Preliminary Products of Precise Orbit Determination Using Satellite Laser Ranging Observations for ILRS AAC
 Author: Kim YoungRok, Park SangYoung, Park EunSeo, Lim HyungChul
 Organization: Kim YoungRok; Park SangYoung; Park EunSeo; Lim HyungChul
 Publish: Journal of Astronomy and Space Sciences Volume 29, Issue3, p275~285, 15 Sep 2012

ABSTRACT
In this study, we present preliminary results of precise orbit determination (POD) using satellite laser ranging (SLR) observations for International Laser Ranging Service (ILRS) Associate Analysis Center (AAC). Using SLR normal point observations of LAGEOS1, LAGEOS2, ETALON1, and ETALON2, the NASA/GSFC GEODYN II software are utilized for POD. Weeklybased orbit determination strategy is applied to process SLR observations and the postfit residuals check, and external orbit comparison are performed for orbit accuracy assessment. The root mean square (RMS) value of differences between observations and computations after final iteration of estimation process is used for postfit residuals check. The result of ILRS consolidated prediction format (CPF) is used for external orbit comparison. Additionally, we performed the precision analysis of each ILRS station by postfit residuals. The postfit residuals results show that the precisions of the orbits of LAGEOS1 and LAGEOS2 are 0.9 and 1.3 cm, and those of ETALON1 and ETALON2 are 2.5 and 1.9 cm, respectively. The orbit assessment results by ILRS CPF show that the radial accuracies of LAGEOS1 and LAGEOS2 are 4.0 cm and 5.3 cm, and the radial accuracies of ETALON1 and ETALON2 are 30.7 cm and 7.2 cm. These results of station precision analysis confirm that the result of this study is reasonable to have implications as preliminary results for administrating ILRS AAC.

KEYWORD
precise orbit determination , satellite laser ranging , GEODYN II , LAGEOS , ETALON , International Laser Ranging Service Associate Analysis Center

1. INTRODUCTION
The International Laser Ranging Service (ILRS) is an international organization for overall management of operation and data processing of satellite laser ranging (SLR) and lunar laser ranging (LLR) systems (Pearlman et al. 2002). Established in 1998 by the International Association of Geodesy (IAG), the ILRS has been supporting research activities associated with provision and management of SLR/LLR observations, prediction and determination of satellite orbits, geodesy, geophysics, lunar research, etc. The ILRS also provides the International Earth Rotation Service (IERS) with essential data for the precise generation and maintenance of the international terrestrial reference frame (ITRF). Together with the International GNSS Service (IGS) and the International VLBI Service (IVS), the ILRS is one of the international organizations of the IAG that provide data of the Earth and its related measurements. Currently in March 2012, the ILRS is operating four operation centers (OCs), two global data centers (GDCs), one regional data center (RDC), 9 analysis centers (ACs), four lunar analysis centers (LACs), and 17 associate analysis centers (AACs). Also, the central bureau (CB) manages and controls the entire activity of the ILRS and the governing board (GB) sets general guidelines of the organization. Fig. 1 shows the whole organization chart of the ILRS.
The official, main products by the ILRS are largely classified into station coordinates and Earth orientation parameters (EOPs). Other products include analysis results of gravitational models of the Earth, precise orbit ephemerides (POEs) derived by precise orbit determination (POD) for satellites, models verifications related to satellite
dynamics, results from complementary POD for supporting other satellite missions, information of the lunar ephemeris and libration for studies on the inside of the Moon and the relativity theory (Pearlman et al. 2002). Among the organization components in the ILRS, the AC and AAC achieve scientific results by processing the SLR data and applying the consequences. By the SLR data processing, the AC creates the ILRS products of EOPs, the ILRS station coordinates, the precise orbits of LAGEOS, which is the representative, SLRdedicated, geodetic satellite, and fundamental physical constants in geophysics. To achieve this, the SLR data processing and analysis of LAGEOS1 and LAGEOS2 must be included in the process and the EOPs including the station coordinate results and the ranges and time biases for individual stations should be generated weekly or subweekly. The AAC provides orbit predictions, timerelated biases, and POEs, and station coordinates for satellites, and is encouraged to perform comparisons between the AC products and the combined solutions by other space geodetic techniques for the production of ITRF and the support for POD. Although the AC and the AAC produce similar outcomes with each other, the role of the AC is to derive them regularly at a stable level while the AAC creates parts of arbitrary products.
The most fundamental product for the operations of the AC and the AAC is the POD results of LAGEOS, but any precision standard for the POD results of LAGEOS is not specifically presented by the ILRS. Hence, an organization who is considering operating an AC or AAC can compare the POD results for LAGEOS between the current AC or AAC of the ILRS and other researches to determine whether the products are appropriate for the operation. The operation of an AC is practically significant in deriving such POD results stably and obtaining scientific attainments from them, while the operation of an AAC is important in deriving reliable POD results which serve as a basis for the AC products and scientific attainments. A country operating an AC of the ILRS is regarded as verified that their technology for system operation and data processing of SLR has reached a level of meeting the international requirements, and an operation of an AAC means that they hold the technology of SLR data processing for reliable products and are ready to apply that technology. The most important meaning of hosting and operating an AC or AAC of the ILRS is that they can internationally lead the researches on the data processing and application of SLR. Currently in Asia, China, Japan, and Australia have joined the ILRS as active members and are operating ACs and AACs. In Korea, the recent development of the accurate ranging system for geodetic observationmobile (ARGOM), a mobile SLR system, by the Korea Astronomy and Space Science Institute (KASI) is stimulating the demand of data processing and application of SLR, and it has become required to acquire the technology of SLR data processing at a level of the ILRS AAC for reliable system verifications and scientific results (Jo et al. 2011).
SLR is known to be the most precise method for measuring the distance between a satellite and a ground station (Seeber 2003). The precision of a single shot is about 550 mm and that of normal point (NP) data, for which the measured values are averaged within the data range of about two minutes to prevent a scattering of the observing data, is as high as 112 mm (Montenbruck & Gill 2000). The most representative products using SLR data are the satellite POD and the POE from it. Recently, as the precision of SLR observations is improving, SLR is increasingly more applied as a tool for verifications of POD results or independent calibrations of observations from other tracking systems such as the global positioning system (GPS), rather than for researches of performing POD only with SLR observations (Zhu et al. 1997, Barlier et al. 2001, Schumacher et al. 2001, Urschl et al. 2005, 2007, Kim et al. 2009, Hwang et al. 2011). However, the high precision of distance measurement of SLR data is a merit also for POD, and SLR data are still used frequently for orbit determinations for the SLRdedicated geodetic satellites. Particularly, in the cases of LAGEOS1 and LAGEOS2, which are constantly observed by various countries, the postfit residuals obtained at the final stage after a converging process of estimation after the POD using SLR observations are used as a measure to check the state of a ground station and to determine whether the capability of operating a ground station meets the ILRS standards. Therefore, it should be most urgent for securing the data processing technology at a level of the ILRS AAC to acquire reliable results through the POD of SLRdedicated geodetic satellites such as LAGEOS1 and LAGEOS2.
In this study, as a preliminary research for an operation of an ILRS AAC, we performed POD followed by analysis and orbit quality assessment of the generated POE results for LAGEOS1, LAGEOS2, ETALON1, and ETALON2, the representative SLRdedicated geodetic satellites, using GEODYN II by NASA/GSFC, the representative program for POD and parameter estimation. NP data, which currently is the primary releasing form of ILRS data, are used for the SLR observations. To verify the POD results, we first analyze the postfit residuals which are most widely used in confirming performances of orbit determination of SLRdedicated geodetic satellites. Additionally, an external orbit comparison is performed to verify the reliability by a comparison with orbit determination results by another independent organization, where we use the consolidated prediction format (CPF) provided by the Predictions Formats Study Group at the ILRS for the external orbit (http://ilrs.gsfc.nasa.gov/products_formats_procedures/predictions/cpf.html). Finally, we perform a station precision analysis to confirm the results of ILRS station precision.
2. PRECISE ORBIT DETERMINATION
2.1 Satellites for Geodetic Missions
Currently in March 2012, 37 SLR satellites in total are carrying out their missions related to space geodesy except for the LLRrelated satellites (http://ilrs.gsfc.nasa.gov/satellite_missions/list_of_satellites/). Such SLR satellites are playing important roles in obtaining results from the studies on Earth tide, oceans, the atmosphere system, and their interactions with each other. Particularly, as the precision of SLR observations and PODs using them improves, by data processing of LAGEOS1 and LAGEOS2, which are the representative, SLRdedicated, geodetic satellites, the postfit residuals are as small as 1 cm. LAGEOS1, LAGEOS2, ETALON1, and ETALON2 are the most representative SLRdedicated geodetic satellites of which data are processed at the AC and AAC of the ILRS and information is presented in Table 1. The actual appearances of the satellites are shown in Fig. 2 (http://ilrs.gsfc.nasa.gov/satellite_missions/list_of_satellites/). As seen in Fig. 2, the shapes of LAGEOS1, LAGEOS2, ETALON1, and ETALON2 are spherical, of which the advantage is the minimal effect by a perturbation such as solar radiation pressure. Also, most SLRdedicated geodetic
satellites suffer not much from air drag since they are in the medium earth orbit or higher orbits. Thus, these spherical types of SLRdedicated geodetic satellites can be used as the best tools for confirming the level of a dynamic model.
2.2 The Concept of POD
In general, POD of a satellite means to determine the state vector of the satellite at a given time precisely by using the measurements and an estimation theory and obtain a POE with a cmlevel precision for positioning. The state vector are expressed by the position and velocity of the satellite, the solar radiation pressure constant (C_{R}) and the air drag constant (C_{D}) in the dynamic model, empirical accelerationrelated constants, the position of the ground station in the measurement model, the zenith delay of the atmospheric model, and a range bias. A wide range of satellitetracking data from GNSS, SLR, DORIS, radio, and optical observations are used for the measurements. The batch estimation of LeastSquare Batch Filter and the sequential estimation of extended Kalman filter are popular estimation methods for orbit determination, where the leastsquare batch filter is most widely used for POD. More recently, also a batch filter using the unscented transformation (UT), which is robust against a nonlinearity, has been studied (Park et al. 2010, Kim et al. 2011).
For POD, a dynamic model is required to set the equation of motion considering various perturbations on the satellite, and predict the next state vector by integrating the state vector numerically with time. The dynamic model is largely divided into gravitational perturbations and nongravitational perturbations, and is expressed by Eqs. (1) and (2).
Here,
and
denote the position and velocity vectors of the satellite, respectively,
G the gravitational constant of the Earth,M_{E} the mass of the Earth, andthe perturbation expressed in acceleration. Typical examples of this perturbation include an effect by the asymmetric field of the Earth's gravity, gravitational effects by the Sun, the Moon, and the planets in the solar system, the solar radiation pressure, the Earth albedo, air drag, the general relativity, the polar motion of the Earth, and the Earth and ocean tides.
In the next step, a measurement model is required to be built to acquire tracking data of the satellite and generate observations. The principle of distance measurement using a SLR system is simple. The distance between the ground station and the satellite is calculated by measuring the round trip time of laser from the ground station to the laser retroreflector array (LRA) on the satellite. Errors from various sources are involved in this measurement, but most SLR systems have an advantage of relatively simple modeling of observation since a delay error by the ionosphere, which is inverse proportional to frequency squared, can be ignored by using a Nd:YAG laser at the optical wavelength of 532 nm for the observation. On the other hand, it is important to calculate the error from the tropospheric refraction precisely owing to the significant influence by the weather condition in the atmosphere. The distance measured by a SLR system between the reference point of laser transmission/reception at the ground station and the laser reflector on the satellite can be expressed by Eq. (3) (Tapley et al. 1985).
Here,
ρ denotes the distance between the reference point of laser transmission/reception at the ground station and the laser reflector on the satellite,c the speed of light in vacuum, Δt the round trip time of the laser, Δ_{ρtrop} the error by the tropospheric delay, Δ_{ρgrel} the error from the relativity theory, Δ_{ρC.M.} the error related to the position and center of mass of the LRA,b the system delay error determined by a verification and correction, and ε is for observational errors which cannot be modeled. It is not necessary to estimate the error related to the system delay since the NP data provided are already corrected at the ground station for that error of the system delay. The impact of the unmodelable observational error is usually not so large, but sometimes it can be so great to affect the precision significantly. In this case, individual stations of the ILRS may provide error information and new NP data updated using the SLReport (http://ilrs.gsfc.nasa.gov/contact_ilrs/mail_services/slrreport/index.html) even after the generation and release of the NP data. After the dynamic model and the measurement model built, the final residual of orbit determination and POE are obtained from an iteration of POD with the estimation theory applied to make the OC residual between the measured distance of the satellite (observation, O) and the modeled distance (computation, C) which is repeated until meeting some desired converging criteria.2.3 POD Strategies
In this study, we use SLR NP data for the observational data for the POD of LAGEOS1, LAGEOS2, ETALON1, and ETALON2, of which the NP data are provided by the two GDC of the ILRS through their homepage or anonymous FTP (http://ilrs.gsfc.nasa.gov/products_formats_procedures/ftp_archives/index.html). Here, we obtaine the NP data through the ftp server (ftp://cddis.gsfc.nasa.gov/pub/slr/data/npt/) provided by the Crustal Dynamics Data Information System (CDDIS) at the NASA.
Data for one week from June 2 to June 8, 2008 are used, and the state vector result from the previous orbit determination is used for the prior value for each satellite in the POD. The required information for the orbit determination of each satellite is presented in Table 1, which is available from the information provided by the ILRS. For the POD, we adopt a weeklybased processing of SLR observations using GEODYN II which is one of the software tools used at the AC or AAC.
Table 2 summarizes the modeling information of GEODYN II for the POD. We use the grace gravity model (GGM02C) by Tapley et al. (2005) for the Earth gravity model. Because of the relatively higher altitude of the measured satellites compared to general LEO satellites, dimensions of the gravity field are limited to 30 × 30 which are consistent with the current dimension limit at the ILRS AAC for efficient PODs considering altitudes. For the planetary ephemeris for the gravity of the Sun, the Moon, or the planets in the solar system, we use DE1403 which uses the derivatives from the Jet Propulsion Laboratory (JPL) DE403 (Standish et al. 1995). The Jacchia model (Jacchia 1971) is used for the atmospheric density model, the ITRF2005 SLR rescaled (Altamimi et al. 2007) for the station coordinates, and the IAU2000 model (Mathews et al. 2002) for the precession and nutation related values. We use the model by Mendes et al. (2002) for the tropospheric delay, and the models of IERS Conventions 2003 (McCarthy & Petit 2004) and GOT99.2 (Ray 1999) for the Earth and ocean tides, respectively. A leastsquare batch filter is applied as the estimation theory to estimate the parameters including the position and velocity of the satellite, the position and velocity of the ground station, the solar radiation pressure constant (C_{R}), a constant related to an empirical general acceleration, and the range bias. The air drag constant (C_{D}), which is often one of the parameters to be estimated in a general POD process, is not included in this study as in the cases at other ACs or AACs since the effect by the atmospheric density is ignorable for the SLRdedicated geodetic satellites at such high altitudes as LAGEOS or ETALON. On the other hand, while at some ACs or AACs, the solar radiation pressure constant (C_{R}) may be excluded from their estimations or set the range bias zero in their PODs, we estimate as many major parameters as possible for results in more general situations.
3. ORBIT QUALITY ASSESSMENT
In general, verification methods for the results from orbit determination are largely classified into three categories. The first one is the analysis of postfit residuals, in which the precision is verified by the residual values of orbit determination obtained finally after the iteration of the POD estimation, the second one is the overlap comparison, which checks how the results are selfconsistent by overlapping the starting and ending points of a continuous range of orbit determination, and the final one is the external orbit comparison where the POD results are compared with those from other models or softwares. In the cases of SLRdedicated geodetic satellites, the precision is mostly verified by the postfit residuals which corresponds to the precision in the direction of the distance since the precision in the radial direction is high because of the precise measurement of distance while the precisions in the along and crosstrack directions are low. Particularly, for the SLRreference satellites with a geometric appearance of sphere such as LAGEOS and ETALON, the residual of orbit determination itself has the highest priority as a standard in the determination of the precision of orbit determination. If a POE is available for a comparison, it can be indirectly checked through the external orbit comparison in what error range the currently generated orbit is consistent with another orbit. A disadvantage in the case of a SLRdedicated geodetic satellite is that the verification is confined in the precision range of the compared orbit itself because of the small number of POEs available for the comparison. Also, in the case of SLRdedicated geodetic satellites, each station performs analysis of precision for NP data and their results can be used as another indirect verification for the precision of POD results. In this study, we verify the precision of the obtained orbits by the analysis of postfit residuals, the external orbit comparison, and the station precision analysis.
3.1 Postfit Residuals
We check first the postfit residuals for the verification of the POD results. In the estimation process of orbit determination, the OC residual between the measured distance of the satellite (O) and the computed distance (C) is obtained at each iteration step. The postfit residual is the
final OC residual after the orbit determination is completed by meeting the converging condition for the estimation. Therefore, confirming this postfit residual is one of the direct methods for verifying the precision of determined orbits. Particularly, this method is applied as the primary verification of the orbit determination results for the SLRreference satellites since the precision of the NP data is very high in the cases of those satellites. Fig. 3 shows the postfit residuals for LAGEOS1 and LAGEOS2, and Fig. 4 shows those for ETALON1 and ETALON2. In Table 3, the postfit residuals of each satellite are presented in root mean square (RMS). We can see that the residuals are 1.0?2.0 cm RMS for LAGEOS1 and LAGEOS2 and 2.0?3.0 cm RMS for ETALON1 and ETALON2. In general, the postfit residuals after an orbit determination for LAGEOS1 and LAGEOS2 are known to be 1.0?2.0 cm, while those values obtained by Zhao et al. (2008) from PODs at a 3day interval for the SLR NP data of LAGEOS1 and LAGEOS2 from 2005 to 2008 were about 1.2 cm RMS in average for both LAGEOS1 and LAGEOS2. In the study by Otsubo (2000), the postfit residuals were obtained to be 1.5?2.0 cm RMS for 7day data of the LAGEOS satellites and 1.5?4.0 cm RMS for 14day data of the ETALON satellites. Noomen (2001) showed that the postfit residuals obtained by the previous studies were 1.0?3.0 cm for LAGEOS1 and LAGEOS2. The Natural Environment Research Council (NERC) Automatic Global SLR Normal Point Quality Analysis in U.K., one of the ILRS ACs, reported postfit residuals of about 2.0 cm RMS based on their 67day data of 10 stations (http://sgf.rgo.ac.uk/slrweb/auto_analysis.html). Comparing with those results, we can see that the postfit residuals from our POD have a consistent precision with those from the previous studies and from the ILRS AC. This implies that this study of using GEODYN II for SLR data processing and POD can obtain the results at a level of an ILRS AAC.
3.2 External Orbit Comparison (CPF)
In the cases of LEO satellites or GPS satellites where a number of POEs are available from orbit determinations by various organizations, the method of external orbit comparison, in which the confidentiality is secured by comparing individual precise orbits, is mainly used for the verification of orbit precision. On the other hand, in the cases of SLRdedicated geodetic satellites at high altitudes like LAGEOS and ETALON, the postfit residuals are mainly used for the precision verification rather than the external orbit comparison since precise orbits for the comparison of precision are not released so often and the precision of the SLR distance measurement itself is too high. Only in the cases of SLRdedicated geodetic satellites, the ILRS provides CPF of which the positional precision is known to be from a few to a few tens meters (http://ilrs.gsfc.nasa.gov/products_formats_procedures/predictions/cpf.html). A disadvantage of CPF is that the precision can be verified only within a range of general orbit precision of CPF since this is not a POE and the orbit precision is not clearly presented in many cases depending on the time periods. To generate CPF as a product of an ILRS AAC in the future,
however, we try to convert the results of orbit determination to the form of CPF and use them for the external orbit comparison to compare the orbit precisions. We assume that the orbit precision of CPF stays within the general precision range of CPF (from a few to a few tens meters) for the comparison in the radial direction since the CPF over the period of our study does not include any information on the orbit precision either. This means that the comparison results are not for an absolute orbit precision but for a relative precision compared to the CPF. This may rather be a method of confirming the relative precision of the used CPF, by putting together the results of the postfit residuals and the external orbit comparisons with CPF.
Figs. 5 and 6 show the comparison results for the component of radial direction between the CPF of each satellite and the results from this study, and Table 4 summarizes the precision in the radial direction in RMS. As a result, in the radial direction, we obtain the precision of 4?5 cm for LAGEOS1 and LAGEOS2, and 7?30 cm for ETALON1 and ETALON2. Considering that the resulting precision is at a level of a few to a few tens centimeters in the radial direction, we can see that our results are different
from CPF by a few to a few tens centimeters in the radial direction. This result is within the general error range of the CPF precision, and it is indirectly confirmed that CPF contains relative errors of a few to a few tens centimeters in the radial direction compared to our results.
3.3 ILRS Station Precision Analysis
We perform an assessment of the ILRS station precisions using the postfit residuals for an analysis and indirect comparison of the POD results. For this purpose, we first derive RMS values of the postfit residuals obtained from the PODs of LAGEOS1, LAGEOS2, ETALON1, and ETALON2 for each ILRS station, and then apply those values to derive and analyze the precision for each station.
The ILRS provides the SLR global performance report quarterly based on the rapid orbital analysis or quick look analysis by ACs (http://ilrs.gsfc.nasa.gov/stations/site_info/global_report_cards/perf_2011q4_wLLR.html). The SLR global performance report cannot directly be compared to the postfit residuals from a POD since this report contains mainly the precision of the NP data itself, the range bias for the distance measurements, and statistical information related to them, for the SLRdedicated geodetic satellites. However, this report can be used to confirm indirectly the performance of the current POD results by comparing the precisions of the NP data itself and the POD results. The AC/AAC report section in the ILRS report introduces from time to time the postfit residual results after PODs by ACs or AACs for SLRdedicated geodetic satellites, but we exclude this report from the comparison since its data are neither plenty enough nor organized as a whole, and instead we adopt the AC results of orbit analysis and the mean NP precision in RMS of the LAGEOS satellite presented in the SLR global performance report. The AC results of orbit analysis and the mean NP precision in RMS of the LAGEOS are derived together at the same time for the entire data of a quarter and do not represent the weekly precision used in this study, which can still be predicted indirectly through the precision of the entire quarter. Here, we compare the precision indirectly with the assessment result of each ILRS station precision using the SLR global performance report in the corresponding quarter to the period of this study.
Tables 57 shows the results of station precision. Brief information for each station is presented in Table 8. The results for all the satellites are summarized in Fig. 7. The results of individual stations show that the station precision is similar with each other in postfit residual in the cases of LAGEOS1 and LAGEOS2. It is confirmed that the precision of LAGEOS2 is higher than that of LAGEOS1 in general. The precisions of most stations are around 1 cm RMS while the RMS values of a few stations (7406, 7811) are rather large to decrease the precision of the POD results from all the LAGEOS satellites. Also in the cases of ETALON1 and ETALON2, the postfit residuals show similar precisions between different stations, but this is not clearly confirmed due to the small number of stations used. However, it is confirmed that the POD precision of all the satellites can be degraded when there are stations with poor RMS values as in the cases of the LAGEOS satellites.
The results of the ILRS SLR global performance report in the quarter including the same period are summarized in Table 9. The foremost values are the AC results of orbit analysis in RMS and the values in parentheses are the mean NP values of single observations by the LAGEOS satellites in RMS. The results from the Deutsches Geodaetisches Forschungsinstitut (DGFI) among the ACs are used for the results of orbit determination. The DGFI results are from the weekly processing of SLR observations using the DGFI Orbit and geodetic parameter estimation software. Fig. 8 compares the postfit residuals from our POD for LAGEOS2, the DGFI results of orbit analysis, and the mean LAGEOS NP precision from the ILRS in RMS. From this comparison, we can confirm in most cases that our postfit residuals are better than the DGFI results of orbit analysis or the mean LAGEOS NP precision of the ILRS, and that we obtain precise orbits from our POD.
4. CONCLUSIONS
In this study, we performed a POD using SLR observations and a verification of the resulting precision for LAGEOS1, LAGEOS2, ETALON1, and ETALON2, the representative SLRdedicated geodetic satellites, as a preliminary study to prepare for an ILRS AAC. As a result of the verification of postfit residuals, we obtained the precisions at levels of an ILRS AC with 1?2 cm RMS for LAGEOS1 and LAGEOS2 and 2?3 cm RMS for ETALON1 and ETALON2. From the comparison with the ILRS CPF using the method of external orbit comparison, it was confirmed that the differences in the radial direction are 4?5 cm RMS for LAGEOS1 and LAGEOS2 and 7?30 cm RMS for ETALON1 and ETALON2. Through the analysis of station precision we found that the stations with high precisions and those with poor precisions can be distinguished to be reflected to a POD strategy, and that the precision of our results are similar to or better than those of the orbit analysis by an ILRS AC or the ILRS NP precision in RMS. One of the most important roles of the ILRS AACs is to perform PODs and derive reliable products for geodetic satellites, particularly for the LAGEOS satellites. In conclusion, our results from the SLR data processing and POD using GEODYN II are meaningful in a preliminary stage to reach the level of an ILRS AAC in the performance and results of SLR data processing.

[Fig. 1.] International Laser Ranging Service organizations (http://ilrs.gsfc.nasa.gov).

[Table 1.] Satellites of geodetic missions (http://ilrs.gsfc.nasa.gov/satellite_missions).

[Fig. 2.] LAGEOS1, LAGEOS2, ETALON1, ETALON2 (http://ilrs.gsfc.nasa.gov/satellite_missions/list_of_satellites/).

[Table 2.] Dynamic and measurement models for POD.

[Fig. 3.] Postfit residuals (LAGEOS1, LAGEOS2).

[Fig. 4.] Postfit residuals (ETALON1, ETALON2).

[Table 3.] The result of postfit residuals.

[Fig. 5.] The differences of radial component (LAGEOS1, LAGEOS2).

[Fig. 6.] The differences of radial component (LAGEOS1, LAGEOS2).

[Table 4.] The result of external orbit comparison.

[Table 5.] The result of station precision analysis (LAGEOS1).

[Table 6.] The result of station precision analysis (LAGEOS2).

[Table 7.] The result of station precision analysis (ETALON1, ETALON2).

[Table 8.] The information of ILRS stations.

[Fig. 7.] The postfit residual precision of each International Laser Ranging Service station.

[Fig. 8.] The normal point precision and postfit residuals of each International Laser Ranging Service station.

[Table 9.] The result of SLR global performance report (LAGEOS).