UNCLASSIFIED D U N TN SECURITY CLASSI I ICA It IN OF TIllS PAGE REPORT DOCUMENTATION PAGE Ia. REPOFRTTSECZLRIY CILASSIFICAl ION It H STP IF'T i Vt MAlRINf(,S UNCLASSIFIED 2a. SECUHITY CLASSIFICATION AUTHORITY 3 i .1'Iý III ION AVAIl AI3ILII YV ! rEPORT N/A Approved for public release; 2b, DECLASSIFICA1 IONDOWNGRADiNC- SCHE DULE distribution unlimited. ,., 4. PERFORMING ORGANIZATION REPORT NUM[lEHi5) L, I. I I-N , i HIF .AI.,, I IN 1H T NUMBER(S) N/A NIA 6a NAVi Of PERFORMING U)iGANIZA1ION 6h. OFF ICE SYMBOI 7.,I NA7t 01" V(M N 0-51(, OQ (,ANIZATION Defense mapping Agency "(III l Hydrographic/Topographic Center DMAHTC/GS N/A _ _ _ _ _ _ _ 6c. ADDRESS I I, ."I _.s' 1 I /11'(,st StDHFl (I . ..... Il /WC1 EELECTE2 6500 Brookes Lane "P. B Washington, D.C. 20315-0030 NAAPR 2 3 8 Sa, NAME ~.'I '. SP0:.Wlt, 11 OFtF I( SY-~MBOL 9PROIC(JRFI- ENT iNSTI-I)IMENI DNION NUMBER R C, AN, ZA r IO H 1r1 ,, Defense Mapping Agency EDMAHQ/PAO A Sc ADDRESS W... . . ' 1 /1 " .!) 1 -1 t'I'VCE Of F U,,,NG NOS P'RilRAM PRF(-,.IF C T TASK WORK UNIT , IRME: NO Building 56, U. S. Naval Observatory (gM PrOIt (AS WO UI Washington, D.C. 20305-3000 1 I '1 1'" ,Ih,,, ... .... . The DMA/GPS Earth 4.- Orientation Prediction Service JN/A ,N/A /A N/A FinaNA-l 28 April 1.986 14~ 00 Fourth International Geodetic Symposium on Satellite Positioning, 28 April - 2 May 1986, It0- . 4Global Positioning System (GPS) - UTI-UTC . V O8 v 05 Earth orientation prediction Polar motion _q Since mid-1984, the Defense Mapping Agency (DMA) has been computing predictions of pole Q position (x and y) and time difference (UTI-UTC AUT) to support the NAVSTAR/GPS orbit determination process. These predictions are based upon the "derived Earth orientation para- meters" published in the U. S. Naval Observatory's Earth Orientation Bulletin (Series 7) and are obtained by fitting these data to a set of models specified in the DMA/GPS Interface - - Control Document. This paper presents a review of the models and processes by which the Earth orientation predictions are computed at DMA. The results of a study to assess the accuracy of these predictions are also presented. Finally, several proposed methods for improving the pre- diction accuracies without altering the basic models are discussed and evaluated. FIE- __iLE COPY "__ _ _ __ _ _ _ _ _ 20 Il'! IIA- 1 f AP; HI I 1 14 1 lAALI ' I I I I k I I IS I C A II 10IN I A ;',' II [. ... ...... , "X I.. .' i . ..... UNCLASSIFIED 22a I... ,I .I HryLl .> . i' 1,1k t I vl, 1 [ " . ., I 5 1, ?, (1If I( SYMPOL John A. Bangert (202) 227-2753 1 DMAHTC/GSGT DD FORM 1473,83 APR UNCLASSIFID ...... * ... I , kA A-,II II AI ON 0f1 I fIS PAGI
Transcript
UNCLASSIFIED D U N TNSECURITY CLASSI I ICA It IN OF TIllS PAGE
REPORT DOCUMENTATION PAGEIa. REPOFRTTSECZLRIY CILASSIFICAl ION It H STP IF'T i Vt MAlRINf(,S
UNCLASSIFIED2a. SECUHITY CLASSIFICATION AUTHORITY 3 i .1'Iý III ION AVAIl AI3ILII YV ! rEPORT
N/A Approved for public release;2b, DECLASSIFICA1 IONDOWNGRADiNC- SCHE DULE distribution unlimited. ,.,
4. PERFORMING ORGANIZATION REPORT NUM[lEHi5) L, I. I I-N , i HIF .AI.,, I IN 1H T NUMBER(S)
N/A NIA6a NAVi Of PERFORMING U)iGANIZA1ION 6h. OFF ICE SYMBOI 7.,I NA7t 01" V(M N 0-51(, OQ (,ANIZATION
FinaNA-l 28 April 1.986 14~00 Fourth International Geodetic Symposium on Satellite Positioning, 28 April - 2 May 1986,
It0- . 4Global Positioning System (GPS) - UTI-UTC .
V O8 v 05 Earth orientation prediction
Polar motion_q
Since mid-1984, the Defense Mapping Agency (DMA) has been computing predictions of poleQ position (x and y) and time difference (UTI-UTC AUT) to support the NAVSTAR/GPS orbit
determination process. These predictions are based upon the "derived Earth orientation para-meters" published in the U. S. Naval Observatory's Earth Orientation Bulletin (Series 7)and are obtained by fitting these data to a set of models specified in the DMA/GPS Interface - -
Control Document.
This paper presents a review of the models and processes by which the Earth orientationpredictions are computed at DMA. The results of a study to assess the accuracy of thesepredictions are also presented. Finally, several proposed methods for improving the pre-diction accuracies without altering the basic models are discussed and evaluated.
FIE-__iLE COPY "__ _ _ __ _ _ _ _ _
20 Il'! IIA- 1 f AP; HI I 1 14 1 lAALI ' I I I I k I I IS I C A II 10IN
I A ;' ,' II [. ... ...... , "X I.. .' i . ..... UNCLASSIFIED
22a I... ,I .I HryLl .> . i' 1,1k t I vl, 1 [ " . ., I 5 1, ?, (1If I( SYMPOL
John A. Bangert (202) 227-2753 1 DMAHTC/GSGT
DD FORM 1473,83 APR UNCLASSIFID
...... * ... I , kA A-,II II AI ON 0f1 I fIS PAGI
.6.
THE DMA/ GPS EARTH ORIENTATION PREDICTION SERVICE
JOHN A- BANGERTDEFENSE MAPPING AGENCY ,.WASHINGTON, DC 20305-3000 ,
U.,
SUMMARY
Since mki-1984, the Defense Mapping Agency (DMA) has been computing predictions
of pole position (x and y) and time difference (UTI-UTC = AU1) I support the
lNavstlariPS orbit detennintion process. These predicons are based upon the 'derived
Earth oinatn n parameters' published in the U. S. Naval Observaiory`s Earth Orientation
B Buetin (Series 7) and are oburted by fitting tese dam'o aset of m•dels specifid in the
DM.VGPS Interfaee Control Document
This paper presents a reviev of the models and processes by vhjch the Earth
orznnton predictions are computed at DMA. The results of a study o assess the accuracy
of these predictions are also presented. Finally, several proposed methods for improv•ing
the prediction accuracies vithout altering the basic models are discussed and evaluated.
1.0 INTRODUCTION
The GPS Master Control Suetion (MCS) has, as one of its primary fuclinhs, the
requirement to provide the GP S satellitew vith ephemeris anrd clck information that can be
tansmitted 1 users in the navigatin message. Tracking data collecmd by five monizr
starrns (MSs) are sent o the MCS and used, in combimaon vith reference traeecories, lo
compute estimates and make pre&dcions of ephemeris and ckck sates for the satei [111.
These ephemeri and clock computations require the ability tD transform beteen an
Earth-fixed reference sysem and a bast inertal system. Completion of this
trnsformaton requires estimates of the Earth orientaton parametrs (EOP).
The BOP consist of the polar coordinats (x and y) and the time difference UTI-UTC.
The polar coordinates reprecent the positon of the tre celestal pole vith respect a a.
* ~reference point fixed to thme crust of tit Earth (the Conventional Internabonal Origin, or
CIO pole). The x coordinate i, posite m the direction of Greenvich and the y coordinate
is positive tvards the vest [21. UT1-UTC (AUT) represents the difference betwen the
ro onal time scale, UTI, and the uniform time scale, UTC (Coordinated Universal
Time). It can be applied tD UTC t recover time baed on the true roiationl rate of the %
Earth (UTI). Prediction of the EOP must be based on extrapolatn of observations.
The Defense Mapping Agency (DMA) is required to supply predttns of the HOP to
Af remaining Kkand Lkam set equal I zero and the perkds R, and R2 are nt used.
The coefficient I and J an dearmined by kest-squa=s uljusmmet Del•s of 6he
processimg sceario for AUT viil be given in Section 2.3.
o•*-.N
'.' .,.,
2.3 EOP PREDICTION SOFTWARE
Predictions of the EOP are mede through the use of a FORTRAN computer program
(EOPP). This program vas designed and coded by Mr. Gregory Arnold of DMA in 1984,
and revised by the author in late 1985. The program first extacs the most recent 435 days
of pole position data and the most recent 32 days of AUT data from the data base. The 435
days of pole coordinates span (approximately) one Chandler period. The decision to use
32 days of AUT data for predton purposes ye based on a study performed at USNO
[4 1. This study indicatd that The smallest root mean square predictn errors (compared
Io Bill data), using a model similar fthe one described in Section 2.2.2, vere whjved-
using 32 days of AUT data.
The EOPP program then performs an unveighted bath least-squares fit lo the x data,
using the model descnrbed in Sectn 2.2.1. Based on the results of this fit, the data awe
edited so that any point vhose post-fit residual lies outside three slardard deviations is
lagged. The bath least-squares fit is repeated using the untgged data. A similar
procedure is fofloved for the y dala. Since 1 January 1986, a method of "bias adjustmentrhas been used to improve the accuracy of the pole position predictns. This technique,
vhxch vill be discussed further in Secton 4, involves the post-fit adjustment of the x anl y
model bis tenms (A and E) by the value of the residual at the kmt untagged data point,
This essentially forces the residual at the last data point io zero.
The redurtion of the AUT data is slightly more complicated. First, the input &UT
lu are adjusted for the seasonal vamron by application of equation (5). The resulting
v-alues represent U172-=TC (see equaton (4)). These values are then fit, by bath least-
squares, Io a straight line (see equatn (6)). The values are ten ediled in the same manner
as the pole data, and the fit repealed sing the untagged valms. The seasonal variations awe
subtmced from UT2-UTC Io obtain estimafts of AUT.
2.3.1 THE EOP PREDICTION RECORDS
The EOPP program produces, as output, a set of five caid-image records containing all
information necessary to perform the EOP predictions. The format of these records isspecifed in ICD-GPS-211 and is given in Table 1. In additin tro the coefficients resulting
from the klat-squares ajustTents (A, C1 , C2 , DI, D2 , E, G1, G2 , H1 , H2 , I, and 3),
the perioIs (Pl, P2 , Q,Q,2 , RI,R 2 , R3 andR 4), and epochs (taand t aregiven.
Record 5 also contains the offset betveen International Awmic Time (TAI) and UTC.T EOP prediction records are supplied Io the MCS on a magnetic ape and are also
placed in a fiMe on the GE Mark III neavork for immediate avaibility. In the near future,
esmtblisunt of a direct daa link between DMA and the MCS wllM enable DMA t pass the
'A•* -.4.
. * 'I'¢2N
,. .%j.
EOP prediction records to the MCS in the most timely manner 13 1.
3.0 AOU. CY OF THE DMAEOP PREDICTIONS
3.1 PROCEDUREEach frn the EOPP prgram is execumd, te newly-compuled set of EOP prediction
records is appended iD a permanent data base. This data base vas examined carefulty, anda number of duplicat set of prediction records were removed. A tol of 72 sets ofpredictin records remained aer this editing was completd. The fist of these sets wasproduced in July 1984 and te last set used in this study was produced in December 1985.
The valres from each set of prediction records (see Section 2.3.1) were hnsermd ini themodels specified in Section 2.2 and 40-day predictns of the EOP were computed. Ineach case, the f=st day of prediction vas the day immediatly follbvin the lat day of dataused 1o detenizne a parfcular set of predictn records. The predicins were compuled In5-day in•rements.
These predxicns were directly compared with the actual values of the EOP deltrmmedby USNO and differences (in the sense, observation minus predkted value) werecompuvd. Afar all 72 sets of predriton records were processed, root mean square (mis)prediction errors at each 5-day increment were computed.3.2 ACCURACY OF POLE POSITION PREDICTIONS
Figure 1 presents a plot of the mis error in the pole position predtbos as a functionof the age of te prediction. It can be seen tat tie x component of the pole was predicvdSwith an zms eor that grew nearly linearly from approximately 0.013 arcsec 5 days afterthe last day of data, t approximately 0.027 arcsec 40 days after the last day of data. Therms predicon error in the y component of the pole grew from approximately 0.009 arcsecID 0.016 aresec over the sao= pidettn inteal. Pedictions based on all 72 sets of EOP
predic-tn records descnbed in Section 3.1 entered int the detemation of these imserror. Note tiat a prediction error of 0.03 arcsec is approximately equivalnt lo an errorof I meter at the saflce of the Earth.3.3 ACCURACY OF THE AUT PREDICTIONS
Figre 2 is an analogous plot which gives the nms error in predting AUT as afuncton of the age of the predictior When the as errors based upon all 72 sets of EOPpredition records were plotted, it vas noticed that the prediction errorm did rot increasewith tre. A detaled examination of te individual values indicaied tiat predictions based
on the firt 7 sets of EOP prediction records exhibited utusually large prediclion errors(20-30 arcsec) These large predictn errom appear ID be due io an iwonect treatment of
. .. . . . . . ..
tse zeascnal variton trms (see Section 2.2.2) in the first 7 runs of the EOPP program.
Thus, a more realistic essesment of the AUT predition errors can be made by elimirating
the first 7 sets of EOP prediction records W recomputirg the rms errors based on 0ie
remaining 65 sets. These errors are also plored m Figure 2. It can be seen that the rms
predictin error grows from 2.4 msec 5 days aftr the lst day of daa *to 7.5 msec 40 days
aflr the le3t day of da%. A prediction error of 2.2 msec is approximatly equivalent lo a
prediction error of I meler at te surface of the Earth.
4.0 EVALUATION Q_ METHODS FOR IMROVING PREDICTION ACCURACIES4.1 OVERVIEW
A short study vas underuken to investiga several tchniques vith poential t.
improve the acuracy of the EOP predictions. It must be emphasized that any
improvements I the EOP processing scenario must be consistent with the models and
output specifications given in ICD-GPS-211 (see Sections 2.2 and 2.3. 1). Given these -.restictions, data veighting schemes were given the most atntion.
The procedure for evalu g these potential improvements vwes follovs. First, 25
rest dala ses vere created through exthceors from f DMA dam bae (see Section 2. 1).The first dat set commenced on MJD 44413 (23 June 1980). The first day of daa for
each subsequent set was ircremented by 30 days, so that the last dau set began on MMD
45133 (13 June 1982). Each data set cowisted of 435 days of EOP values. All 435 days
of pole data ard the !ast 32 days of AUT data were utlized throughout testing. Each of the
25 test data sets s processed by the "produ.tiona version of the EOPP program,
predicton records were generatd and evaluatd, and nus predicton errors vere compuled
based on the results of all 25 *est runs.
After ite addition of each potential improvement v the EOPP program, ibe 25 wst runs
were redone. Again, the EOPP prediction records were evaluated ard mIs predictionerrors generafed. These nms prediction errors (at 5-day intervals) were then subuwted
from th analogous prediction errors computed usirig the prodwtion" results. The
differences between rms prediction errors are a measure of te improvement or degradation
of the predictions resulting from the processing modification. Each potential processingimprovement vill be discussed separately.
4.1.1 BIASADJtUS'TENTAfter te completion of each EOPP test run, the post-fit residuals vere examined. T..-
value of the residual at the last unged data point vas added o the bias term (A, E, or 1)
of the particular model (see Section 2.2). This procedure forces the "rev residual of the
,•.:,; .. ... . . . . . . . . . . . ...... .
last data point z be zero. Thuw, predirtions based on the adjustd coefficient should
begin unbkiased. Baced upon the favorable resulb of a previou study 181, this method hes
been routiely applied ?D the pole position predicmn results since 1 January 1986 (seeSection 2.3).4.1.2 CONSTRAINE SOLU7ION
A very large veight (106) vwa assigned ID the last data point This essentially
* constrained the least-squares solutin, resulting in a very small residual at the last day ofdata Agiin, predictions based on fthi solution should begin unbiased.
4.1.3 TIME-WEIGHTED SOLUTIONSThree different veighnn schemes, each a functin of ime, 'were investigatd. 71
generlapproachinvovdapplying apaxrthicrv hing functionIotthelast30 days of
* pole data and the last 14 days of AJT dal. These numbers 'were chosen rather arbitrarly,based on an examination of production run post-fit residuals.
4.1.3.1 RAMP WEIGHTING FUN4C7IONWeight for the affeced EOP values 'were deemrrnerd by a linear function of =ie. The
'weights kwere scaled so that the last dat point received a 'weight of 10 (largest 'weight).
4.1.3.2 EXPONENTIAL WEIGHTING FUNCTIONWeights for the affecied EOP values 'were computd wsing an exponential faction of
nine. Again, 'weights 'were scaled so ta~t the ]ast dam point received the laragest 'weight (a -
73lue of 10).4.1.3.3 STEP WEIGHTING FUNCTION
Weight for the affected HOP values 'were set equal ID the same valve (0).
* 4.2 RESULTS* 4.2.1 X-COORDINA77 QF THEPOLE
Figure 3 presents the differences betveen the rins prediction errors: obained using tiiavarious processing modiftatious and fth unr predictin errors obtained from the
productrio results. Each processing modification yielded a overall trmprovement In theaccuracy of the x-coordinate predictins. Thie bWas aidjustment and consUtained solutinmethcds yielded the largest iuprovements in predictin accuiay. Use of the exponential,stp, and romp 'weighting functins produced very similar improvements 'wbich vere less
than the inproveenzts obumed throgh *ke use of It first tvo methods.*4.2.2 XQQORDINAE OF
Figure 4 presents a similar plot of the uris pred~ictin error differences for the
y-coordmina of the pole. Again, ewh processing inodfifran resnltsd in an overall
* Improvement in predition accuray. Ts inprovemient, however, vwas much smeler then
the improrvement in predicton accurcy evident in the x-coordinate results. In general, the
improv'ement in prediction acccu y vw quit simnilr for all of the testd tchniqqus.
4.2.3 AUT-
Figure 5 prov.des the rms prediction error differences for AUT. It is evident that only
the bins adjustment method resulted in an overall improvement in prediction accuracy. 9k
This improvement is quite snal (at the helf-msec evel). Use of the remainng tchniqwusresulvd, generally, in no overall improvement in the AUT prediction accuracy.
5.0 SUMMARY OF RESULTS AND CONCLUSIONS
DMAL has been supplying sets of EOP prediction records to the MCS on a weekly
basis since mnd-1984. These FOP pediction records are based on unweighted bath
lest-squsres adjitients v te EOP da~a (x, y, and AU*I) supplied by USNO. The
&cmay of the EOP predrtkns can be assessed by comparing the predictions with the
atual USNO EOP values available at a later time. This has been done for 72 sets of EOP
predictn records produced from July 1984 o December 1985. The nms prediction errors
for t2e x coordinate of the pole did not exceed 0.03 arcsec (approximately one meter on the
surface of t•e Earth) over prediction intervals of 40 days. The rms predicton errors for the
y coordinate of the pole did not exceed 0.02 aresec over the same prediction interval. A
processing error vas discovered vhich adversely affected AUT predictons from the first 7
sets of EOP prediction records. When these 7 sets were omitted from analysis, the m.s
predictlon errors for AUT were found i be less than 8 msec over the 40 day preditn
Several techniques with potental for improving the accuray of the EOP predictions
were evaluated. These techniques incl•ded post-fit adjutment of the molel bias trns,"contrinn the least-squares solutin through the last data point, and three weighting.-..
futins (a ramp, an exponential, ad a step function) applied tio 1he ast 30 days of pole
values ard the last 14 days of AUT dat. Generally, anlof these techniques improved the
pole positon prediction accuaies during the test period. The improvement ranged from
appmimia-ely 0.010 arcsec l approximately 0.020 arcsec for the x component, depending
upon *rchnique and the prediction age. The improvement was 1lss for the y component,
r ranqgi from approximately 0.002 arczec To approximately 0.005 arcsec, again depending
upon nmetbo and prediction age. However, only the bies adjusment techni•ie
improved the AUT predictons. Ths improvement vas minimal. The remaining methods
generally produced no improvement in prediction accuracy.
It is important • note that no attempt yes made in this study to determine an optimal
. . . . . . . . ... ~ . . .. .-.. ° -.
technique or procedure for improving the EOP predictions. Cerainly, other veighting
functions and 'veght values could be •tsd. Experiments could be perfommed vhich vai
the amount of dat Viehtd. Hovever, t2 resulv presented in tis paper indicate thattechniques which favor the last days of data lead ID improved predictions of the pole"•"
coordinat~s whenL the models specified in Section 2.2.1 are utilized. Ths results also,"'
indlicate that the same techniques appbed lo the AUT predictions are not likly lo lead b)-..
improved preditns hen the model specei in Section 2.2.2 is emppeyed.,"
6.0 ACKNOWLEDGEMENTS
The author vishe3 ID acknovledge valuable discussions vith Dr. W. Wooden, D.
McCarthy, and A. Babcock. Mr. B. Forre,,er prepared the mauscript k
•, ~~7.0 REFERENCES ,:.
1. Ruissell, S. S. and Scbaibly, J.H. "Control Segment and User Performance", in Global
Postdo ;ym, P.M. Janiczek (ed), Irstituie of Navwigaton, Washington,
