JNC 2011 Reference Systems Tutorial

5/26/2018 JNC 2011 Reference Systems Tutorial

1/95

Fundamental ReferenceSystems

Dr. Brian Luzum

Dr. Georg e Kaplan

Mr. John Bangert

U.S. Naval Observatory


2/95Naval Oceanogr aphy 2

Outl ine

Reference Systems and Reference Frames

Earth Orientat ion Parameters

Time

Software



In t roduc t ion to

Reference Sys tems

and Reference

Frames



What is a Reference System?

A 4-D coordin ate sys tem

3 spat ial coord inates, 1 t ime coo rdinate

A mathematical abstract ion that al lows u s to combine,compare, or o therwise relate posit ional measurements takenat dif ferent t imes and/or from dif ferent places

Defined by specif icat ion of

Orig in of co ord inates

Direct ion of axes

Standardized algor i thms (software) that al low raw

measurements to be transform ed into the system

Some reference systems are defined by their relat ion sh ip toothers

xy

z

xy

z

z

zz

x



Primary Reference Sys tems

Two p rimary reference systems are of interest:

Barycentr ic Celestial Reference Sys tem (BCRS)

A lso referred to as the International Celestial Reference

Sys tem (ICRS)= The sys tem o f star catalog d ata

replacing the J2000.0 sy stemor the FK5 system

International Terrestr ial Reference Sys tem (ITRS)

= The wo rld geodetic s ys tem = WGS-84 = GPS

= Earth -Centered-Earth -Fixed (ECEF)



Todays Problem: BCRS ITRS

Celestial coordinates

expressed in BCRS

(ICRS)

Terrestrial coordinatesexpressed in ITRS

(ECEF)

At any g iven t ime,what is the

relat ionship?



Reph rased, Todays Prob lem is . . .

How to trans form vectors between the BCRS(ICRS) and the ITRS (ECEF)

Vectors are sets of 4 numbers (3 spat ia l coo rdinates and 1 t ime

coo rdin ate) represent ing locat ion (or i ts t im e der ivatives) or

direct ion (or i ts t ime der ivat ives)

There are som e intermediate reference sys tems that

are often used as waypo ints:

BCRS GCRS CIRS TIRS ITRS

relat iv ist ic rotat ions

t ransformat ion (a function of EOPs)



Real-World App l icat ions

Looking up:In what direct ion is a ground -based senso rpointed?

Look ing dow n:What spo t on Earth wi l l be seenby aspace-based sensor?

Navigat ion:What is the posit ion, veloci ty , accelerat ion ,

and/or rotat ion of a vehicle in inert ia l space? With respect tothe ground?



A Few Ideas About the Primary

Reference Systems

The or ientat ion of the coo rdinate axes must b e specif ied,

in pract ice, by th e pos it ion vecto rs of real objects

cont ro l po in tsor anchors

The ensemble of these defin ing objects, and their

co ord inates, are referred to as a reference frame

The ob jects themselves are provid ed by nature; their

assigned co ord inates def ine the direct ions o f the co ord inate

axes



Reference Frame Contro l Po ints

Terrestrial Celestial

Survey Markers

Instrument Sites

Radio Galaxies

Stars



The Terrestr ial Reference Sys tem

ITRS specif icat ions :

Origin at geocenter (center of mass o f Earth + oceans +atmosphere)

Relat iv ist ic local Earth framew ith uni t of t ime given by TCGsecond and uni t of length g iven by SI meter

Direct ion of axes

Init ial ly given b y BIH sy stem orientat ion at 1984.0

Axes rotate with the crust time evolu t ion of orientat ion w il l create no residu al globalrotat ion w ith respect to the crust

Realizations reference frames :

ITRFyyyy: 3-dim ension al si te coord inates and v eloci t ies

(yyyy ind icates year o f so luti on ; e.g., ITRF2005 or ITRF2008)

Site select io n criter ia: 3 years ob servat ions avai lable, on r ig idplates away from cru stal deformat ions , veloci t ies known to betterthan 3 mm /year



The Celestial Reference System

BCRS (ICRS) specif ications :

Origin at solar sys tem barycenter

Relativist ic metric tensor s pecif ied in IAU resolutio n B1.3 of 2000

Defining ob jects are un resolved, station ary, and stableextragalact ic radio so urces

Direct ion of axes Fixed in space do n ot rotate with respect to def in ing ob jects

As near as possib leto sys tem defined by the Earth mean equator and equinox of J2000.0(i.e., ICRS J2000.0 sy stem)

Independent of t im e and specif ic realizat ions (if the objects that define their direct ioneventually change)

Realizations two reference frames: ICRF2: Catalog of 3414 extragalactic radio sou rces (295 definin gsources)

HCRF: Catalog of ~100,000 stars from th e Hipparco s catalog

(85% of entire catalog; astrometrical ly wel l-behaved stars)



Dens if icat ion o f Reference Frames

Addi t ion of new contro l points, wi th coord inatescons istent wi th those of def in ing po ints

Al lows for high er sp atial densi ty

Allow s for m ore even co verage of the Earth or celest ialsphere

On the celestial sphere, allows fo r reference frame to berepresented at wavelengths other than radio (=5 cm ) oropt ic al (=0.5 m)

For example, IR, mm , or UV

Continued



Densif icat ion of Reference Frames

(cont.)

On the Earth, any civ i l ian GPS receiver effectiv elydens if ies the ITRF at 10-meter-level accu racy (a fewmeters or better for DGPS)

Celestial extensio ns of the ICRF and HCRF:

VLBA Calibrato r Survey (VCS6)

Tycho -2 Catalog

UCAC2 (to V=16) and UCAC3 (UCAC4 in pro cess )

USNO B1.0

2MASS (IR)

Solar sy stem ephemerides (e.g., JPL DE405) aligned to ICRF

Accu racy of representat ion var ies con siderably Let thebuy er beware!



Compl icat ions in Establ ish ing

Reference Frames

Problem is over-determ ined: only need two ob jects to defineor ientat ion of axes

Therefore, if N objects in a catalog , there are ~N2/2

independent reference frame defini t ions wh ich wi l l not , in

general , be con sistent due to errors in coordin ate values

Not too bad a prob lem as long as errors are random

If errors are a funct ion of p os it ion, the reference frame is

warped (sys tematic distor t ions )

Also pro blematic i f errors are a funct ion o f other

character ist ics:

For stars, br ightness or co lor

For Earth stat ions , type of ins trument / techniq ue


16/95

(2.37, +26.1)

(1.52,3.4)

(0.89, +18.4)

(1.32, +5.9)

(3.10, +1.7)

(1.21, +22.8)

(2.05,1.7)


17/95

(2.37, +26.1)

(1.52,3.4)

(0.89, +18.4)

(3.10, +1.7)

(1.21, +22.8)

(2.05,1.7)


18/95

Using a warped reference

frame errors in

coordinates a function of

position


19/95

Using a warped reference

frame errors in

coordinates a function of

position

Each measured positionof the target is slightly

wrong, because the star

positions on which it is

based are slightly wrong


20/95

What our tracking

measurements actually

mean


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What our tracking

measurements seemto

mean


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1950

1976

1990

2005

Actual Path

Measured Path

Why Star Posit ions , and the Reference

Frames They Define, Degrade w ith Time

E M f th ICRF R d i


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Naval Oceanogr aphy 23

Even Many of the ICRF Rad io

Sources Seem to Move

From USNO Radio

Reference Frame

Image Database

(RRFID), A. Fey et al.

A Si i l P b l i th T t i l


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A Sim i lar Prob lem w ith Terrestr ial

Frames Stat ions Do Move

Final l The Bar centr ic to


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Final ly: The Barycentr ic to

Geocentr ic Trans form at ion

BCRS GCRS CIRS TIRS ITRS

relat iv ist ic rotat ions

t ransformat ion (a function of EOPs)

How do we go from the Barycentr ic Celest ia l Reference System (BCRS)

to th e Geoc entr ic Celestial Reference Sys tem (GCRS)?

No te: GCRS = Earth -Centered Inerti al (ECI)

That is, how do w e transform star coord inates f rom the solar system

barycentr ic sy stem of the star catalogs to the geocentr ic system in

wh ich w e actual ly o bserve the stars on a given date?


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Naval Oceanogr aphy26

BCRS

GCRS

solar systembarycenter

BCRS and GCRS


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BCRS to GCRS Trans format ion

Posit ion s in star catalogs represent where the stars would beseen from an ideal ized barycentr ic s yst em at a certain epoch.

To get observed geocentr ic coordin ates of s tars for a given

date and time, they need to be adjus ted for:

Orbi tal mo t ion, if par t of a binary or mul t ip le system

Proper mot ion (3-D space veloc i ty)

Parallax

Gravitat ional l ight def lect ion

Aberrat ion o f l ight

There are comparable adjustments for planetary or spacecraft

ephemerides expressed in the BCRS

Relat iv is t ic terms in the

aberrat ion fo rmu la

ef fect ively imp lement

the BCRS to GCRS

transformat ion


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Why A l l This is Impo rtant

An y l ist of real objects and th eir coord inates def ines a referenceframe

It can be good , bad, or something in b etween

I t may not be cons istent w ith th e ICRF or HCRF (for celest ial

coo rdin ates) or the latest ITRF (for terrestr ial coor din ates)

If i t is based on old d ata, i ts accu racy has pro bably degraded

signi f icant ly

It is a bad idea to keep u sing s ome l is t of co ord inates handed down

from generation to generation

The FK5 is ob solete!

Please consult USNO!


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Earth Orien tat ion

Parameters (EOP):

Def in i t ions and theiruse in trans format ions

Defini t ion o f Earth Orientat ion


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Naval Oceanogr aphy

Defini t ion o f Earth Orientat ion

Parameters

Earth orientat ion parameters (EOPs) desc r ibe the

direct ion of axes f ixed to the Earth in space

used to transform between gro und based coordinates

(terrestr ial reference frame) and inert ialc oordinates(celestial reference frame)

5 EOPs

2 polar motio n (PM-x and PM-y)

1 Earth ro tatio n ang le (UT1-UTC)

2 celestial pole (and or X and Y)


31/95


Three Aspects of Earth Rotat ion

1 Path of rotation axis inspace (wrt GCRS)

precession / nutation

1

2

3

2 Path of rotation axis

across Earths crust

(wrt ITRS)polar motion

3 Rotation angleUT1

All are functions of time

Two schemes for t ransfo rm ing


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ITRSGCRS vWSNPBv =

Polar

Motion

Sidereal

Time

Nutation

Precession

Frame

Bias

ITRSGCRS v'WRQv =Precession+ Nutation+ Frame

Bias

EarthRotation

PolarMotion

NEW:

OLD:

Two schemes for transfo rm ing

between the ITRS and GCRS



33/95


ITRSGCRS vWSNPBv =

Polar

Motion

ITRSGCRS v'WRQv =Polar

Motion

NEW:

OLD:




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Polar Mot ion

Left-handed coord inatesystem

2 dom inant mo t ions

Chand ler wobb le (430 d)

Annual wobble (365 d)

Other smaller amp l i tude

stochast ic mot ions

Causes of po lar mo t ion Oceans (pressu re>current)

Atm osp here (press.>wind )

Hydro logy?


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Spectrum

Prograde Annual Wobble

Prograde Semi-annual Wobble

Atmospheric Tides

Precession

Nutations

Free Core Nutation

1 2-2 -1Frequency in the Terrestrial Reference Frame (cycles per day)

2 3-1 0 1

0

Frequency in the Celestial Reference Frame (cycles per day)

POLAR MOTION

NUTATION

ChandlerWobble



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ITRSGCRS vWSNPBv =Sidereal

Time

ITRSGCRS v'WRQv =Earth

Rotation

NEW:

OLD:




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UT1-UTC

Dominant mot ions Trend

Decadal

Annual /semiannual

Tidal Other smal ler ampl i tude

mot ions

Causes of UT1-UTC

Tidal decelerat ion

Internal changes ininer t ia tensor

Atmosp here (wind s)

Solid Earth t ides


38/95


UT1-UTC Spect rum

Frequency

annual

semi -annual

southern

oscillation

quasi-biennial oscillation

40-50 -day oscillations

monthly

fortnightly

atmospheric tides

decade fluctuations

(from core?)

atmospheric modes

solid Earth and ocean tides

0.1

year-1

0.2

year-1

1

year-1

0.1

month-1


39/95


Leap Seconds

Leap seconds are a convent ional at tempt toalign Earth rotat ion t im e (angle) w ith clo ck t im e(UTC)

|UT1-UTC| < 0.9 s

Leap seconds occur at end o f June or Decemberbu t the t ime between leap seconds isunpredictable

Expected to occur w i th increasing frequency

Problematic for operat ional sys tems

Internat ional Telecommun icat ions Union (ITU) iscons ider ing a redefini t ion o f UTC to el im inateleap seconds

UT1 and UTC would diverge

Potent ia l Impact o f Leap Second


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Potent ia l Impact o f Leap Second

El iminat ion

No impact i f system doesnt assume that

UT1UTC, and

makes no

assumpt ionregarding s ize ofUT1-UTC

Impact i f sys tem

assumes that

UT1UTC, or

assum es a l imi t onthe size of UT1-UTC


41/95


Suggest ions Regarding Leap Second

If you are using UT1UTC,need to determ ine impact

of chang ing to input UT1-

UTC into operat ional

procedures

If you assumenumerical restr ic t ionson UT1-UTC, need todeterm ine impact onel iminat ing

restr ic t ions

Any signi f icant problem with operat ional procedures shou ldbe reported to USNO



42/95


ITRSGCRS vWSNPBv =Nutation

Precession

Frame

Bias

ITRSGCRS v'WRQv =Precession+ Nutation+ Frame

Bias

NEW:

OLD

:

Two schemes for transfo rm ingbetween the ITRS and GCRS


43/95


Precession and Nutat ion

Precession: the long-term,

smooth, secular motion

23.5circle around theecliptic pole in 25,800 years

Nutation: the smaller, short-

term periodic motions

Largest component: 18x12

arcsecond ellipse traced out in

18.6 years

Precession / nu tat ion : The changing direct ion of the Earthsaxis in space (now specif ical ly with respect to the GCRS) due

to to rques exerted by th e Moon, Sun, and planets

(Diagram from G. Beutler)


44/95


Celes tial Pole

Dominant mo t ions at

frequencies

18.6-year

Semiannual

For tn ight ly

Causes of precession -nutat ion are gravi tat ionalpul l of celest ia l bod ies onthe equator ia l bu lge ofEarth

Very w el l determin ed Small component not

caused by g ravi ty

C


45/95


Celestial Pole Models

Since direct ion o f celest ia l pole in space is affected mainlyby gravi tat ional attract ion of Sun , Moon, and planets, i t is

very p redictable

Current models IAU 2000 nutat ion and IAU 2006 precession

Residu als between models and obs ervat ions (dand d ordX and dY) due to Free Core Nu tation (FCN)

Other variable amp litud e terms (e.g. annual)

Errors in models

Estimated error in models ~0.5 mas

Precession / Nutat ion Observat ion s


46/95


Precession / Nutat ion Observat ion sLatest Resultswrt P03 / IAU2000A

Model errors

~0.5 mas

(Figure from Capitaine et al. 2008)

C l t i l P l M d l


47/95


Celestial Pole Models

Older models IAU 1980 nu tation and IAU 1976precession

Residuals between m odels and observat ion s (dand d) predom inan tly due to

Errors in m odels

Est imated error in models ~10 mas

Error is systemat ic, no t random

Precession / Nutat ion Observat ion s


48/95


Precession / Nutat ion Observat ion sLate 90s Resultswrt Lieske / Wahr

(Figure from Ma et al. 1998)

Model errors

~10 mas


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49

Time Scales

B i
http://tf.nist.gov/cesium/parcs.htm


50/95


Concepts

Frequency

Repeatable

phenomenon

Length o f the

t ime uni t

Epoch Naming

convent ion

Sources o f Time

Ast ronomy

Based on

Earths rotat ion

Atom ic Clocks

Based on

frequency of anatom ic trans i t ion

Basics

Time Scales


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51

Time Scales

UT1 (Universal Time)Measure of Earths rotation angle wrt Sun

Determined by conventional expressionEarth Rotation Angle

Greenwich Mean Sidereal TimeUT0 = UT1 including polar motion

UT2 = UT1 with conventional Seasonal Correction

Earth Rotation

Coordinated Universal Time (UTC)

* TAI corrected by leap seconds

* Basis for civil time

International Atomic Time (TAI)

Atomic Time

Space-Time Coordinates

Terrestrial Time (TT)

Geocentric Coordinate Time (TCG)

Barycentric Coordinate Time (TCB)

Ephemeris Time

Earth Revolution

Dynamical Time

Terrestrial Dynamic Time (TDT)

Barycentric Dynamic Time (TDB)

Sidereal TimeMeasure of Earths rotation anglewrt Celestial Reference Frame

Determined by conventional

expression

Echelle Atomique Libre (EAL)

Time Scales


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52

Time Scales

UT1 (Universal Time)Measure of Earths rotation angle wrt Sun

Determined by conventional expressionEarth Rotation Angle

Greenwich Mean Sidereal TimeUT0 = UT1 including polar motion

UT2 = UT1 with conventional Seasonal Correction

Earth Rotation

Sidereal TimeMeasure of Earths rotation anglewrt Celestial Reference Frame

Determined by conventional

expression


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53

Sidereal Time Solar Time

Universal Time (UT)


54/95


Time measured by the Earths rotat ion wi th respect to the Sun

Elementary conc eptual def in i t ion b ased on the diurn al mo tion of th eSun

Mean so lar t ime reckon ed from m idnight o n the Greenwich m erid ian

Tradi t ional def in i t ion of the second used in astronom y

Mean s olar second = 1/86 400 mean so lar day

Three Forms

UT1 is m easure o f Earths rotat ion angle

Defined

By observed sidereal time using conventionalexpression

GMST= f1(UT1) by Earth Rotation Angle

q = f2(UT1)

UT0 is UT1 plu s effects o f polar mo t ion

UT2 is UT1 co rrected b y co nvent ionalexpression for annual var iat ion inEarths rotat ional speed

Universal Time (UT)

Mean Time vs Apparent Time


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Mean Time vs . Apparent Time

Time interval between su ccess ive passages of the Sun over a meridian is

not constant

Inc l ination o f the Earths axis

Eccentr ic i ty of the Earths orb i t

Dif ference between mean t ime and apparent t ime is cal led the equat ion

of t ime

Mean noon precedes apparent noo n by 14.5 minu tes on February 12

App arent noon p recedes mean noo n by 16.5 minutes on Novemb er 3

inclination effect

combined effect

eccentricity effect

Time Scales


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56

Time Scales

International Atomic Time (TAI)

Atomic Time

Echelle Atomique Libre (EAL)

Atom ic Time


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Atom ic Time

First cesium -133 atomic clo ck establ ished at National Phys ical

Labo ratory (NPL) by Essen and Parry in 1955 Frequency o f cesium transi t ion measu red in 1955 in terms o f the

second of UT2

9 192 631 830 10 Hz Frequency o f cesium transi t ion measu red by Markow itz, Hal l ,

Essen, and Parry du ring 19551958 in terms of the second o f ET

9 192 631 770 20 Hz Defini t ion o f the SI second adopted b y th e 13th CGPM in 1967

Secon d o f atomic t im e = second of Eph emeris Time (ET)

Second = duration of 9 192 631 770periods of radiation corresponding to

the transition between the two

hyperfine levels of the ground state of

the cesium-133 atom

In ternational A tom ic Time (TA I)


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In ternational A tom ic Time (TA I)

Coordin ate t ime scale in a geocentr ic reference frame with the SI

second realized on the rotat ing geoid as th e scale unit Continu ous atomic t im e scale determ ined by Bureau Internat ional

de lHeure (B IH) sin ce 1958, now m aintained by Bureau

Internatio nal des Poid s et Mesu res (BIPM)

TAI = UT2 on Janu ary 1, 1958 0 h

Fol low -on from A.1 (maintained at USNO with in pu t from 9 other laborator ies or ig inal ly.

- now only USNO)

AM (at BIH with in pu t from m any laborator ies)

A3 at BIH with in pu t from 3 best laborator ies

Others

Becam e AT (or TA) in 1969, TAI in 1971

Time Scales


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59

Time Scales

Coordinated Universal Time (UTC)

* TAI corrected by leap seconds

* Basis for civil time

Coo rd inated Universal Time (UTC)


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Name Coord inated Universal Time(UTC) adop ted by IAU in 1967

From 1961 to 1972 UTC contained both frequency offsets andfract ional (less than 1 s) steps to maintain agreement with UT2

within about 0.1 s

In 1970 form alized by International Radio Consu ltative Committee

(CCIR) of Internation al Telecommun ication Union (ITU) in 1962

ITU-R TF.460-6 STANDARD-FREQUENCY AND TIME-SIGNALEMISSIONS(1970-1974-1978-1982-1986-1997-2002)

Inco rporated by reference into the Radio Regu lat ions

UTCTAI

Adjustments

Leap Seconds may be introduced as the last

second of any UTC month.

December and June preferred, March and

September second choice.



61/95


In 1972 present UTC sys tem w as imp lemented, with 1 s (leap seco nd ) steps

but n o frequency offsets to maintain agreement w ith UT1 with in 0.9 s Def in i t ion of UTC is a comp rom ise to provid e both the SI secon d and an

approx imat ion to UT1 for celest ial navigat ion in same radio em issio n


YEAR

1960 1970 1980 1990 2000 2010

0

10

20

30TAI-UT1

TAI-UTC

Leap Seconds Introduced

Standard Time


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Standard Time

U. S. Code specif ies UTC offset by integral hours as standard t im e

Federal (DoD and DoT) Radionavigat ion Sys tems document specif iesUSNO as time/frequency s tandard fo r all U. S. radion avigationservices

DoD Master Posit ion Navigat ion and Timing Plan s pecif ies USNO asstandard t ime/frequency fo r DoD

SEC regulat ions specify NIST as s tandard for t im ing sales o fsecur i t ies

Federal Standard 1002A - 1990 (Time and Frequency Info rmation inFederal Telecommunicat ions Sys tems) specif ies NIST as standard

USNO and NIST have Memorandum of A greement

UTC(USNO) and UTC(NIST) do no t d if fer by more than 100 nano secon ds .

Typically they do no t di f fer by mo re than a few tens of n anoseconds

Time scales of both in st i tut io ns are traceable to each oth er at thenanosecond level

GPS Sys tem Time (GPS Time)


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GPS Sys tem Time (GPS Time)

Each satel l i te carr ies a su i te of cesium o r rubid ium atom ic clock s

Sate ll i te and global t racking network atom ic cloc ks are used to form a

common s tat is t ical t ime scale known as GPS Time

No leap secon ds

Origin is m idn igh t of J anuary 5/6, 1980 UTC

Steered to w ithin 1 s o f UTC(USNO), except no leap s econd s are inserted Relat ionsh ips with TAI and UTC (with in s tat ist ical error)

GPS Tim e = TA I19 s = con stant

Re-compu ted every 15 m inutes basedon satel l i te ranging m easurementsmade by GPS monitor stat ions

OCS softw are est imates clockdif ferences of GPS satel l i te andmon i to r s tat ion c locks

Satel l i te cloc k dif ferences up loaded toeach satell i te app roxim ately o nce aday

The addi t ional correct ion contained inthe GPS broadcast message al low s aGPS t imin g us er to pro du ce TAI orUTC time.

Implement ing GPS Time


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USNO cont inuous ly moni tors GPSsatel l i tes

Provid es GPS Master Contro l

Stat ion dif ferences between GPS

Time and UTC(USNO)

Master Control Stat ion KalmanFilter (MCSKF) generates c lock

solu t ions to m inim ize UTC(USNO)-

GPS

Correct ions to create both GPS

Time and GPS

s del iveredpredic tion of UTC(USNO) are

appl ied in GPS receiver by

apply ing co rrect ion c onta ined in

the GPS data message

Implement ing GPS Time

Tell ing GPS Time


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Tell ing GPS Time

GPS Time counts in weeks and second s of a week from midn ight ofJanuary 5/6, 1980 UTC

Weeks begin at the Saturday/Sunday transi t ion

Days of th e week are numbered, with Sund ay being 0; Saturday isday 6

GPS week 0 began at th e begin nin g o f the GPS Time Scale. ( 60 x 60 x 24x 7)

Within each w eek the t ime denotedas the second o f the week

Number between 0 and 604,800

(60 x 60 x 24 x 7)

Time scales from GPS


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Time scales from GPS

SV Clocks

CesiumRubidium

Monitor StationClocksCesium

GPS System

Time

Monitoring

Data

GPS Time

SV Time

SV Nav Message

UTC(USNO) - GPS Time

SV Time UTC(USNO)GPS Time

GPS

USERS

USNO

Time Scales


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Ephemeris Time

Earth Revolution

Relativis t ic Time Scales


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Relativis t ic Time Scales

Ephemeris Time (ET) was based on the

Newto nian theory of gravi tat ion andmade no dist inct ion between p roper

t ime and coo rdinate t imeProper t ime: Reading of an ideal cloc k

in i ts own rest frame

Coord inate t ime: Time coord inate in

given sp ace-t ime c oord inate system

Between 1976 and 2000, the IAU

adopted new relat iv ist ic t ime scales

con sistent with the general theory of

relat iv i ty who se unit is the SI second

Note that relativis t ic times aretheoretical

- Time not kept on a clock

Time Scales
http://www.allposters.com/GetPoster.asp?APNum=263090&CID=5A485803D7764E81A8BF1D96CC003D81&PPID=1&search=einstein&f=c&FindID=17144&P=1&PP=6&sortby=PD&cname=Albert+Einstein&SearchID=


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Space-Time Coordinates

Terrestrial Time (TT)

Geocentric Coordinate Time (TCG)

Barycentric Coordinate Time (TCB)

Terrest rial Time (TT)


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Terrest rial Time (TT)

In 1991 IAU ren amed TDT as Terrest rial Time

(TT) Uni t is the SI second on the geoid and is def ined

by atomic cloc ks on the surface of the Earth

Origin o f January 1, 1977 0 h

TT = TAI + 32.184 s

Maintains c ont inu i ty w ith Eph emeris Time (ET)

Theoret ical equivalence of t ime m easured b y

quantum mechanical atomic interact ion and t ime

measured b y g ravi tat ional p lanetary interact ion

To be used as the time reference for apparent

geocentr ic ephemerides

An y dif ference between TAI and TT is a

cons equence of the physical defects of

atomic t im e standards, and has probably

remained with in the appro ximate l imi ts of10s. It may increase slow ly in the futur e as

t ime standards impro ve. In mos t cases, and

part icular ly for the pub l icat ion of

ephemerides, th is d eviat ion is negl ig ib le

T since 1600


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T since 1600

After F.R. Stephenson and L.V. Morrison, Phil. Trans. R. Soc. LondonA351, 165 202 (1995)

TT

ET

1977.0

Ju lian Date


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Ju lian Date

Used for cont inuous counts o f days

Joseph Justu s Scal iger in 1583 used three cycles :

The Jul ian calendar in use unti l the Gregorian calendar reform of 1582

The Golden Numbercycle assoc iated with Meton in the fi f th centu ry B.C., equated 19 yearswi th 235 months .

A tax cycle or indic t ionof 15 years us ed in legal and financial org anization of th e RomanEmpire

Year could be characterized b y i ts posi t ion (S) with in a 28-year solar cycle, i ts p osi t ion

(G) with in th e 19-year cycle of Golden Numbers, and its pos it ion (I) with in the Romantax cycle

Becaus e 15, 19 and 28 have no common factors S, G,

and I repeat after 281915 = 7980 year s. Scal iger cal led this a Jul ian per iod, not in hono r of his

father as is frequently asserted, but becaus e of the

inv olvement of the Jul ian Calendar.

Know ing that the year 1 B.C. was ch aracterized by S=1,

G=1, I=3, Scal iger c om put ed th at S=1, G=1, I=1 occ urred

for 4713 B.C. This p rovided h im with the star t ing year

Modified Julian Date (MJD) is defined as JD2400000.5

Timescale shou ld be speci f ied when precis ion matters,

e.g., MJD 47479.25 TA I.

Traceabil i ty
http://upload.wikimedia.org/wikipedia/commons/b/b6/Joseph_Justus_Scaliger.JPG


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Traceabil i ty

International Organizat ion fo r Standardizat ion (ISO) International Vocabulary ofBasic and General Terms in Metrology, traceabi l i ty is defined as:

The property of a result of a measurement or the value of a standard whereby it can berelated to stated references, usually national or international standards, through anunbroken chain of comparisons all having stated uncertainties.

GPS Time can be made direct ly tr aceable to UTC

Measured difference between UTC and GPS Time is reported in the BIPM Circular T, withan accur acy of 10 ns.

GPS Time directly traceable to UTC by being tr aceable to UTC(USNO), whic h is also

traceable to UTC via the Circu lar T.

Alternate means of dir ect traceabi l i ty may also be establ ish ed via any oth er nationallaborator y, such as NIST.

Phi losoph y is that only a user shou ld decide traceabi li ty issu es because only thatuser know s the speci f ics of their system

User

National

Standard

International

Standard (BIPM)

Time / Frequency

Transfer

Time Dissemination


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ComputerModem

GPS(8 ns)

Two-way SatelliteTime Transfer

(1ns)

Internet(1ms)

Master Clock

Alternate Master Clock

Ships, Submarines, Aircraft Ground Forces

Shore Activities

Space Commands

NGA GPS

CommunicationsCenters

Operation Centers

GPS DSCS

Classified Programs

GPS

DSCS

SatelliteTracking Ranges

Satellite GroundControl Stations

NGA

DSN

Loran-C NAVSECGRU

USERS

Voice


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Software for Trans form ing

Between Celes t ial andTerrestr ial Sys tems

Scope


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Naval Oceanogr aphy

p

Au thor i tat ive so ftware

Tied to internat ional standards

Produc ed or vetted by DoD SMEs

Free

Source-cod e produc ts

Web-based calcu lator

76

Source-Code Products


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Naval Observatory Vector Astrometry Software(NOVAS)

Standards of Fundamental Astronom y (SOFA)

NOVASN l Ob V A S b i


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Complete sof tware package for pos i t ional astronom y

Instantaneou s coordin ates and radial veloci ty o f any s tar orplanet

e.g., apparent, topoc entric, astrometric places

Observer at geocenter, on or near surface, on near-Earth sp acecraft

Terrestrial celestial transformation

Bui ld ing b locksand sup por t func t ions for these calcu lat ions

e.g., precessio n, nutation, frame bias, star-catalog tran sformation s, etc.

Produced and suppor ted by USNO

Used for US sect ions of The Astron om ical Almanac

Status

Version 3.1 released in March 2011

Python edi tion n ear ly com pleted

Naval Observatory Vector As tronomy Subrou t ines

SOFASt d d f F d t l A t


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Col lect ion of rou t ines w hich implement of f ic ial algor i thms for

fundamenta l-astronom y computations Primar i ly supp orts celest ial terrestr ia l trans form at ion

ast ronomyrout ines

e.g., calendars, t ime scales, precession, nutation , star space mo tion, and starcatalog transform at ions

vector /matr ix

rout ines Service of IAU Divis ion I

Managed by international review board

Basis for IERS Convention s Chapter 5 software

Used for UK sect ions of The Astron om ical Almanac

Status

Lates t release 2010-12-01

Standards of Fundamental Astronom y

NOVAS/SOFA Comparison


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Similar i t ies

Both come from author i tat ive sources

Bo th suppo rt latest IAU resolut ions

Bo th are consistent w i th IERS Convent ions fo rpract ical levels of accu racy

Bo th have Fortran and C versions

Bo th con tain testbedand demons trat ionprograms



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Developed independently Except NOVAS u ses SOFA code fo r IAU 2000A nu tation

NOVAS current ly has b roader scope

i .e., instantaneous coo rdin ates o f celest ial bo dies (Sun, Moon ,planets, stars, etc.)

NOVAS con tains i ts own improv ed low -precis ion

nutation model

2000K : 0.1 mas level, 1700 to 2300 (tru nc ated IAU 2000A)

Documented in USNO Circular 181

NOVAS uses an alternat ive algo r i thm for locat ion o f

CIO

Differences



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Differences (con t inued)

SOFA includes su ppo rt for older models e.g., IAU 1976 precessio n, IAU 1980 nutatio n

SOFA inc ludes small co rrect ion s to IAU 2000A

nutat ion

SOFA has finer stru ctu re

NOVAS/SOFA Numerical Comparison


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Test: Compare ITRF GCRS transformation using

SOFA and NOVAS February 2009: latest Fo rtran SOFA and NOVAS F3.0g

(beta)

May 2010: latest C edit ions of SOFA and NOVAS

Results: Differences ~ 1.8 as

Attr ibutable to very sm al l terms from IAU 2006 precession mo delthat were inclu ded in SOFA imp lementat ion of IAU 2000A nutat ionmodel

Differences drop to ~ 0.2 as when these terms are

removed

Ful l discussion in NOVAS Users Guides

Which Produc t Should I Use?


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Use NOVAS When You need coord inates of celest ia l bodies (Sun, Moon , planets,

stars , etc.)

You r project requires use of DoD or GOTS cod e

Use SOFA When

You r project requires us e of off ic ia l IAU co de You n eed to com pute the actual transform ation matr ices

You also need c ode for now-obsolete models

Both products are authoritative, well-documented,relatively easy to use, and comply with IERS Conventions

and IAU recommendations.

USNO Equ ino x-Based ITRF-to -GCRS Calcu latorBackground


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Background

Upgraded equ inox -based transfo rmation matr ix calculator is being

tested at the USNO EO Department server athtt p://maia.usno .navy .m il/t2c36e/t2c36e.htm l

The IERS Convent io ns (2010) TN36-based v al idation code for compu t ingthe equino x-based ITRF to GCRS transfo rmat ion

Written in FORTRAN

Rely ing heavi ly on code from http:/ / tai.bipm.org/ iers/conv2010/conv2010.htmland SOFA.

Observable quanti t ies are obtained from a versio n of fin als2000A.dai ly

Later ob servables c an be obtained from evaluat ion of the NGA 5- liner

Nutat ion and t ida l model changes

Major ch anges are updates to the nutat ion and long -period t idal mod els Interpolation of observable quanti t ies, intermediate quanti t ies, and oth erou tpu t quant i t ies are simi lar to the TN32-based calculator

Calcu lator User-In terface
http://maia.usno.navy.mil/t2c36e.htmlhttp://tai.bipm.org/iers/conv2003/conv2003_c5.htmlhttp://tai.bipm.org/iers/conv2003/conv2003_c5.htmlhttp://maia.usno.navy.mil/t2c36e.html


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Naval Oceanogr aphy

Equ ino x-Based ITRF-to -GCRS CalculatorUser Interface (co ntin ued)


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User Interface (co ntin ued)

User chooses dates and tim e intervals

Code p roduces a f i le containin g th e ITRF-to-GCRS

transform at ion and desired intermediate quant i t ies

Standard outpu t is the trans formation matr ix from terrestr ia l

to celest ia l frames

Option al quaternion /euler-parameter ou tpu t

Option s for intermediate quanti t ies include the polar mo tion,

GMST, Equation of the Equinoxes, Precession, Nutat ion, and

combined bias-precession -nutat ion matr ices or quaternion s

Future developments include

CIO/CIP com pat ible (as op po sed to equino x b ased) us ing 2006

IAU Precessio n Mod el

Calculator Outpu t


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Naval Oceanogr aphy

Terrest rial-to-celest ial (T2C)rotation matr ix

Intermediate rotat ion m atr ices

are below the T2C matr ix

Resources A Sample


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IERS Conventi on s (2010):

http://maia.usno.navy.mil/conv2010/conventions.html

Conventions userssurvey available at

http://maia.usno.navy.mil/conv2010/Conventions_Survey.html

USNO Circu lar 179 (PDF vers ion ):

http://aa.usno.navy.mil/publications/docs/Circular_179.php

IERS FAQs: http://www.iers.org/IERS/EN/Service/FAQs/faq__cont.html

IERS Earth rotat ion data (Bu l let ins A & B):

http://www.iers.org/IERS/EN/DataProducts/EarthOrientationData/eop.html?__nnn=true

The Astronom ical Almanac:

http://aa.usno.navy.mil/publications/docs/asa.php

Software Resources


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NOVAS

http ://www.usno .navy.mi l /USNO/astronom ical-appl icat ions/software-products/novas/

SOFA

http:/ /www.iausofa.org/

USNO Earth Orientat ion Matr ix Calcu lator

http://maia.usno.navy.mil/t2crequest/t2crequest.html

Backups


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Polar Mot ion


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OLDTransformation:

( ) ( )

=

=

PPP

PP

PPPPP

PXPY

ycosxcos0xsin

ysinycos0

ycosxsinysinxsinxcos

yRxRW

NEWTransformation:( ) ( ) ( )

++

++

=

=

PPPPP

PPPPPPP

PPPPPPP

PXPYZ

ycosxcosysinxcosxsin

scosysinssinycosxsinscosycosssinysinxsinssinxcos

ssinysinscosycosxsinssinycosscosysinxsinscosxcos

yRxRsRW

xPand yPare the pole coordinates

sis new and is given by

T704000.0s =

nutationpptidalppUSNO/IERSpppp y,xy,xy,xy,x ++=

tidalppUSNO/IERSpppp y,xy,xy,x +=

o Terms with periods


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ICD-GPS-200C

GPS time is established by the Control Segm ent and is referenced to a UTC (as maintained by the U.S. NavalObservatory) zero time-point defined as m idnig ht on the nigh t of Janu ary 5, 1980/mor ning o f January 6, 1980. Thelargest unit us ed in stat ing GPS time is one week defined as 604,800 second s. GPS time may dif fer from UTCbecause GPS time shall be a con tinuo us tim e scale, while UTC is corrected periodic al ly with an integer num ber ofleap seconds . There also is an inherent but bou nded d rif t rate between the UTC and GPS time scales. The OCSshal l contro l the GPS t ime scale to be with in one microsecond of UTC (Modulo o ne second) .

2003 CJCS Master Posit ion ing, Navigation and Timing Plan (CJCSI 6130.01C )

The accuracy of th e GPS transfer of UTC is measu red at the Master Clock of th e United States, which is loc ated atthe USNO. The USNO calculates the accuracy and delivers it to the Operational Control Segment (OCS). The OCSmaintains acc urate time transfer by calculat ing GPS time, calculat ing ind ividu al space vehicle (SV) correct io ns to

GPS time, and uplo ading c orrect ion s into the SV databases for subsequ ent re-broadc ast to users. The OCSmaintains a steady state time transfer accuracy of th e GPS signal to an error of less th an or equal to 20nanoseco nds (nsec) (95 percent) relat ive to UTC (USNO) (threshold) and 10 nsec (95 percent) relat ive to UTC(USNO) (objective).

GPS Timeis us ed to in dicate the internal GPS System Time as defined in sect ion 3.3.4 of ICD-GPS-200C (2003).

" UTC(USNO) via GPS" is us ed to ind icate GPSs del ivered pr edict ion of UTC (USNO).

In mathemat ical expressions where "UTC(USNO) via GPS" migh t be considered to be awkward, tUTC

may b e subst i tuted. Only in text f i les that do not permi t the display of subscr ipts should t_UTCbe used as a subst i tute

for tUTC

This nom enclature may be extended, i f requi red, to speci f ic appl icat ions of GPS for other m eans oft ime dissem ination by addin g the techniq ue emplo yed, e.g. UTC(USNO) via GPS common view

Dynam ical Time


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In 1976 IAU def ined dyn amical t ime scales con sistent

with g eneral relat iv i ty to dist ing uish b etween t imescales with o r igins at the geocenter and th e

barycenter.of th e solar sys tem

Named Terrestrial Dynamic al Time (TDT) andBarycen tr ic Dyn ami cal Time (TDB) in 1979 At the in stant 1977 January 01 d 00h 00m 00s TAI, the

value of the new t im e scale for apparent geocentr icephemerides is 1977 January 1d 00h 00m 32.184 exactly.

The unit is a day o f 86400 SI second s at mean sea level.

The t imescales for equat ions o f mo t ion referred to the

barycenter of the solar system is s uch that there wi l l be

only p er iodic var iat ions between these t imescales and

those o f the apparent geocentr ic ephemerides.

TDT maintains c ont inu i ty wi th ET By c hoo sing an appropr iate scal ing factor TDB

determined from TDT by a conv ent ional mathematical

expression

Barycentr ic Ephemeris Time (Teph)


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Coord inate t ime related to TCB b y anoffset and a scale factor

Ephemerides (e.g.DEnnn) based uponthe coo rdinate t ime Tep hare automatical lyadjusted in the creat ion pro cess so thatthe rate of Tep hhas n o overal l di f ferencefrom the rate of Terrestr ial Time (TT)

Therefore also no overal l di f ference fromthe rate of B arycentr ic Dynam ical Time(TDB).

Space coordin ates ob tained from theephemerides are consis tent with TDB.

JNC 2011 Reference Systems Tutorial

Documents

reference systems tutorial

outl ine reference systems

naval oceanogr aphy

ransformat ion

accelerat ion

navigat ion

reference frame contro

primaryreference systems