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GPS-Based Orbit Determination for KOMPSAT-5 Satellite Yoola Hwang, Byoung-Sun Lee, Young-Rok Kim, Kyoung-Min Roh, Ok-Chul Jung, and Haedong Kim

Korea Multi-Purpose Satellite-5 (KOMPSAT-5) is the first satellite in Korea that provides 1 m resolution synthetic aperture radar (SAR) images. Precise orbit determination (POD) using a dual-frequency IGOR receiver data is performed to conduct high-resolution SAR images. We suggest orbit determination strategies based on a differential GPS technique. Double-differenced phase observations are sampled every 30 seconds. A dynamic model approach using an estimation of general empirical acceleration every 6 minutes through a batch least-squares estimator is applied. The orbit accuracy is validated using real data from GRACE and KOMPSAT-2 as well as simulated KOMPSAT-5 data. The POD results using GRACE satellite are adjusted through satellite laser ranging data and compared with publicly available reference orbit data. Operational orbit determination satisfies 5 m root sum square (RSS) in one sigma, and POD meets the orbit accuracy requirements of less than 20 cm and 0.003 cm/s RSS in position and velocity, respectively. Keywords: KOMPSAT-5, orbit determination, GPS, double-difference data, empirical acceleration, dynamic model. Manuscript received Jan. 14, 2011; accepted Mar. 19, 2011. Yoola Hwang (phone: +82 42 860 6832, email: [email protected]) and Byoung-Sun Lee (email: [email protected]) are with the Broadcasting & Telecommunications Convergence Research Laboratory, ETRI, Daejeon, Rep. of Korea. Young-Rok Kim (email: [email protected]) is with the Department of Astronomy and Space Sciences, Yonsei University, Seoul, Rep. of Korea. Kyoung-Min Roh (email: [email protected]) is with the Space Geodesy Research Group, KASI, Daejeon, Rep. of Korea. Ok-Chul Jung (email: [email protected]) is with the LEO Satellite Mission Operations Department, KARI, Daejeon, Rep. of Korea. Haedong Kim (email: [email protected]) is with the Department of Aerospace Engineering, Sejong University, Seoul, Rep. of Korea. doi:10.4218/etrij.11.1610.0048

ETRI Journal, Volume 33, Number 4, August 2011

© 2011

I. Introduction Korea Multi-Purpose Satellite-5 (KOMPSAT-5) is the first satellite in Korea to produce synthetic aperture radar (SAR) images and support radio occultation. KOMPSAT-5 is to be inserted into a 550 km altitude circular dawn-dusk orbit with a 97.6-degree inclination in 2011. The spacecraft was built by the Korea Aerospace Research Institute (KARI), while the mission control element (MCE) system for operating the satellite on the ground was developed by the Electronics and Telecommunications Research Institute (ETRI). The primary missions of KOMPSAT-5, called GOLDEN, are as follows: - Geographic information system (GIS) - Ocean management - Land management - Disaster monitoring - ENvironment monitoring The secondary mission of KOMPSAT-5 is to generate an atmospheric sounding profile and support global positioning system (GPS) radio occultation using atmosphere occultation and precision orbit determination (OD) [1]. Figure 1 shows KOMPSAT-5 at a nominal attitude in ‘rightlooking’ mode. The Z-axis of the satellite is tilted from its nadir by –33.7 degrees by the defined body-fixed coordinate system. The X-axis is along the solar panel rotation axis, and the Y-axis completes the right-hand system. The main payloads carried by KOMPSAT-5 are SAR, two GPS receivers, and a laser-reflector. The two GPS receivers receive dual-frequency and single-frequency signals, respectively. The single-frequency GPS receiver, TOPSTAR 3000 [2], shares the operation heritage of KOMPSAT-2. The dual-frequency IGOR GPS receiver [3], which is the follow-up to the BlackJack GPS receiver, is carried to obtain accurate

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+X

Flight dynamics subsystem (FDS) Mission analysis • • • •

Flight direction

+Z –33.7° Roll tilt from nadir

Precision orbit determination

Operational orbit determination Orbit prediction Orbit maneuver planning Fuel accounting

Common library

• Precision orbit determination by DGPS technique • Simulated DGPS data generation • Precision orbit determination by using SLR data

System management • System management • Database management

Database

Nadir

Fig. 1. KOMPSAT-5 nominal attitude (images courtesy of KARI).

satellite positioning for SAR missions and radio occultation. Unfortunately, both GPS receivers are not activated simultaneously due to the limited capacity of the mass memory of the on-board computer in KOMPSAT-5. The singlefrequency TOPSTAR-3000 GPS receiver will be used as a backup receiver. The IGOR GPS receiver will provide a carrier phase with a data rate of 0.1 Hz. Assessments of the IGOR GPS receiver performances and precise OD (POD) capability are achieved through various internal and external testing validation methods such as satellite laser ranging (SLR) fit and orbit comparisons [4]. SLR is used to independently validate the orbit precision. The mission requirement of operational OD (OOD) is to satisfy a 10 m root sum square (RSS) in one sigma, and POD accuracy is required to satisfy 20 cm and 0.03 cm/s root mean square (RMS) in 3D position and velocity, respectively. First, the BlackJack receiver for the CHAMP satellite showed a 30 cm RSS [5], and the SAC-C satellite, which carries the same type of BlackJack GPS receiver, using a double-difference or singledifference method, satisfies 20 cm and 0.02 cm/s in positioning and velocity accuracy, respectively [6], [7]. For the GRACE satellite, many POD research groups have shown highly accurate positioning determination results within a 10 cm RSS [8]-[10]. The POD results of the European satellite, GOCE, using the mission of Earth-gravity estimation, also met the orbit accuracy requirements of 50 cm and 2 cm RMS for a rapid science orbit and precise science orbit, respectively [11], [12]. The main purpose of this paper is to show how well the requirements of the KOMPSAT-5 satellite can be satisfied using IGOR and TOPSTAR-3000 GPS receiver data based on current OD techniques implemented in ETRI-GPS-Precise-OrbitDetermination (EGPOD) software. An overview of the OD process method using GPS data from KOMPSAT-5 is provided, and test results satisfying the mission requirements are included.

II. Implementation of OOD and POD MCE, the ground mission control segment for the

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Graphical user interface

Operator

External interfaces

Fig. 2. FDS architecture.

KOMPSAT-5 satellite operation, consists of telemetry, a tracking and command subsystem, satellite operation subsystem, mission planning subsystem, flight dynamics subsystem (FDS), and satellite simulator. The ground control system follows the heritage of KOMPSAT-2. The FDS provides satellite flight dynamics operation and support functions, such as orbit prediction and determination, event prediction, fuel accounting, and antenna pointing data generation for satellite tracking. Figure 2 shows the architecture of FDS, which is divided into four parts: satellite mission analysis for operation, POD for accurate image processing and radio occultation, systems management, and a graphical user interface (GUI). KOMPSAT-5 supports on-board satellite operations using an on-board GPS navigation solution. MCE also uses GPS navigation solution data to determine the operational orbit for the satellite and on-ground operations. The dynamic models implemented for OOD processing based on GPS navigation solution data are as follows: 36×36 Earth-gravity model (EGM) by degree and order [13], solar radiation pressure, drag, and Sun and Moon gravity. A batch least-squares estimator (BLSE) filter is used to determine the operational orbit. The POD of KOMPSAT-5 is used for the enhancement of SAR image quality. The POD process is operated at the KOMPSAT ground station of KARI, and the POD product is provided to an image reception and processing element system or to users requesting accurate KOMPSAT-5 positioning information. Figure 3 shows the OD package diagram designed for implementation. Users are interfaced with the OD system through a GUI. Initial orbit for POD is obtained using the results from the OOD module. A POD consists of three parts: ‘POD_CTRL’ interfacing with the user’s input, ‘preprocessing’


Precise orbit determination GUI

80 60

User input Precise orbit determination

nyal fair

pol2

40

POD_CTRL User input

20

User input

Preprocessing

madr

guam braz

–20

Observing data

Orbit stack data for POD initial condition

sey1

nklg

thti

karr sant

–40

suth

tidb

POD stack data –60

Operational orbit determination

tskb iisc

0

Estimation

DGPS raw data Observing data

gode kokb

DB

GPS result fitting to SLR normal point

SLR data fitting

syog mcm4

–80 –150

–100

–50

0

50

100

150

Fig. 3. Orbit determination package diagram.

Fig. 4. IGS stations for KOMPSAT-5 (2009).

for processing raw GPS data from KOMPSAT-5 and international GNSS service (IGS) [14] sites, and ‘estimation’ for determining satellite ephemeris and relevant parameters. All measurements, results, and necessary constant parameters are stored in a database. Details of the fidelity dynamics and measurement models for POD are provided in the next section.

20 min. Ambiguity resolution is solved using an ionospherefree linear combination as a floating number, as shown in KOMPSAT-2 data processing [6]. GPS time is internally used for all measurement data epochs. Attitude information relating to the precise observation range and macro box-wing model uses an internal local-vertical local-horizontal (LVLH) coordinate system. For single-frequency GPS validation of a TOPSTAR-3000 receiver, a group and phase ionosphere calibration (GRAPHIC) [16] technique that averages the pseudorange and carrier phase data is used for removing ionospheric delay [17]. GPS data obtained from an IGS site produces ionosphere-free data through a linear combination (LC) using a different frequency. Thus, the double-difference data is combined by each ionosphere-free single-difference data set. One singledifferenced data type is LC ionosphere-free, and the other is made up of GRAPHIC ionosphere-free measurements. Double-difference data for an IGOR receiver is produced using ionosphere-free data of a dual-frequency LC for both a ground station and LEO satellite.

III. OD Strategies 1. GPS Data Process The POD process requires continuous tracking of a visible GPS satellite by ground and flight GPS receivers. GPS data processing of KOMPSAT-5 POD will use the KOMPSAT-5 GPS flight receiver data, accurate GPS satellite ephemeris provided by IGS, and GPS measurements from an IGS ground network whose position is accurately known. A precise GPS satellite ephemeris, which has a 15 min time interval, is interpolated using a Hermitian method every 30 s to calculate accurate GPS measurements from a GPS satellite to KOMPSAT-5 and IGS ground stations. Raw GPS data from KOMPSAT-5 is also sampled every 30 s for a doubledifference data product. Thus, double-difference GPS measurements are produced using two GPS satellites and two GPS receivers that consist of a low Earth orbit (LEO) satellite and IGS ground station. The double-difference method eliminates hardware bias as well as clock errors of the GPS receiver and GPS satellites at the same epoch. Networks using 19 IGS ground stations distributed throughout the world are used for double-difference data generation as shown in Fig. 4. These sites are expressed by International Terrestrial Reference Frame (ITRF)-2005 [15]. Cycle slips are detected and repaired using a polynomialfitting method. In its geometry, the arc length of doubledifference data maintains a signal-phase lock for 15 min to


2. OD Technique In general, an OD is necessary to conduct mission objectives, to calculate orbit modifications, and to navigate science data records. Recent LEO satellite missions require highly accurate orbit results. Orbit accuracy depends on the dynamic model as well as data quality, such as noise, performance of the GPS receiver, and clock accuracy. POD was adjusted using BLSE in EGPOD software [6]. A dynamic solution estimating the general empirical acceleration from many parameterizations, which trades off a dynamic model and kinematic method, improves the orbit accuracy on the order of centimeters. Table 1 summarizes the dynamic and measurement models for a KOMPSAT-5 POD. For an altitude of 550 km, the drag

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Table 1. POD dynamic and measurement models. Item

Description

Geopotential gravity model

EIGEN-05S (120×120) for GRACE and simulated KOMPSAT-5 GPS data [18] EGM-96 (70×70) for TOPSTAR 3000 GPS data

Earth orientation IERS Bulletin final (Polar motion, UT1-TAI) parameters Cycle slip Polynomial fitting detection and repair detection Linear combination of L1 and L2 for dualfrequency GPS data (IGS ground stations and Ionosphere delay GRACE, simulated KOMPSAT-5 data) GRAPHIC method for KOMPSAT-2: [6], [17] Troposphere delay Modified Hopfield model [19] Relativity effect Rotational deformation Earth solid tide, ocean tide Solar radiation pressure Earth radiation pressure Atmospheric density N-body, planet ephemeris Precession and nutation Reference coordinates Ground coordinates General acceleration

Earth rotation and velocity of light Pole tide model Colombo model [20] Conical shadow model

IV. Validation of Orbit Results Three test cases were used for KOMPSAT-5 OD verification. First, since real on-board data of KOMPSAT-2 is available, OOD and POD results are tested and compared with each other. The GRACE satellite was pre-studied for its IGOR receiver performance, and the requirements of KOMPSAT-5 OD were validated through internal and external comparisons: The results of the GRACE satellite POD were validated using SLR data in an absolute comparison sense and compared with other POD results. Finally, the results of POD using simulated KOMPSAT-5 GPS data are illustrated for their position and velocity accuracy.

Knocke’s 2nd-order zonal model [21]

1. OD Test Results by TOPSTAR 3000 Receiver

MSIS-90 [22]

KOMPSAT-5 carries TOPSTAR 3000 as a backup GPS receiver. TOPSTAR 3000 provides a reference time signal, GPS navigation solution, and raw single-frequency GPS data. The reference time signal from TOPSTAR 3000 supports the time synchronization between the satellite’s on-board processors and the GPS. In KOMPSAT-5, TOPSTAR 3000 will receive a maximum of twelve-channel GPS data through two antennas. For KOMPSAT-5, each GPS measurement has information of the receiving antenna. However, although offset biases (0.5 m, +/–0.5 m, 0.707 m) for the body-fixed frames of the two GPS antennas exist, information on each antenna for each GPS satellite is not available in KOMPSAT-2 data due to the limitation of TM data. Table 2 shows the orbital overlapping solution for 4 h overlap statistics for a five-day data set from the 2nd to the 9th of September, 2009. Here, the orbit obtained during the middle 4 h out of the overlapping period is different on successive days. One hour on each end of a 6 h overlap is rejected in order to avoid an end effect. An antenna offset is not considered, and LVLH attitude information is internally used. The overlapping orbital solution for the KOMPSAT-2 satellite showed a 63.8 cm RMS in 3D. A single-frequency POD requirement of 1 m orbit accuracy was fully met in this test. OOD using a navigation solution for a TOPSTAR-3000 GPS receiver was compared with POD to evaluate the OOD performance. POD and OOD use different dynamic models. For example, under Earth’s gravity, OOD uses EGM-96 with

Sun, Moon, seven-planet, JPL’s DE405 1982 IAU J2000 coordinate ITRF2005 [15] Sine and cosine coefficients for along-track and cross-track (1 cpr for TOPSTAR 3000 and simulated KOMPSAT-5 data , 6 min for GRACE satellite)

coefficient was estimated once per arc. An EIGEN [18] EGM of 120 degrees and 120 orders was used for geopotential coefficients. Internally, the J2000 coordinate system is used for the satellite motion equations. For a GPS satellite orbit, a precise IGS ephemeris was fixed without estimation. GPS antenna offsets for GPS satellites and LEO satellite are also considered. These offsets are subtracted for each GPS PRN measurement. Initial satellite position, velocity, and the coefficients of drag and solar radiation pressure are estimated for a whole data arc length. In order to obtain an accurate ephemeris, the following sine and cosine terms for general empirical acceleration along the cross-track and along-track components were parameterized for

490

the GRACE satellite every 6 min. One cycle per revolution (1 cpr) for general empirical acceleration was optimized for TOPSTAR-3000 GPS data and simulated KOMPSAT-5 GPS data. All sigma values for general empirical acceleration were given by 1.0e-9. Tropospheric delay for the IGS ground stations was estimated every 30 min during OD.

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C (cm)

3D (cm)

Sept. 2-3, 2009

17.6

44.1

16.6

50.3

Sept. 3-4, 2009

24.5

63.1

14.4

69.2

Sept. 4-5, 2009

24.1

59.1

24.4

68.3

Sept. 5-6, 2009

23.4

59.3

14.8

65.4

Average

22.6

56.9

18.0

63.8

Table 3. Orbit errors of ETRI OOD and MC OOD compared with ETRI POD for a five-day period from Aug. 15, 2006. POD - MC OOD (m)

POD - ETRI OOD (m)

Arc

R

A

C

3D

R

A

C

3D

15

1.37

3.72

1.10

4.11

1.39

3.88

0.96

4.23

16

0.57

2.15

0.97

2.43

0.55

2.39

1.36

2.80

17

0.91

2.63

0.41

2.82

0.91

2.73

1.98

3.49

18

0.74

2.59

1.01

2.88

0.72

2.78

1.69

3.33

19

0.72

2.73

1.06

3.02

0.76

2.56

2.21

3.47

36 degrees and 36 orders. POD considers the Earth and ocean tides, solar radiation pressure perturbation according to the box-wing macro-model, and drag along with an accurate atmosphere density model. Additionally, POD can compensate for unknown dynamic models using general empirical acceleration estimation. For the assessment of orbit accuracy, OOD and POD are compared for the dates of August 15 through August 19, 2006. The POD results are assumed as a reference orbit. ETRI OOD and POD with EGPOD software and MC OOD solution using MicroCosm software [23] are used. Table 3 shows the orbit discrepancy between POD and MC OOD as well as POD and ETRI OOD for each direction component for August 2006 data [17]. The estimated orbit information is compared with the Earth-centered Earth-fixed (ECEF) coordinates. POD was broken into a 24 h arc out of a 30 h arc length for a comparison with the results of OOD. OOD accuracy satisfies approximately 3 m to 4 m RSS in one sigma. Thus, ETRI OOD satisfies the requirement of 10 m RSS in one sigma for the given operation.

2. GRACE Satellite OD Results Using a BlackJack Receiver Real on-board GRACE satellite data is used for KOMPSAT5 OD pre-analysis as the 485 km altitude of the GRACE satellite is lower than KOMPSAT-5. Also, a BlackJack GPS receiver (the IGOR receiver in KOMPSAT-5 is a type of


Radial (m)

A (cm)

Along-track (m)

R (cm)

No Hermitian Hermitian

0.2

Cross-track (m)

Table 2. Orbit overlapping solution without considering an antenna offset with LVLH attitude information [17].

0 –0.2 0

2

4

6

8

10

12

14

0

2

4

6

8

10

12

14

0

2

12

14

0.2 0 –0.2 0.2 0 –0.2 4 6 8 10 Time, days past epoch Jan. 7, 2009

Fig. 5. GRACE satellite position differences for two weeks from Jan. 7, 2009.

BlackJack receiver) is carried in the GRACE satellite. The GRACE satellite was chosen since precise orbit is required to obtain a highly precise EGM. The POD accuracy based on a dynamic model approach strongly depends on the precise EGM. The EIGEN-05S model is used for the GRACE satellite POD, which has been recently released. We prepared a two-week data set for the period of January 7 through January 20, 2009. The GPS data was processed normally, and there were no large data gaps. Figure 5 and Table 4 show the orbit differences between the POD results using EGPOD and precise publicly released GRACE ephemeris. GPS carrier phase data from a 24 h arc was processed for 14 days during the EGPOD process. Two types of comparisons between the two ephemerides were made, namely, No Hermitian and Hermitian. The former type is a direct comparison without any corrections, and the latter is made after removing biases in the scale and rotational angles between the two orbit solutions. By compensating (estimating) these biases, the possible systematic errors derived by using different EOP or sensor offset values can be compensated. The No Hermitian comparison in Fig. 5 plots the orbit from EGPOD minus the publicly released orbit. The Hermitian results were obtained using Bernese software [24]. The position differences were 10.84 cm and 9.7 cm RSS for No Hermitian and Hermitian, respectively. As seen in Table 4, cross-track coordinate errors were reduced by 1.5 cm RMS in the Hermitian comparison. In Fig. 6, the velocity differences are illustrated for a 14-day period beginning from January 7, 2009. The velocity is also compared with the public released ephemeris without consideration of the coordinate conversion and different EOP parameters. The velocity difference of each direction roughly

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4.0

Table 4. Position differences between reference orbit and EGPOD results. R (cm)

A (cm)

C (cm)

3D (cm)

No Hermitian

5.42

6.58

6.70

10.84

Hermitian

5.12

6.12

5.12

9.70

3.0 RMS (cm)

Jan. 7-20, 2009

24 h GPS RMS 28 h GPS RMS

3.5 2.5 2.0 1.5 1.0

Radial (cm/s)

0.5

RMS=0.0086 cm/s

0

0.1

2

4

6

8

10

12

14

6

8

10

12

14

12

14

RMS=0.0087 cm/s

0 –0.1

0

0.1

2

4

RMS=0.0077 cm/s

0 –0.1

0

2

4 6 8 10 Time, days past epoch from Jan. 7, 2009

Fig. 6. GRACE satellite velocity differences for two weeks from Jan. 7, 2009.

20

SLR residuals Daily SLR RMS

15

RMS (cm)

10 5 0 –5 –10 –15 6

January 7 8

10 12 14 16 18 Time, dates past epoch Jan. 7, 2009

20

Fig. 7. 14-day SLR residuals (in blue star) and daily RMS (in red circle) for GRACE satellite POD results.

shows 0.008 cm/s RMS. This means that the velocity accuracy is satisfied using our OD strategies in EGPOD software. An SLR residual evaluation of KOMPSAT-5 is independently used to assess the absolute accuracy of a GPS-based orbit solution. A 14-day assessment of the SLR residuals is given in Fig. 7. In this validation, laser ranging data from specific stations is included to obtain one-dimensional orbit errors. The SLR stations considered from International

492

8

9

10 11 12 13 14 15 16 17 18 Time, dates past epoch Jan. 7, 2009

19

20

Fig. 8. Daily mean RMS of GPS measurement residuals for GRACE satellite.

0 –0.1

Cross-track (cm/s) Along-track (cm/s)

0 Jan. 7

RSS=0.0144 cm/s

0.1

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Laser Ranging Services are as follows: Changchun (7237), Graz (7839), Herstmonceux (7840), Potsdam (7841), Mt. Stromlo (7825), Simosato (7838), Yaragadee (7090), and Zimmerwald (7810). The red circles indicate daily SLR RMS due to differences between SLR data and POD results. The average residual SLR error shows 6.39 cm RMS for the 14 days. It can be stated that the orbit product satisfies the requirement of 20 cm POD accuracy with the SLR adjustment. Figure 8 shows the daily measurement residuals for 24 h and 28 h GPS carrier phase data. Despite the fact that the GPS RMS should be smaller than 1 cm, because the noise level of BlackJack GPS receiver carrier-phase observations is roughly 5 mm [9], the corresponding mean GPS measurement RMS errors for two weeks indicate 3.1 cm and 3.3 cm for 24 h arcs and 28 h arcs, respectively. This is mainly because different dynamics of a macro box-wing model are applied to the GRACE satellite. We simply use arbitrary reflectivity and areato-mass ratio values for the macro box-wing model. Also, LVLH attitude information is internally used instead of exact external attitude data. The 24 h and 28 h double-difference GPS data has a tradeoff in terms of the dynamic and measurement models. The orbit result based on a 24 h data arc length shows a smaller RMS than that of a 28 h data arc length. This means the dynamic model has slightly more errors than the measurement model. Because the number of dynamic model errors increases with an increasing arc length, the effects of the measurement errors are reduced [8]. Thus, the GPS RMS for a 28 h arc length with more propagated dynamic errors shows larger errors than that for a 24 h arc. Table 5 shows an overlapping orbital solution for the GRACE satellite. The POD was produced using every 28 h data arc, which provides 4 h common data with adjacent dates. To consider the end effect, 30 min edge points were excluded for the orbit overlapping solution. As seen in Figs. 5 and 6, every end point of a 24 h arc reveals a peak in the position and velocity differences. The mean RMSs of the orbit overlapping


Table 5. Overlapping orbit solution for GRACE POD.

Table 6. Osculating orbit for KOMPSAT-5 simulation data generation. Parameter

Value

Arc

R (cm)

A (cm)

C (cm)

3D (cm)

Jan. 7-8, 2009

2.49

3.86

1.77

4.92

Orbit type

Sun-synchronous, dawn-dusk 00:00:00.00, Feb. 7, 2010

Jan. 8-9, 2009

2.92

5.70

1.93

6.69

Epoch (UTC)

Jan. 9-10, 2009

2.36

3.51

2.10

4.72

Coordinates

True-of-date (TOD)

Jan. 10-11, 2009

3.81

6.81

1.89

8.03

Semi-major axis

6937.413066 km

Jan. 11-12, 2009

2.87

6.05

1.22

6.81

Eccentricity

0.001202349

Jan. 12-13, 2009

2.65

7.09

2.27

7.90

Inclination

97.60941408°

Jan. 13-14, 2009

4.48

7.68

1.75

9.06

Right ascension of ascending node 339.3836770°

Jan. 14-15, 2009

2.96

6.67

1.51

7.45

Argument of perigee

67.235337°

Jan. 15-16, 2009

3.51

6.73

0.62

7.62

Mean anomaly

292.811439°

Jan. 16-17, 2009

3.33

6.53

1.61

7.50

Jan. 17-18, 2009

4.19

8.75

1.08

9.76

Jan. 18-19, 2009

3.69

7.49

2.44

8.69

Jan. 19-20, 2009

2.05

4.73

1.31

5.31

Average

3.18

6.28

1.65

7.23

solution are 3.18 cm, 6.28 cm, and 1.65 cm for radial, alongtrack, and cross-track directions, respectively. The orbit overlapping solution is a good test of orbit precision. While the average orbit differences from the publicly released precise ephemeris for a 24 h data arc length shows approximately 10 cm, the orbit overlapping solution has a larger difference than we expected by a scale of 4.7 cm to 9.8 cm, as shown in Table 5. The dynamic approach using the 6 min general empirical acceleration estimation still did not completely compensate for the errors in the dynamic model. As previously mentioned, as data arc length increased, dynamic model errors also accumulated. Thus, the orbit differences from common data sets at the end points of a data arc are caused by the propagation of dynamic errors.

3. Test Results by Simulated KOMPSAT-5 GPS Data The KOMPSAT-5 ground track repeats every 28 days with 421 revolutions. Table 6 shows the KOMPSAT-5 osculating orbit used to consider the ground-track repeat and dawn-dusk orbit characteristics for the 00:00:00.00, February 7, 2010 epoch. Raw GPS data is generated for a five-day data length using the dynamic and measurement model errors given in Table 7. Raw GPS data of the IGS stations in Fig. 4 is also generated. Tropospheric delay of the ground stations has a 1% error in the zenith delay parameter. The albedo and emissivity of Earth’s radiation are considered with 3% random errors. In the measurement data where 5% of bad data is intentionally included, 15 cm GPS ephemeris errors are randomly given.


Table 7. KOMPSAT-5 dynamic and measurement model errors for simulation data generation. Item

Model error

Cycle slip - error (%)

0.01

Bad data point- error (%)

0.05

Tropospheric delay - Zenith delay parameter (%) - Correlation time (s) Station position - X (m) - Y (m) - Z (m) Solid earth tide - X (%) - Y (%) - Z (%) Tectonic plate motion - X (m/year) - Y (m/year) - Z (m/year) Earth’s radiation - Albedo - Emissivity GPS orbit - Position-X (m) - Position-Y (m) - Position-Z (m) Satellite attitude - Roll (degree) - Yaw (degree) - Pitch (degree)

1.0 43200.0 0.02 0.02 0.02 5.0 5.0 5.0 0.005 0.005 0.005 0.03 0.03 0.15 0.15 0.15 0.05 0.05 0.05

Station position and satellite attitude errors are also modeled. The noises of pseudorange and carrier phase data are randomly given as 0.2 m and 2 mm, respectively. These measurement residuals explain the differences between the observed data and computed values for GPS carrier phase data.

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Table 8. Postfit residuals and percentage of used data for simulated KOMPSAT-5 GPS measurement. Date

% of used data

RMS (cm)

Feb. 7, 2010

87.3%

12.2

Feb. 8, 2010

93.5%

8.5

Feb. 9, 2010

94.4%

8.1

Feb. 10, 2010

94.0%

7.8

Feb. 11, 2010

91.2%

8.4

RSS=13.2 cm

Cross-track (m)

Along-track (m)

Radial (m)

0.4

RMS=5.0 cm

0.2 0 –0.2 –0.4 0 1.0

20

40

60

80

100

120

40

60

80

100

120

40 60 80 100 Time, hours past epoch from Feb. 7, 2010

120

RMS=11.9 cm

0.5 0 –0.5 –1.0 0 0.2

20 RMS=2.8 cm

0.1 0 –0.1 –0.2 0

20

Radial (cm/s)

Fig. 9. Satellite position differences from truth orbit and KOMPSAT-5 POD using simulated data.

Cross-track (cm/s) Along-track (cm/s)

Table 8 [25]. The evaluation of the measurement residuals indicates the data quality and dynamic model accuracy. For the simulated GPS data, more than 87% of edited data is available in the preprocessing procedure since we put random errors of 0.01% and 0.05% for cycle slip and bad data, respectively. In this case, the elevation angle was cut-off by zero degrees. In order to validate the POD test results using the simulated KOMPSAT-5 GPS data, the truth orbit is assumed as follows: The truth orbit is propagated using the same dynamic model used in POD for the initial osculating orbit from February 7, 2010, shown in Table 6. The results of POD for a five-day period were compared with the truth orbit. Figures 9 and 10 illustrate the position and velocity differences between the truth orbit and KOMPSAT-5 POD using the simulated data, respectively [25]. The position and velocity errors show 13.2 cm and 0.014 cm/s RSS in one sigma. This accuracy is a bit higher than the previous test cases mainly due to large random noise levels of the GPS satellite ephemeris. However, these accuracies in position and velocity are good enough to meet the POD requirements of KOMPSAT-5. Since the POD is processed with a 24 h arc length for five-day data, orbit errors show regular peaks every 24 h at the end points of the arc in Figs. 9 and 10.

RSS=0.014 cm/s

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Fig. 10. Satellite velocity differences from truth orbit and KOMPSAT-5 POD using simulated data.

The measurement residuals using GPS double-difference carrier phase data show roughly 8 cm to 12 cm as given by

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V. Conclusion KOMPSAT-5 OD results obtained from single-frequency and dual-frequency GPS data are presented in this paper. The tests are performed using on-board KOMPSAT-2 data for single-frequency GPS data, and GRACE satellite and simulated KOMPSAT-5 data for dual-frequency data. The current dynamic model and measurement error correction techniques implemented in EGPOD software were introduced, and various assessments of orbit accuracy were performed. A primary dual-frequency IGOR GPS receiver will be used to support SAR images, and TOPSTAR 3000 is used as backup positioning equipment for operational and precise orbit determination for IGOR tracking failures or interruptions. Orbit validation using TOPSTAR-3000 GPS receiver data was achieved through a comparison of real on-board KOMPSAT-2 data. The single-frequency requirement, 1 m RSS, was satisfied by the KOMPSAT-2 overlapping orbital solution. Results of the GRACE satellite and KOMPSAT-5 POD using simulation data show roughly 10 cm and 13.2 cm positioning errors. This means that the orbit accuracy requirements of KOMPSAT-5, less than 20 cm positioning errors, are completely satisfied. The requirement of velocity accuracy for SAR missions is more important than the positioning error requirement. Thus, KOMPSAT-5 meets 0.03 cm/s RMS in velocity accuracy for both test cases. Further improvement of


orbit accuracy can be achieved through a refined dynamic model in drag, a macro box-wing model, accurate attitude data, GPS satellite antenna offsets, and by fixing ambiguities in the parameter estimation.

References [1] S.R. Lee, “Overview of KOMPSAT-5 Program, Mission, and System,” IGARSS 2010, Honolulu, HI, July 25-30, 2010, pp. 797800. [2] J.L. Gerner et al., “TOPSTAR 3000 – An Enhanced GPS Receiver for Space Applications,” EESA, Bulletin 104, Nov. 2000. [3] O. Montenbruck et al., “Preflight Validation of the IGOR GPS Receiver for TerraSAR-X,” GTN-TST-0200 ver. 1.2, May 2, 2005. [4] Y. Yoon et al., “TerraSAR-X Precise Trajectory Estimation and Quality Assessment,” IEEE Trans. Geosci. Remote Sens., vol. 46, no. 6, Jan. 2009, pp. 1859-1868. [5] H. Rim et al., “CHAMP Precision Orbit Determination,” Adv. Astronautical Sci., vol. 109, 2002, pp. 493-500. [6] Y. Hwang et al., “Orbit Determination Using Single and DoubleDifferenced Methods: SAC-C and KOMPSAT-2,” Adv. Space Res., vol. 47, no. 1, 2011, pp.138-148. [7] Y. Hwang et al., “Precise Orbit Determination of LEO Satellite using Dual-Frequency GPS Data,” J. Astronomy Space Sci., vol. 26, no. 2, 2009, pp. 229-236 (in Korean). [8] Z. Kang, P. Nagel, and R. Pastor, “Precise Orbit Determination for GRACE,” Adv. Space Research, vol. 31, no. 8, 2003, pp. 18751881. [9] Z. Kang et al., “Precise Orbit Determination for the GRACE Mission using Only GPS Data,” J. Geodesy, vol. 80, no. 6, 2006, pp. 322-331. [10] Z. Kang et al., “Impact of GPS Satellite Antenna Offsets on GPSBased Precise Orbit Determination,” Adv. Space Research, vol. 39, 2007, pp. 1524-1530. [11] H. Bock et al., “Precise Orbit Determination for the GOCE Satellite using GPS,” Adv. Space Res., vol. 29, 2007, pp. 16381647. [12] P.N.A.M. Visser et al., “Orbit Determination for the GOCE Satellite,” Adv. Space Res., vol. 43, 2009, pp. 760-768. [13] F. Lemoine et al., “The Development of the Joint NASA/GSFC and the National Imagery and Mapping Agency (NIMA) Geopotential Models,” EGM96, NASA, TP-1998-206861, 575, July 1998. [14] http://igscb.jpl.nasa.gov [15] Z. Altamimi et al., “ITRF2005: A New Release of the International Terrestrial Reference Frame based on Time Series of Station Positions and Earth Orientation Parameters,” J. Geophys. Res., 112(B9), B09401, 2007.


[16] T.P. Yunck, “Orbit Determination,” Global Positioning System, B.W. Parkinson and J.J. Spilker (Eds.), Washington DC: Theory and Applications AIAA Publications, 1996. [17] Y. Hwang et al., “KOMPSAT-2 Orbit Determination Status Report,” Proc. AIAA/AAS Specialist Conf., Toronto, Ontario, Aug. 2-5, 2010, AIAA-2010-8260. [18] C. Foerste et al., “EIGEN-GL05C – A New Global Combined High-resolution GRACE-based Gravity Field Model of the GFZGRGS Cooperation,” General Assembly European Geosciences Union (Vienna, Austria 2008), Geophys. Res. Abstracts, vol. 10, Abstract No. EGU2008-A-06944, 2008. [19] V. Mendes et al., “Improved Mapping Functions for Atmospheric Refraction Correction in SLR,” Geophys. Res. Lett., vol. 29, no. 10, 2002. p. 1414. [20] O. Colombo, “NASA Technical Memorandum Altimetry, Orbits and Tides,” NASA-TM-86180, 1984. [21] P. Knocke, J. Ries, and B. Tapley, “Earth Radiation Pressure Effects on Satellites,” Proc. AIAA/AAS Astrodynamics Conf., Minneapolis, Minnesota, Aug. 15-17, 1988, pp. 577-586. [22] A. Hedin, “Extension of the MSIS Thermosphere Model into the Middle and Lower Atmosphere,” J. Geophys. Res., vol. 96, no. A2, 1991, pp. 159-1172. [23] T. Martin, MicroCosm® Software Manuals, ver. 1999, chap. 3, Van Martin Systems, Inc., Rockville, MD, Nov. 2000. [24] http://www.bernese.unibe.ch/course/info.html [25] Y. Hwang, B.S. Lee, and J. Kim, “KOMPSAT-5 Precise Orbit Determination Using Simulated GPS Data,” Proc. Korean Aerospace Spring Conf., Apr. 2010 (in Korean).

Yoola Hwang received the BS in astronomy and space sciences from Yonsei University, Seoul, Rep. of Korea. She received her MS in aeronautics and astronautics from Purdue University, W. Lafayette, and the PhD in aerospace engineering sciences from University of Colorado, Boulder, USA. In 2004, she joined ETRI, Daejeon, Rep. of Korea, where she has been involved in developing the satellite ground control system. She is currently working on flight dynamics of LEO and GEO satellites and the GNSS project. Her research interests are orbit determination and prediction, navigation, interplanetary mission design, and GNSS application. She is a member of the Korean Space Science Society, Korea Society for Aeronautical and Space Sciences, American Institute of Aeronautics and Astronautics, and American Astronautical Society.

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Byoung-Sun Lee received the BS, MS, and PhD in astronomy and space sciences from Yonsei University, Seoul, Rep. of Korea, in 1986, 1988, and 2001 respectively. In 1989, he joined ETRI, Daejeon, Rep. of Korea, where he is currently a principal member of the research staff. From 1989 to 1994, he participated in the KOREASAT project. He worked at LockheedMartin Astrospace, USA, and Martra-Marconi Space, UK, developing KOREASAT satellite control system from 1992 to 1994. From 1995 to 2005, he was involved in the project for developing the KOMPSAT1 and KOMPSAT-2 satellite mission control element. From 2003 to 2010, he contributed to the development of the COMS satellite ground control system. He is now working for the KOMPSAT-3 and KOMPSAT-5 project as a system engineer. His research interests are tracking and orbit determination of satellites, satellite mission analysis, and station-keeping maneuvers of the collocated geostationary satellites. He is a member of the American Astronautical Society, the Korean Space Science Society, and Korea Society for Aeronautical and Space Sciences. He has been a member of the executive committee in the Korea Astronomy and Space Sciences Society since the year of 2006.

Ok-Chul Jung received the BS and MS in aerospace engineering in 2003 and 2005 from Chonbuk National University, Jeonju, Rep. of Korea. In 2005, he joined the Satellite Ground Control Technology Team at ETRI. He is currently a research engineer in LEO Satellite Mission Operations Department in Korea Aerospace Research Institute. His research interests include space flight dynamics and control and satellite operations engineering. Haedong Kim received the BS and MS in aerospace engineering from Seoul National University, Seoul, Rep. of Korea, in 1989 and 1991, respectively, and the PhD in aeronautics and astronautics from Purdue University, IN, USA, in 2001. He is currently an assistant professor in the Department of Aerospace Engineering at Sejong University, Seoul, Rep. of Korea. His main research interests are computational fluid dynamics, helicopter flight simulation, numerical method, spacecraft dynamics, and MEMS gyro. He is a member of the Korea Society for Aeronautical and Space Sciences and American Institute of Aeronautics and Astronautics.

Young-Rok Kim received the BS and MS in astronomy and space sciences from Yonsei University, Seoul, Rep. of Korea, in 2003 and 2005, respectively. He is currently a PhD candidate in astronomy and space sciences at the same university. His research interests are orbit determination, estimation, and GNSS/SLR applications. He is a member of the Korean Space Science Society, Korea Society for Aeronautical and Space Sciences, and American Institute of Aeronautical and Astronautics. Kyoung-Min Roh received his BS, MS, and PhD in astronomy and space sciences from Yonsei University, Rep. of Korea, in 1997, 1999, and 2006, respectively. From 2007 to 2008, he worked as a postdoctoral researcher at GeoForschungsZentrum, Germany, where he was involved in GRACE baseline determination and satellite orbit design of Swarm mission. Since 2008, he has been with Korea Astronomy and Space Science Institute as a senior research staff member of the Space Science Division. He is currently involved in development of high precision GNSS data processing software. His research interests include satellite GNSS data processing, high precision orbit determination, and their applications to space geodesy.

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