho bd didu chinh pha/tdn sd) vao luc 00:00 UTC de ddng hd tham chieu bam theo dugc thdi gian ly tudng
7.Tfnh lugng dieu chinh tan sd cdn thidt thue td (cho bd dieu chinh pha/tdn sd) vao luc 00:00 UTC. Bang lugng dieu chinh nay, ddng hd tham chieu bdm theo dugc TA(VMI), day ciing chfnh la lugng diSu chinh tdn sd dugc thue. hien vao luc 00:00 UTC trdn bd dieu chinh pha/tdn sd.
Co the gidi thfch ve lugng dich tdn d 7. nhu sau : viec didu chinh ddng hd tham chieu de CO UTC(VMI) bam theo thang thdi gian ly tudng la khdng can thidt vi ta khdng biet thang thdri gian ly tudng, ta chi cdn dieu chinh de co dugc UTC(VMI) dn dinh nhdt theo TA(VMI), cdn su sai khdc tuyet ddi giira UTC(VMI) va UTC se dugc bd xung khi cdn thidt (vf du nhu khi ta mudn duy tri /UTC-UTC(VMI)/ < 100 ns). Tuy nhien, trong trudng hgp nay cdn dac biet luu y den do dn dinh cua thang thdi gian. Vide thirc hien didu chinh tren bd didu chinh pha/tdn sd dugc tien hanh than trgng tir bang tay (dung chuong trinh lay so lieu tir he thdng do vd tfnh toan theo cdc buoc tir 1 den 7 ndu tren rdi didu chinh hoan toan bang ban phfm cua bd dieu chinh pha/tdn sd), ban tu ddng (thue hien tdt cd cac budc tu 1 den 7 neu tren rdi dieu khidn bd dieu chinh pha va tdn sd bdng phdn mem dieu khien) va cudi cung la thirc hien tdt cd cac cdng vide tren bdng phdn mem dieu khien.
Mdt vdn de ndy sinh trong qua trinh tfnh toan TA(VMI) la gia tri trgng sd cua cac ddng hd VMI dang duy tri boat ddng cua 03 ddng hd nguyen tir ceasium 5071 A, trong do chiec thu nhdt thudc loai chat lugng binh thudrng dugc bdt ddu su dung tir nam 1998, chiec thu hai thudc loai chdt lugng cao dugc bat ddu sir dung tir nam 2006, chide thu ba thudc loai chdt lugng binh thudng dugc bat ddu su dung tir nam 2007. Tir phuang trinh (1) nhdn thdy rang dong gop ciia mdi ddng hd vao thdi gian trung binh phu thugc vao trgng sd ciia no.
Tuy nhidn trgng sd cua mdi ddng hd lai phu thudc chat lugng (do dn dinh) ciia ddng hd;; do.
Do do, mac dii trgng sd cdc ddng hd dugc dat ngdu nhien khi bdt.dau tfnh todn, ngay sau do chiing dugc tfnh lai theo do dn dinh thue te ciia cac ddng hd. Ta thdy rang trgng sd ciia ddng hd thu nhdt (ddng hd cu nhdt) co trgng sd thdp nhdt chi xap xi 0.01, ddng ho thii hai (chdt lugng cao) cd trgng sd Idn tai gdn 0.9, ddng hd thir ba (chat lugng binh thudng nhung mai dua vao sur dung) co trgng sd xdp xi 0.1. Ro rang la thdi gian trung binh TA(VMI) duoc thye hien chu yeu bdi ddng hd co chdt lugng cao. Vdn de ddt ra la co ndn giai ban gid tri trgng sd ddng hd de tdng cudng vai tro ciia cac ddng hd cd chdt lugng khdng cao ddi vdi thdi gian he thdng hay khdng, do la didu ma chiing tdi tiep tuc nghien cuu trong thdi gian tdi.
Sau khi dicLi chinh dong hd tham chicni iheo TA(VMI) va UTC la cd UTC(VMl). So lieu U'lX^VMI) ihdn^j qua .so sanh vc linh irung gian dugc giri ldi BIPM dd dugc danh _gia^ va duoc cdng bo o Ciivulai-T tren wehsiic cua BIPM. Ddng ihdi, so Ijdu cac ddng hd cung dugc giri ldi BIPM gop phan xay dung ihang ihdi gian nguyen Ur qudc id TAI. Tren hmh 2 hi so hcu UTC(VMl) diiov cdng bo gdn dfiy nhal trdn c;ic Circular-T sd 263,264,265.
u
D
I
U P
80 60 40 20 0 -20 -40 : -60 - -80
55139
T T
1
t i
55149 55159 55169 55^79 55189 55199 55209 55219 M J D
Hinh 2. So lieu UTC(VMI) dugc BIPM cong bo.
IV. Ket luan
Mdi vien do ludng qudc gia deu phai tu xay dung thang thdi gian trung binh ciia rieng qudc gia dd. De xdy dung mdt thang thai gian thue, thudt toan TAI ciia NIST thudrng dugc cac phdng thi' nghiem do ludng thdi gian va tan sd qudc gia dp dung. Phong do ludng thdi gian yd tdn sd ciia Vien do luang Viet Nam da xdy dung thudt todn va cdc budc thue hien chi tiet de cd dugc mdt thang thai gian qudc gia dua tren thang thdi gian trung binh. Dd ciing la CO sd de tidp tuc phdt trien he thdng vdi sd ddng hd Idn ban ciing nhu dua cdc ddng hd thudc loai chudn ddu khac vao he thdng trong tuong lai.
Tai lieu tham khao:
[1] Allan, D.W., 1987, "Time and frequency (time domain) characterization, estimation, and prediction of precision clocks and oscillators," IEEE Trans. Ultrasonic, Ferroelectrics, and Frequency Control, vol. 34, n. 6, pp. 647-654.
[2] Weiss, M. A., Allan D. W., Peppier T. K., 1989, 'A Study of the NBS Time Scale Algorithm," IEEE Transactions on Instrumentation and Measurement, vol.38, n. 2, pp.
631-635.
[3] Tavella, P., and Thomas, C , 1991, "Comparative Study of Time Scale Algorithms,"
Metrologia, vol. 28, pp. 57-63.
[4] Weiss, M. A. and Weissert T., 1991, "AT2, A new time scale algorithm: ATI plus frequency variance," Metrologia, vol. 28, pp. 65-74.
[5] P. Tavella and C. Thomas, "Comparative study of lime scale algorithms", Metrologia, Vol. 28, pp.57-63,1991.
[6]Tavella P., Azoubib J., Thomas C , "Study of the Clock Ensemble Correlation in ALGOS Using Real Data," in Proc. 5th European Frequency and Time Forum, 1991, pp.
[7] Hanado Yuko, Imae Michito, Aida Masanori, Hosokawa Mizuhiko, Ito Hiroyuki, Nakagawa Fumimaru, and Shimisu Yoshiyuki, "Algorithm of Ensemble Atomic Time", NICT website.