Validation of Geostationary Satellite Orbit Determination UsingSingle-Station Antenna Tracking Data

Yoola Hwang∗ and Byoung-Sun Lee†

Electronics and Telecommunications Research Institute, Daejeon 305-700, Republic of Korea

Bang-Yeop Kim‡

Korea Aerospace Research Institute, Daejeon 305-333, Republic of Korea

Hae-Yeon Kim§

National Meteorological Satellite Center, Jincheon 365-830, Republic of Korea

and

Haedong Kim¶

Sejong University, Seoul 143-747, Republic of Korea

DOI: 10.2514/1.A32334

A method to precisely estimate the azimuth bias for the geostationary satellite is introduced and evaluated with

orbit-determination results. The issue analyzed in this paper is the singularity associated with the simultaneous

estimation of the satellite’s position and azimuth bias using tracking data from a single ground station when it is

locatednear the longitude of the ground control center. The presentmethodof orbit estimation eliminates the azimuth

bias of real tracking data using redundant ranging data from an external station and the predicted azimuth data. The

accuracy of the orbit determination employing the corrected azimuth data is verified by comparing it to the ephemeris

adjusted using ranging data from two ground stations. To confirm the accuracy, the longitude and latitude of the

satellite ground track are compared with the optical telescope scanning results. The accuracy of the present orbit

determination satisfies within 2.0 km root sum squares when compared with the ephemeris made by orbit

determination using ranging data from two stations.

Nomenclature

Az,bAz, νAz

= azimuth, azimuth bias, and azimuth noise(respectively), deg

C = uncorrelated measurement noisec = consider parameterEl, bEl, νEl = elevation, elevation bias, and elevation noise

(respectively), degdD = differential of longitudinal drift rate, deg ∕daydex, dey = differential of eccentricity vectordix, diy = differential of inclination vector, degdλ0 = differential of mean subsatellite deviation from

nominal longitude, degFk,Ak = mapping matrix that relates between differential

tracking data expressed by the coefficients ofconstant, linear, and sinusoidal terms and thedifferential orbital elements

fkc, fks,fk1, fk0

= corresponding superposition coefficients ofcosine, sine, linear, and constant of each trackingtype (respectively); k equal to ρ, El, Az

G = measurement model

~H = measurement sensitivity matrix

HX, Hc = observation mapping matrix with respect tosolve-for parameters and consider parameters,respectively

n = the mean motion of the reference orbitthat is consistent with Earth’s rotation rate,rad∕s

Pc, P = consider covariance and covariance matrix,respectively

R⇀

ECI,

R⇀

GS;ECEF

= satellite position in Earth-centered inertial frameand location of ground station in Earth-centered–Earth-fixed frame (respectively), km

TECEFTopocentric = geometric transformation matrix from Earth-

centered–Earth-fixed to topocentric frame

TECIECEF = geometric transformation matrix from Earth-

centered inertial to Earth-centered–Earth-fixedframe ground station, km

t = observation time of measurement, svx; vy; vz = satellite’s velocity componentsW = weighting matrixX = solve-for parameterx; y; z = satellite’s position componentsβ = angle between the ground station and the center of

Earth from satellite, deg

γ = angle between the azimuth direction andequatorial plane, deg

ρ, bρ, νρ = range, range bias, and range noise (respectively),km

ρ⇀Topocentric = range of geostationary Earth orbit satellite to

ground antenna in topocentric frame, kmρE;i,ρN;i, ρU;i

= east, north, and up components of satelliteposition in topocentric frame; i equal to 1 and 2 foreach z; full states with respect to orbital elementsand measurement bias

ρi = distance from each ground station tospacecraft, i equal to 1 and 2 for each groundstation, km

Presented as Paper 2011-508 at the AAS/AIAA Astrodynamics SpecialistConference, Girdwood, AK, 31 July 2011–4 August 2011; received 9February 2012; revision received 29March 2013; accepted for publication 30April 2013; published online 9 August 2013. Copyright © 2013 by theAmerican Institute of Aeronautics and Astronautics, Inc. All rights reserved.Copies of this paper may be made for personal or internal use, on conditionthat the copier pay the $10.00 per-copy fee to the Copyright Clearance Center,Inc., 222 RosewoodDrive, Danvers,MA 01923; include the code 1533-6794/13 and $10.00 in correspondence with the CCC.

*Senior Research Staff, Satellite Systems Research Section, ETRI, 218Gajeong-ro, Yuseong-gu. Member AIAA.

†Section Manager, Satellite Systems Research Section, ETRI, 218Gajeong-ro, Yuseong-gu.

‡TeamHead,Geostationary SatelliteOperationTeam,KARI, 115Gwahak-ro, Yuseong-gu.

§Deputy Director, Satellite Planning Division, NMSC, 64-18 Guam-gil,Gwanghyewon-myen.

¶Associate Professor, Department of Aerospace Engineering, 98 Gunja-dong, Gwangjin-gu.

1248

JOURNAL OF SPACECRAFT AND ROCKETS

Vol. 50, No. 6, November–December 2013

Dow

nloa

ded

by Y

OR

K U

NIV

ER

SIT

Y L

IBR

AR

IES

on A

ugus

t 13,

201

4 | h

ttp://

arc.

aiaa

.org

| D

OI:

10.

2514

/1.A

3233

4

I. Introduction

THE Communication, Ocean and Meteorological Satellite(COMS), which is based on the latest version of the Eurostar

3000 series spacecraft platform, entered thegeostationary transfer orbiton the top of Ariane 5 on 26 June 2010. COMS is unique in that itcarries three different types of payloads (communication,oceanographic, and meteorology) in a single platform. The satelliteground control system for the COMS was developed based on thetechnologies built up through the Korea Multi-Purpose Satellitesprogram. The performances of orbit determination (OD) software forgeostationary Earth orbit (GEO) using a radio-frequency (RF) antennaof single ground station as well as low-Earth-orbit satellites usingGPSdata developed by the Electronics and Telecommunications ResearchInstitute (ETRI) has been validated in previous studies [1–3].The first issue with the COMS OD occurs when the longitudinal

distance between the satellite (128.2 deg east longitude) and theground station (Daejeon, 127.35 deg east longitude) is small,rendering the longitude and drift rate unobservable when usingranging data and not allowing elevation data to contribute to OD inthe geometry where ranging data fail [4,5]. In this case, only theazimuth data determine orbit elements related to constant and linearterms such that the simultaneous estimation of the satellite positionand azimuth bias makes singularity. However, for this special case,the satellite missions are planned because of advantages derived frombandwidth occupancy and the ocean-monitoring payload. The closerthe distance between the satellite and the ground station is, the betterthe ocean-monitoring performance. Furthermore, two additionalgeostationary satellites with monitoring missions for meteorology,the environment, space weather, and oceanography are planned to belocated at the same longitude because of bandwidth occupancyissues. Therefore, it is crucial to solve the observability lack in thetracking data for a single ground station.Another issue with the COMS OD is in its image navigation and

registration (INR). Precise INR is crucial to monitor the ocean andmeteorology using the COMS. However, whereas most GEOmeteorological satellites conduct the INR process onboard, COMSdoes so at the ground station, and processing the INR data on theground requires the outcome of the OD process. Accurate OD andorbit prediction are important for high-quality INR. According to theCOMS OD accuracy specifications, errors in the along-track andcross-track estimates should be less than 3.18 km� 0.72 km∕dayand 4.09 km, respectively. Orbit propagation for 48 h, including theOD error, should be within the positioning accuracy of 18 km forthree-sigma variance. A prestudy of the COMS OD, using simulatedantenna tracking data that have 0.01 deg noise and 0.04 deg biasesincluding maneuver realization error for orbit model from a singlestation, had showed an accuracy of 5–6 km (root sum square, RSS)without azimuth bias correction [3].To improve the OD accuracy of a geostationary satellite with

single- and multi-tracking data, several research groups have studiedvarious methods [6–10]. In [6], two methods were investigated toimprove the GEO OD accuracy with a limited motion antenna. Thefirst method optimized the antenna-tracking algorithm by employinga symmetry pattern to the tracking of the antenna. The second applieda newweighted value to the measured data after tracking and rangingresidual analysis. TheOD result using a 13m limited-motion antennashowed 2 km RSS in three-sigma positioning accuracy. Anotherimportant factor in the GEOOD accuracy is the systematic error, andthe reduction in biases and noises has therefore been studied to a greatextent. Kawase and Arimoto formulated the errors from the position,velocity, and station-keeping (SK) maneuver of a satellite based oncovariance analysis and expressed them in terms of tracking biasesand noises [7]. Kawase regarded all of the relevant ranging andtracking biases as unknown parameters during the OD and solvedthem in tandem with the tracking data from two satellites and twostations [8]. This method dropped the orbit error from a couple ofkilometers to a level of several hundred meters. As a precisecalibration method to accurately estimate systematic errors from thestation tracking system, in [9], Kawase et al. adjusted the data forpoint optical angle observation and radio tracking with simultaneous

orbital elements and bias estimation so that the predicting satelliterange fell to the level of a few meters after OD. With improvedangular observation data, using the simulatedmeasurements from theRAVEN sensor, Sabol and Culp showed that range bias was reducedand the orbit solution error dropped to an order of a meter [10].Tombasco andAxelrad showed 10machievable geosynchronousODaccuracy using angle-only data [11].In this paper, the azimuth constant bias is estimated using both

ranging as well as angle-tracking data of a single station and rangingdata of an external ground station for redundant observability duringOD. However, because it is very expensive to estimate the bias usingan external ground station, the real azimuth bias is occasionallyupdated. Additionally, the azimuth constant bias is daily calculatedwith the help of the predicted azimuth data whose initial condition ispropagated from theOD results. Thismethod is used tomonitorwhenthe azimuth bias should be updated during satellite operation. TheOD based on the tracking data from a single station [OD based on theTracking data from a Single Station (OD–TSS)] corrected by the twomethods for azimuth bias estimation is validated by comparing theephemeris with that using ranging data from two stations [OD usingRanging data from Two Stations (OD–RTS)]. Finally, the COMSlocation observed by telescope is compared to the ground-trackposition propagated after OD.

II. Observability of Single-Station Antenna Tracking

Because a geostationary satellite keeps a fixed position withrespect to the surface of the Earth, the satellite’s movement providesconstant geometry in a corotating equatorial reference frame.Because of this constant geometry of geostationary orbit, theanalytical modeling of OD is possible to obtain. The analytical modelpermits an analysis of the observability of orbital elements from thetracking data [4,5].The single ground-station-based measurements normally used for

ODare the range (ρ) and the angle-tracking observations (azimuthAzand elevation El). The range data are the distances from the station tothe spacecraft. The angle-tracking data are collected from theautotracking system of the dish antenna. Measurement modeling forthe range and angle-tracking data is expressed by

ρ⇀i;Topocentric � TECEF

Topocentric�TECIECEFR

⇀

ECI − R⇀

GS;ECEF�

� � ρE;i ρN;i ρU;i �T (1)

G�X; t� �" ρAz

El

#�

26664

ρi;Topocentric � bρ � vρtan−1

�ρE;iρN;i

�� bAz � vAz

sin−1�ρU;iρi

�� bEl � vEl

37775 (2)

For OD, as a function of time, the differential tracking data can beexpressed by linearization equations of a satellite’s motion around anominal geostationary position in the equatorial plane as given by[4,5]. The differentials of tracking data imply variations in the rangeand pointing direction from a ground station. The analytical solutionof orbit can be obtained in the first-order perturbation approximationwith respect to a satellite’s position. A satellite’s small motion ingeostationary position is converted to the equinoctial orbital elements(nominal longitude λ0, longitudinal drift rate D, eccentricity ex, ey,and inclination ix, iy) [4,5]. To analytically investigate theobservability in OD, the differential of a tracking matrix can beexpressed by the linear combination of the constant, linear, andsuperimposed oscillator in Eq. (3) [4,5,12]:

f�t� � fk0 � fk1t� fkc cos�nt� � fks sin�nt� (3)

Six orbital elements are determined by combining four coefficientsfor tracking data type [4,5]. The nominal longitude and longitudinaldrift rate are determined by the constant and linear terms, and the

HWANG ETAL. 1249

Dow

nloa

ded

by Y

OR

K U

NIV

ER

SIT

Y L

IBR

AR

IES

on A

ugus

t 13,

201

4 | h

ttp://

arc.

aiaa

.org

| D

OI:

10.

2514

/1.A

3233

4

sinusoidal terms depend on the eccentricity and inclination. Themathematical relations for data fitting are as follows [4,5]:

�fk0;fk1��

2666666666664

fρ0

fEl0

fAz0

fρ1

fEl1

fAz1

3777777777775�

2666666666664

−sin β sin γ − 23ncos β

cos β sin γ − 23nsin β

−cos γ 0

0 −sin β sin γ

0 cos β sin γ

0 −cos γ

3777777777775

×�dλ

dD

��Fk�dλ0;dD�; �fkc;fks��Ak�dex;dey;dix;diy� (4)

When the distance between the satellite longitude and ground stationis close (γ ≈ 0), the inversion of Fk is singular for ranging andelevation tracking data in Eq. (4) [4,5]. Only the azimuth angle-tracking data can provide a nonsingular solution for this special case.Here, if azimuth constant bias exists, the error is translated into anerror of the estimated longitude and drift rate [4]. Thus, in this specialcase, the azimuth bias cannot be determined internally due to the lackof redundancy data, such as the range or elevation related to constantand linear terms, as shown in Eq. (4). Therefore, to solve thisproblem, the azimuth bias should essentially be calibrated usingexternal ranging data or should be fixed during OD, as suggested inSec. Vof this paper.

III. Covariance Analysis

Covariance analysis yields an intuitive estimate of the orbitaccuracy. In the linearized orbital model, the ranging data and angle-tracking data are prepared before theCOMScovariance analysis. Thepartial derivatives of the tracking data with respect to the orbitalelements and measurement bias are as follows [13]:

z ��Xc

�

� � x y z vx vy vz...bρ1 bAz1 bEl1 bρ2

�T (5)

H � �HX...Hc� �

266664

∂ρ1∂X

∂ρ1∂c

∂Az1∂X

∂Az1∂c

∂El1∂X

..

. ∂El1∂c

∂ρ2∂X

∂ρ2∂c

377775 (6)

where the full state z consists of the solve-for parameter X and theconsider parameter c. The solve-for parameter consists of the positionand velocity of the COMS, and the consider parameter has ameasurement bias in covariance analysis as in Eqs. (5), and (6).Subscripts 1 and 2 denote the two ground stations at Daejeon andDongara (115.35 deg east longitude and 29.046 deg south latitude),respectively. Subscript 2 is not used in the covariance analysis of asingle station. The consider covariance matrix of the batch filter iswritten as [12,13]

Pc � P� �PHTXW��HcCH

Tc ��PHT

XW�T P � �HTXWHX�−1 (7)

Four scenarios are considered to investigate the orbit uncertainty forreal tracking data as given in Table 1. Cases 1 and 2 are prepared for24 h data arc lengths, and cases 3 and 4 are prepared for 72 h data arclengths. Case 1 is studied to demonstrate the accuracy of theperformances of OD using a single ground station that estimatesazimuth bias with a 24 h data arc length. Cases 2 and 3, whichestimate orbit using two ranging data, are regarded as the truth orbit.Case 4 is for the validation of OD using the three-day arc length of asingle ground station in this paper. For all of the test cases, the anglenoise is set at 0.015deg,which is the amplitude of anglemeasurement

residuals. The calibrated range accuracy from Daejeon is within10m.The azimuth biases of cases 1 and 4 are assumed to be 0.001 and0.004 deg for the 24 and 72 h data arc lengths, respectively.Table 2 shows the position error determined by the covariance

analysis, which follows the noises and biases of the antenna trackingand ranging data from the Daejeon ground station. The hundredthplace value of the COMS antenna-tracking data is not exact. Inaddition, environmental factors, such as instrumental thermal effectand wind, which are not considered in the systematic error or noise,affect the bias. Therefore, although the bias should be constant,different bias values can be expected depending on the arc length(24 h, cases 1 and 2, or 72 h, cases 3 and 4). Further analysis of theposition error of the COMSwith 0.004 deg azimuth bias shows that ithas a 2.4 km RSS value for the angle-tracking data from the Daejeonground station (case 4). When the range data from both Daejeon andDongara ground stations are used for OD, as in cases 2 and 3,covariance analysis shows that the OD error is 0.633 km (case 2) and0.451 km (case 3) for 24 h and 72 h arc lengths, respectively. For thiscovariance analysis, the GEODA [12] program is used.Table 3 shows the results of the covariance analysis listed in

Table 2 for orbit uncertainty, with the OD error propagated for 48 h.For the azimuth bias of 0.004 deg in the 72 h arc length, thepropagation of the 48 h orbit error reaches roughly 2.59 kmRSS (case4). This is similar to the limit from the geostationary OD erroranalysis report byGoddard Space FlightCenter (GSFC),which statesthat more than two stations should be involved to meet the positionaccuracy of at least 2 km RSS (1σ) [14]. As the covariance analysisyields a positioning error of about 0.45 km for OD–RTS (case 3), theCOMS OD–TSS results, which are compared with the truth orbit forevaluating the orbit accuracy, should take the positioning error intoaccount. The truth orbit is defined as theOD–RTS for a period of 72 h.As shown in Tables 2 and 3, the differences between the ODuncertainties and the orbit propagations including the OD error areless than an order of a hundred meters. This implies that, if the OD

Table 1 Data set for covariance analysis; angle noises: 0.015 deg(in kilometers)

Description Ground stations

Case 1 Azimuth bias roughlycorrected (24 h arc length)

Daejeon (range and angle: 1 hinterval)

Assumed maximumazimuth bias: 0.001 deg

Dongara (range: 4 h interval)

Case 2 Two range data (24 h arclength)

Daejeon (range: 1 h interval) andDongara (range: 4 h interval)

Case 3 Two range data (72 h arclength)

Daejeon (range: 1 h interval) andDongara (range: 4 h interval)

Case 4 Angle bias corrected (72 harc length)

Daejeon (range and angle: 1 hinterval)

Assumed maximumazimuth bias: 0.004 deg

Table 2 COMS initial position uncertainty by covariance analysis

Cases Radial,km

Along-track,km

Cross-track,km

Three-dimensional,km

Case 1 0.022 0.625 0.031 0.626Case 2 0.022 0.632 0.031 0.633Case 3 0.021 0.450 0.019 0.451Case 4 0.157 1.897 1.528 2.441

Table 3 Forty-eight-hour propagated position standarddeviation after tracking intervals (in kilometers)

Cases Radial Along-track Cross-track Three-dimensional

Case 1 0.022 1.000 0.034 1.001Case 2 0.022 1.009 0.034 1.010Case 3 0.021 1.167 0.021 1.167Case 4 0.157 2.078 1.537 2.589

1250 HWANG ETAL.

Dow

nloa

ded

by Y

OR

K U

NIV

ER

SIT

Y L

IBR

AR

IES

on A

ugus

t 13,

201

4 | h

ttp://

arc.

aiaa

.org

| D

OI:

10.

2514

/1.A

3233

4

accuracy is achievable within the tolerance, the requirement of theorbit propagation for 48 h can be fully met.

IV. Data Sampling for Orbit Determination

To process ODusing tracking data of a single ground station, seven-day data sets are prepared. All 5min (per hour) ranging data and angle-tracking measurements are collected from the 13 m RF antenna atthe Daejeon ground station. Ten-minute-long ranging data sets fromthe external site (the Dongara ground station) were tracked every 4 h.These data are used to estimate COMS position, velocity, and antennabias of the Daejeon station at the same time. Both Daejeon andDongara data are prepared for the dates of 1–8 August 2010.The Dongara data are only available during the aforementionedperiods.Ranges and anglemeasurements of the 5minhourly burst databased on three days’ arc length are chosen for COMS OD. Table 4shows the velocity increments due to the SK and wheel-offloading(WoL) maneuvers used for OD. North–south SK (NSSK) andeast–west SK (EWSK) were performed on 3 and 5 August 2010,respectively. Here the velocity increments for NSSK and EWSK aregiven by telemetry information. Each component of the velocityincrements is individually selected as a solve-for parameter in bothOD–RTS at Dongara and Daejeon and the OD–TSS (Daejeon).

V. Azimuth Bias Estimation

Generally, when the longitudinal distance between a groundstation and a satellite is too close, the geostationary orbit cannot bedetermined by only the ranging data from single station, as previouslymentioned [4,5,15]. In such a case, the orbit can be determined byadditional angle-tracking data. However, when the angle-trackingdata include constant bias for this special case, the elimination of thesystematic error in the antenna-tracking data should be accomplishedusing redundant ranging data.The angle-tracking data are recorded every 10 s by the tracking,

telemetry, and command (TTC) control and monitoring (C&M)system at the antenna control unit (ACU) of the Daejeon groundstation. These data are referred to as ACU data in this paper. The rawangle-tracking data are extracted from the ACU data in the form of5min burst datawith a 1 h interval. Ten-minute-long ranging data setsfrom the external site, theDongara ground station,were tracked every4 h.As shown in case 1 of Table 1, the 24 h data arc length forDaejeonstation is used for azimuth bias estimation. The measurement modelsare taken by partial derivative with respect to the epoch stateincluding the azimuth constant bias. In this case, the only states toestimate are the satellite position, velocity, and azimuth constant bias.The sensitivity matrix is as follows:

~H � ∂G�X; t�∂ρTopocentric

�

266666664

−ρE;1ρ1

−ρN;1ρ1

−ρU;1ρ1

0 0 0 0�ρN;1

�ρ2E;1ρ2N;1� 1

��−1−ρE;1

�ρ2N;1

�ρ2E;1ρ2N;1� 1

��−10 0 0 0 1

−ρE;1ρU;1ρ21

����������ρ21−ρ2U

p −ρN;1ρU;1ρ21

����������ρ21−ρ2U

p������������ρ21−ρ2U;1

pρ21

0 0 0 0

−ρE;2ρ2

−ρN;2ρ2

−ρU;2ρ2

0 0 0 0

377777775

(8)

Those states can be simultaneously solved using the batch least-square estimator (BLSE) by the data set of case 1 in the previousSec. III. Here, index 1 means Daejeon data, and index 2 is Dongararanging data. Other bias parameters are fixed as constants. Thus, inthe special case where the spacecraft and station are in closeproximity, the redundant ranging data from the external site make anestimate of the azimuth constant bias possible.As an alternate method, the prediction of azimuth tracking data is

validated showing that the azimuth tracking bias could be estimatedwithout the support of an external site. Figure 1 shows the ACU’sazimuth tracking recordings with a dashed line showing thepolynomial curve fit and a solid line representing the noise and bias-free prediction of the azimuth. The azimuth predictions may containdynamic model errors as well as initial orbit uncertainties. Theconstant azimuth values are calculated from the linear fit of thepredicted azimuth data and the ACU, as shown in Fig. 1a. Thedifference between the constants defines the bias of the trackedazimuth. Figure 1b shows the ACU azimuth data corrected for thisbias. The estimated azimuth bias is applied to the observed rawazimuth burst data for the OD process. During this procedure, theelevation bias is not corrected with the elevation data because this canbe estimated independently during the OD in the normal direction.The range bias from the radio transponder of the ground station iscalibrated and updated by the TTC C&M.In the normal OD operation, the bias of the azimuth data from the

Daejeon station is estimated using the ranging data from the Dongarastation. The ranging data from the Dongara station are 10 min burstsat 4 h intervals. The real ranging and angle-tracking data from theTTC C&M of the Daejeon site are archived for 5 min every hour.The arc length for the azimuth bias estimation is selected for 24 hduring normal operations because the maneuver error is rarelyinvoked. In Fig. 2, the estimated azimuth bias of the Daejeonsite antenna with the burst ranging data from the Dongara site shows0.1148 deg,with a standard deviation of 0.0022 deg during the periodof 2–8 August 2010 (white bar). This estimated azimuth bias value isdirectly applied to the burst azimuth data.When the azimuth data thatare converted from predicted orbit are employed, the burst azimuthbias is also calculated to be 0.1140 deg (black bar). The dailydifference of the two azimuth biases roughly shows 0.0008 deg(∼0.001 deg) over a seven-day period. This means that their relativeposition errors due to different azimuth biases can be less than 0.7 kmwhen the biases are directly corrected to the measurements. The biasof the burst azimuth data is fixed by this averaged azimuth bias forseven days during normal operation, until the next azimuth bias isestimated.Figure 3 shows the corrected azimuth data obtained by applying

the 0.1148 deg bias to the storedACUdata. The 0.1148 degbias valueis calculated by averaging the daily azimuth bias, which is estimatedusing the ranging data from theDongara station, as seen in Fig. 2. The

curve-fitting between the corrected azimuth data with the seven-dayaveraged azimuth bias and the predicted azimuth data show goodagreement.

VI. Orbit-Determination Performances

In this study, the OD is evaluated using real COMS antenna-tracking and ranging data. The COMS consists of a box and one-side

Table 4 Velocity increments according to the maneuver (year 2010)

Start time (CoordinatedUniversal Time)

Type Radial,m∕s

Along-track, m∕s

Cross-track,m∕s

06:45:00.00, daily WoL −0.00137 −0.00158 0.0076215:21:00.00, daily WoL 0.00108 0.000046 0.0038712:04:01.31, 3 Aug. NSSK −0.02507 0.001838 0.8935816:31:12.60, 5 Aug. EWSK 0.00555 −0.059428 0.01664

HWANG ETAL. 1251

Dow

nloa

ded

by Y

OR

K U

NIV

ER

SIT

Y L

IBR

AR

IES

on A

ugus

t 13,

201

4 | h

ttp://

arc.

aiaa

.org

| D

OI:

10.

2514

/1.A

3233

4

solar array. The cross-section area-to-mass ratio is set at0.0122 m2∕kg for the COMS OD. After the maneuver execution,the errors due to the maneuver uncertainty are raised by 1–2% for theNSSK, 2–10% for the EWSK, and 20% for the twice-a-dayWoL [3].The following dynamic perturbations are modeled: Earth GravityModel 96 [16] of 6 deg and sixth order, Luni-Solar gravitationalperturbation modeled by the Jet Propulsion Laboratory (JPL)’s DE405 [17], solar radiation pressure perturbation [18], and velocityincrements by the SK maneuver [19]. A variable time-step Runge–Kutta scheme [20] is used for the equations of motion.For the validation of the azimuth bias estimation, two kinds of

approaches are used; one is by comparing the orbit ephemeris, and theother is by matching the geodetic location. First, the operational OD

is demonstrated by an orbit overlapping solution from the commondata set and compared between the OD–RTS and the OD–TSS. Theiraccuracies are compared to the covariance analysis results, and therelative precision is checked with the tracking and ranging residuals.Second, as an independent validation of the orbit accuracy, thedefinitive geodetic location is compared with the optical scanningresult of the GEO observed from the Kashima Space ResearchCenter (KSRC).**

A. Validation of Orbit Precision

COMS OD estimates the position and velocity of the satellite,the solar radiation pressure coefficient, velocity increments of thesatellite due to the SK maneuver, and the elevation bias. Theestimated azimuth bias is directly added to the azimuth data, andthe velocity increments for the WoL maneuver are applied using thepredicted or estimated value from telemetry. Here, the coefficient ofsolar radiation pressure is estimated when the SK maneuverestimation is not included during OD. The initial epoch state isestimated using BLSE.Table 5 shows the differences of the following ephemeris: OD–

RTS and OD–TSS. Here, the truth orbit is defined as the OD–RTS atthe Daejeon and Dongara stations, and the single-station OD uses theranging and angle-tracking data collected from the Daejeon station.The azimuth tracking bias is corrected by the averaged bias value foran eight-day daily estimated azimuth bias (Fig. 2). As shown in Fig. 2,the daily azimuth bias is slightly different. For 5–6 August, theazimuth bias jumps from 0.0112 to 0.0117 deg. Thus, differentazimuth biases every day brings an orbit error for the three-day dataarc (i.e., the orbit roughly shows 0.7 km position error for 0.001 degazimuth bias). The orbit difference for the period of 6–8August 2010shows a 1.7 km RSS in three dimensions, and the cross-track orbiterror changes by 1.6 km rms after the NSSKmaneuver performance.The three-dimensional orbit error along the radial as well as thealong-track and cross-track directions are also comparable with case4 (2.44 km) listed in the covariance analysis. When the azimuth biasis corrected using the ranging data from the Dongara station, thesatellite position difference from truth orbit (OD–RTS) approx-imately shows a range of 0.60–1.74 km RSS. Although the cross-track error is large, as shown in Table 5, the accuracy requirement ofthe cross-track OD, which should be less than 4.09 km per day, is stillsatisfied.Tables 6 and 7 show the orbit overlapping solutions for the OD–

RTS and the OD–TSS, respectively. The overlapping ephemeris iscompared based on the 24 h results, which is the middle part of thetwo-day common overlapping OD results. The orbit overlappingdifference of the OD–RTS shows a consistent precision, whereas thesingle-station data largely range from 0.5 to 1.4 km due to the

Fig. 1 COMS azimuth data tracked at the Daejeon site.

Fig. 2 Azimuth biases obtained by ranging data from Dongara andprediction data.

Fig. 3 Azimuth data corrected by 0.1148 deg over a period of 2–8 August 2010.

**Data available online at http://spacecom.nict.go.jp/control/telesco/Optical_Scanning/newindex-2010-e.html [retrieved 21 June 2011].

1252 HWANG ETAL.

Dow

nloa

ded

by Y

OR

K U

NIV

ER

SIT

Y L

IBR

AR

IES

on A

ugus

t 13,

201

4 | h

ttp://

arc.

aiaa

.org

| D

OI:

10.

2514

/1.A

3233

4

discrepancy of the daily azimuth bias, such as nonrepeatable errors[3], the angle data quality, and poor SK maneuver recovery. InTable 7, theOD–TSSoverlapping differences of the cross-track of thecommon data arc of 2–3 August, and the along-track of the commondata of 3–4 August are larger than other data arc sets because themaneuver at the end of the data arc OD is not properly recovered.Table 8 shows the distributions of the measurement residuals for

the OD–RTS and the OD–TSS. Range residuals for the two stationsare larger than those for the single station inDaejeon. Residuals of theangle-tracking data, OD–TSS, correlate with the ranging errors. Theangle-tracking data and the ranging data are coupled during the OD.The period of 6–8 August 2010 shows a large angle-tracking errordue to data noise, whereas the range residuals of OD–RTS and OD–TSS scale in similar magnitudes. A large elevation noise (Table 8)caused a large cross-track error for the OD during 6–8 August 2010,shown in Tables 5 and 7.

B. Ephemeris Differences by Azimuth Bias

The azimuth bias was fixed by twomethods using the ranging datacollected from an external site and the predicted azimuth data. Thevalidation of the OD–TSS results was illustrated in the previoussection. Next, the OD result is verified using the predicted azimuthmeasurements by another bias-correction method. The constantazimuth biases, indicated by the black bar in Fig. 2, are applied to theCOMS burst azimuth data.Figure 4 shows the differences in the OD results using two types of

azimuth bias corrections, compared to the OD–RTS. The satelliteephemeris is compared with each one-day OD in the middle of aconsecutive three-day data set for eight days. The three-sigmauncertainty bounds are denoted by the dashed line. Ephemeris

differences between the OD–TSS, which applies the azimuth biascorrected using the prediction data, and the OD–RTS are representedby a solid line. The dotted line represents the difference between theOD–TSS with ranging data from the external site and the OD–RTS.The large difference in the along-track direction reflects on thesatellite position error due to the uncorrected azimuth bias, such asthermal or wind effects, for both cases. Also, the planned velocityincrements for the SK maneuver in generating the predicted data bythe second method, which corrects the azimuth bias using simulationdata, reveal the orbit propagation error due to the maneuverrealization errors relating to its fuel efficiency. However,discrepancies along the radial and cross-track directions rarely existfor both results. In Fig. 4, the greatest along-track difference of0.657 km between the dotted and the solid line is caused by thedifference in the azimuth bias of roughly 0.0008 deg, as seen in Fig. 2.

C. Comparison to Optical Scanned Picture

Ephemeris comparison to investigate orbit error is a method tocheck the orbit consistency alone because the true position of thesatellite is not exactly known. Satellite images taken from a telescopecan prove absolute location in the sky if an exact star catalog or Earth-centered inertial coordinate system is provided for the image. COMSwas tracked by via a KSRC telescope at the location of 140.67 degeast longitude and 35.95 deg north latitude. The precision of positionmeasurements of an optical system using two KSRC telescopes is0.001 deg [21]. The tracked geostationary satellite position based onthe position of the observed stars was converted to longitude andlatitude, a unique technique developed by the KSRC. The COMSimage taken from the telescope is located at around 128.23 deg eastlongitude and 0.003 ∼ 0.005 deg north latitude, as seen in the circlein Fig. 5. (Unfortunately, the digital number is not available from theKSRC at this time.) Figure 5 was cut to enlarge the COMS locationfrom the original image. Each label for the x axis is east longitudearound 128.2 deg, and the y axis shows latitude around an equator.Each grid indicates 0.1 deg interval of longitude and latitude.Table 9 shows the predicted geodetic position of the COMS at

12:12:10 (Coordinated Universal Time) on 21 August 2010,converted from the propagated orbit. The COMS location errorsbetween the ground track and the image from the KSRC are roughlycalculated by the Cartesian coordinate in Table 9. The initial orbit forthe geodetic position was propagated using determined orbitalelements from the single-station tracking data at 23:15:38.27 on the20 August 2010 orbit epoch. The optically scanned COMS locationand the geodetic position estimated by ETRI roughly match on theorder of 10−3. The longitude and latitude are converted into Earth-centered–Earth-fixed coordinates by assuming the altitude to be

Table 6 Orbit overlapping solution for OD–RTS (in kilometers)

Common data Radial Along-track Cross-track Three-dimensional

2–3 Aug. 2010 0.0026 0.118 0.005 0.1183–4 Aug. 2010 0.0031 0.125 0.012 0.1254–5 Aug. 2010 0.0031 0.148 0.012 0.1485–6 Aug. 2010 0.0035 0.125 0.007 0.1266–7 Aug. 2010 0.0035 0.106 0.008 0.106

Table 7 Orbit overlapping solution for OD–TSS (in kilometers)

Common data Radial Along-track Cross-track Three-dimensional

2–3 Aug. 2010 0.122 0.376 1.228 1.2903–4 Aug. 2010 0.083 1.100 0.801 1.3634–5 Aug. 2010 0.061 0.132 0.596 0.6145–6 Aug. 2010 0.054 0.100 0.535 0.5466–7 Aug. 2010 0.133 0.633 1.282 1.436

Table 8 Measurement residuals in rms for five data arc sets

OD–RTS OD–TSS

Aug. 2010 Daejeon ρ, m Dongara ρ, m ρ, m Az, deg El, deg

2–4 6.65 5.35 2.14 0.0047 0.00243–5 6.95 4.82 2.62 0.0055 0.00294–6 6.93 5.55 2.65 0.0051 0.00305–7 7.71 6.65 2.51 0.0049 0.00286–8 4.40 5.36 4.31 0.0054 0.0043

Fig. 4 Orbit differences due to different azimuth bias-correctionmethods (2–7 August 2010).

Table 5 Ephemeris discrepancy between OD–TSS and OD–RTS(in kilometers)

Data arc length Radial Along-track Cross-track Three-dimensional

1–3 Aug. 2010 0.085 0.283 0.839 0.8902–4 Aug. 2010 0.056 0.236 0.554 0.6043–5 Aug. 2010 0.076 0.683 0.751 1.0184–6 Aug. 2010 0.091 0.550 0.896 1.0555–7 Aug. 2010 0.110 0.526 1.081 1.2076–8 Aug. 2010 0.162 0.663 1.597 1.736

HWANG ETAL. 1253

Dow

nloa

ded

by Y

OR

K U

NIV

ER

SIT

Y L

IBR

AR

IES

on A

ugus

t 13,

201

4 | h

ttp://

arc.

aiaa

.org

| D

OI:

10.

2514

/1.A

3233

4

35,786.863 km (Table 9). The three-dimensional position differencesfrom the image approximately show 3 km RSS.

VII. Conclusions

The orbit determination of the Communication, Ocean andMeteorological Satellite involves a problem of poor geometricobservability due to the close distance between satellite and groundstation. To comply with the required accuracy of the orbitdetermination based on tracking-data from a single station, theazimuth tracking bias was eliminated using the data obtained from anadditional site and predicted measurements. First, the estimatedazimuth bias was averaged over a period of seven days, and the meanconstant azimuth bias was applied to the real azimuth data, to removethe bias until the next ranging data of the external site was supplied.Second, the predicted tracking measurements were calibrated by alinear fit, and the raw data were corrected using the azimuth bias.Orbit-determination consistency and accuracy for the Communica-

tion, Ocean and Meteorological Satellite was evaluated by severalmethods, including measurement residuals, orbit overlapping, andephemeris comparison with the truth orbit (orbit determination usingranging data from two stations and optically scanned positions).Differences when compared with the orbit determined using theranging data from two stations showed less than 1.5 km root-sum-squares for two kinds of azimuth correction methods. This implies thatthe azimuth data, corrected by the predicted azimuth measurements,also reached orbit-determination accuracy to process image navigationand registration. When compared with optically scanned satellitetracking results, the geodetic satellite position error was less than0.005 deg, meaning that the satellite position error is smaller than

3.5 km. Therefore, the orbit-determination accuracy of theCommunication, Ocean and Meteorological Satellite, based onsingle-station antenna-tracking data, has been validated for operation.

References

[1] Lee, B.-S., Hwang, Y., Kim, H. Y., and Kim, J., “Design andImplementation of the Flight Dynamics System for COMS SatelliteMission Operations,” Acta Astronautica, Vol. 68, Nos. 7–8, 2011,pp. 1292–1306.doi:10.1016/j.actaastro.2010.09.002

[2] Hwang,Y., Lee, B.-S., Kim,Y. R., Roh,K.M., Jung,O.K., andKim,H.,“GPS-Based Orbit Determination for KOMPSAT-5 Satellite,” ETRI

Journal, Vol. 33, No. 4, 2011, pp. 487–496.doi:10.4218/etrij.11.1610.0048

[3] Hwang, Y., Lee, B.-S., Kim, H. Y., Kim, J., and Kim, H., “OrbitDetermination Accuracy Improvement for Geostationary Satellite withSingle Station Antenna Tracking Data,” ETRI Journal, Vol. 30, No. 6,2008, pp. 774–782.doi:10.4218/etrij.08.0108.0152

[4] Soop, E. M., Handbook of Geostationary Orbits, 1st ed., KluwerAcademic, Boston, 1994, pp. 256–285.

[5] Soop, E. M., “Geostationary-Orbit Determination by Single-Ground-Station Tracking,” ESA Journal, Vol. 4, No. 2, 1980,pp. 159–169.

[6] Wu, F., Liu, J., Liu, Y., Li, Y., Zhu, P., and Du, L., “A Method for theOrbit Determination Accuracy Improvement of a Station with a LimitedMotionAntenna,”Proceedings of SPIE, edited byMa, X., Yang, B., andLi, M., Vol. 7651, International Conference on Space InformationTechnology 2009, Pasadena, CA, 2009, Paper 76513C.

[7] Kawase, S., and Arimoto, Y., “Observation Noise/Bias Errors and theGeostationary Orbit Determination Accuracy,” Transactions of the

Fig. 5 Optical scanned picture of COMS for 21 August 2010 by KSRC (x axis shows longitude by degree, and y axis shows latitude by degree).

Table 9 COMS ground track position for 21 August 2010

Time Longitude (east), deg Latitude (north), deg x, km y, km z, km Three-dimensionalerror rms, km

12:11:50 128.234 0.00321 −26094.848 33120.177 2.360 2.94712:12:00 128.234 0.00310 −26094.848 33120.177 2.279 2.94412:12:10 128.234 0.00318 −26094.848 33120.177 2.338 2.94612:12:20 128.234 0.00316 −26094.848 33120.177 2.232 2.94312:12:30 128.234 0.00314 −26094.848 33120.177 2.308 2.945Image 12:12:10 128.23 0.003 −26092.536 33121.998 2.206 — —

1254 HWANG ETAL.

Dow

nloa

ded

by Y

OR

K U

NIV

ER

SIT

Y L

IBR

AR

IES

on A

ugus

t 13,

201

4 | h

ttp://

arc.

aiaa

.org

| D

OI:

10.

2514

/1.A

3233

4

Japan Society for Aeronautical and Space Sciences, Vol. 37, No. 115,1994, pp. 59–70.

[8] Kawase, S., “Bias Estimation Technique for Geosynchronous OrbitDetermination,” Part 2, Advances in Astronautical Sciences, edited byBishop, R. H., Culp, R. D., Mackison, D. L., and Evans, M., Vol. 102,1999, pp. 1201–1210.

[9] Kawase, S., Kawaguchi, N., and Tanaka, T., “Optical Calibration ofGeostationary Satellite Tracking Systems,” IEEE Transaction on

Aerospace and Electronic Systems, Vol. 17, No. 2, 1981, pp. 167–172.doi:10.1109/TAES.1981.309142

[10] Sabol, C., and Culp, R. D., “Improved Angular Observations inGeosynchronous Orbit Determination,” Journal of Guidance, Control,and Dynamics, Vol. 24, No. 1, 2001, pp. 123–130.doi:10.2514/2.4685

[11] Tombasco, J., and Axelrad, P., “A Study of the AchievableGeosynchronous Angles-Only Orbit Estimation Accuracy,” Journal ofthe Astronautical Sciences, Vol. 58, No. 2, April–June 2011, pp. 275–290.doi:10.1007/BF03321169

[12] Montenbruck, O., and Gill, E., Satellite Orbits Models Methods

Applications, 1st ed., Springer–Verlag, New York, 2000, pp. 257–300.[13] Tapley, B. D., Schutz, B. E., and Born, G. H., Statistical Orbit

Determination, 1st ed., Elsevier, New York, 2004, pp. 387–406.[14] Cooley, J. L., “Error Studies for Ground Tracking of Synchronous

Satellites,” Goddard Space Flight Center (GSFC) Rept. X-551-72-30,Maryland, 1972.

[15] Kawase, S., and Tanaka, T., “A Simple Method for Evaluating theSystem Observability in Satellite Orbit Determination,” IEEE

Transactions on Aerospace and Electronic Systems, Vol. 15, No.1,Jan. 1979, pp. 152–156.doi:10.1109/TAES.1979.308807

[16] Lemoine, F. G., Kenyon, S. C., Factor, J. K., Trimmer, R. G., Pavlis, N.K.,Chinn,D. S., Cox,C.M.,Klosko, S.M., Luthcke, S.B., Torrence,M.H., Wang, Y. M., Williamson, R. G., Pavlis, E. C., Rapp, R. H., andOlson, T. R., “The Development of the Joint NASA GSFC and theNational Imagery and Mapping Agency (NIMA) Geopotential ModelEGM96,” NASA TP-1998-206861, 1998.

[17] Standish, E. M., “JPL Planetary and Lunar Ephemerides, DE405/LE405,” NASA Jet Propulsion Lab. Interoffice Memorandum 312.F-98-048, 1998.

[18] Wertz, J. R., andLarson,W. J. (ed.),SpaceMissionAnalysis andDesign,3rd ed., Microcosm Press, Hawthorne, CA, 1999, pp. 109–146.

[19] Lee, B.-S., Hwang, Y., Kim, H. Y., and Kim, J., “East–West Station-Keeping Maneuver Strategy for COMS Satellite Using IterativeProcess,” Advances in Space Research, Vol. 47, No. 1, 2011, pp. 149–159.doi:10.1016/j.asr.2010.09.002

[20] Jackiewicz, Z., and Zennaro,M., “Variable Step Size Explicit Two-StepRunge–Kutta Methods,” Mathematics of Computations, Vol. 59,No. 200, 1992, pp. 421–438.

[21] Takahashi, M., “Observing Geostationary Satellite with OpticalTelescopes,” NICT News, No. 352, July 2005, pp. 3–4.

C. McLaughlinAssociate Editor

HWANG ETAL. 1255

Dow

nloa

ded

by Y

OR

K U

NIV

ER

SIT

Y L

IBR

AR

IES

on A

ugus

t 13,

201

4 | h

ttp://

arc.

aiaa

.org

| D

OI:

10.

2514

/1.A

3233

4