Precise Orbital and Geodetic Parameter Estimation using SLR Observations for ILRS AAC
 Author: Kim YoungRok, Park Eunseo, Oh Hyungjik Jay, Park SangYoung, Lim HyungChul, Park Chandeok
 Organization: Kim YoungRok; Park Eunseo; Oh Hyungjik Jay; Park SangYoung; Lim HyungChul; Park Chandeok
 Publish: Journal of Astronomy and Space Sciences Volume 30, Issue4, p269~277, 15 Dec 2013

ABSTRACT
In this study, we present results of precise orbital geodetic parameter estimation using satellite laser ranging (SLR) observations for the International Laser Ranging Service (ILRS) associate analysis center (AAC). Using normal point observations of LAGEOS1, LAGEOS2, ETALON1, and ETALON2 in SLR consolidated laser ranging data format, the NASA/GSFC GEODYN II and SOLVE software programs were utilized for precise orbit determination (POD) and finding solutions of a terrestrial reference frame (TRF) and Earth orientation parameters (EOPs). For POD, a weeklybased orbit determination strategy was employed to process SLR observations taken from 20 weeks in 2013. For solutions of TRF and EOPs, loosely constrained scheme was used to integrate POD results of four geodetic SLR satellites. The coordinates of 11 ILRS core sites were determined and daily polar motion and polar motion rates were estimated. The root mean square (RMS) value of postfit residuals was used for orbit quality assessment, and both the stability of TRF and the precision of EOPs by external comparison were analyzed for verification of our solutions. Results of postfit residuals show that the RMS of the orbits of LAGEOS1 and LAGEOS2 are 1.20 and 1.12 cm, and those of ETALON1 and ETALON2 are 1.02 and 1.11 cm, respectively. The stability analysis of TRF shows that the mean value of 3D stability of the coordinates of 11 ILRS core sites is 7.0 mm. An external comparison, with respect to International Earth rotation and Reference systems Service (IERS) 08 C04 results, shows that standard deviations of polar motion
X_{P} andY_{P} are 0.754 milliarcseconds (mas) and 0.576 mas, respectively. Our results of precise orbital and geodetic parameter estimation are reasonable and help advance research at ILRS AAC.

KEYWORD
precise orbit determination , terrestrial reference frame , Earth orientation parameters , satellite laser ranging , GEODYN II , LAGEOS , ETALON , international laser ranging service associate analysis center

1. INTRODUCTION
The International Laser Ranging Service (ILRS) manages satellite laser ranging (SLR) and lunar laser ranging (LLR) data and their operations (Pearlman et al. 2002). The ILRS has been supporting research related to SLR/LLR observations, including satellite orbits, geodesy, geophysics, and lunar science. The ILRS consists of operation centers, global data centers, a regional data center, analysis centers (ACs), lunar analysis centers, associate analysis centers (AACs), and some working groups. A central bureau and governing board also manage activities of the ILRS. Products of the ILRS are largely categorized into precise orbit ephemerides (POEs), geocentric coordinates and motions of stations, and Earth orientation parameters (EOPs). Among the ILRS components, AC and AAC produce scientific results and analysis by processing SLR tracking data. The AC makes the ILRS products of EOPs and station coordinates on a weekly or subweekly basis. The SLR data processing of global LAGEOS1 and LAGEOS2 observations should be included in their orbit solution. The AAC produces satellite orbit predictions, time biases, POEs, station positions, and velocities at irregular intervals. For July 2013, the ILRS operates 8 ACs and 16 AACs as shown in Tables 1 and 2 (http://ilrs.gsfc.nasa.gov/science/analysisCenters/).
The precise orbital and geodetic parameters estimation is the most fundamental procedure of an AC or AAC. In particular, the primary source for AC and AAC products are the results of POD and solutions of a terrestrial reference frame (TRF) and EOPs using SLR observations from SLRdedicated geodetic satellites such as LAGEOS1, LAGEOS2, ETALON1, and ETALON2. Therefore, an organization that is trying to operate an AC or AAC must generate the results of POD and solutions of a TRF and EOPs using SLR observations from SLRdedicated geodetic satellites. In Korea, the accurate ranging system for geodetic observation mobile (ARGOM) of the Korea Astronomy and Space Science Institute (KASI) has been developed (Jo et al. 2011, Park et al. 2012). A preliminary study on SLR data processing, at a level suitable for ILRS AAC, was performed by POD of LAGEOS1, LAGEOS2, ETALON1, and ETALON2 using SLR observations (Kim et al. 2012). To secure the SLR data processing technology, at a level for ILRS AAC, it is necessary to obtain solutions of a TRF and EOPs for SLRdedicated geodetic satellites.
In this study, as research for preparing an ILRS AAC, we performed precise orbital and geodetic parameter estimation using SLR observations. We analyzed POD results and solutions of a TRF and EOPs for LAGEOS1, LAGEOS2, ETALON1, and ETALON2, the representative SLRdedicated geodetic satellites. The GEODYN II and SOLVE software programs developed by NASA/GSFC were used for precise orbital and geodetic parameter estimation (Pavlis et al. 1998, Ullman 2010). Normal point (NP) data from ILRS stations in consolidated laser ranging data format (CRD) were used for measurements. To verify our orbit solutions, we first analyzed the POD results of LAGEOS1, LAGEOS2, ETALON1, and ETALON2 by postfit residuals. Next, we performed a precision analysis of our solutions by applying both a stability analysis of TRF and an external comparison of EOPs with solution, EOP 08 C04 (http:// hpiers.obspm.fr/eoppc/) by International Earth rotation and Reference systems Service (IERS).
2. PRECISE ORBIT DETERMINATION
2.1 Satellites for Geodetic Missions
In July 2013, 40 SLR satellites are carrying out their missions, excluding the LLRrelated satellites (http:// ilrs.gsfc.nasa.gov/satellite_missions/current_missions/). Among SLR satellites, LAGEOS1, LAGEOS2, ETALON1, and ETALON2 are the most representative geodetic satellites. These satellites have been playing a key role in studies on geodynamics, geodesy, and satellite orbital motion, and in related research areas. Information about each satellite is presented in Table 3 (http://ilrs.gsfc.nasa. gov/satellite_missions). As seen in the table, because LAGEOS1, LAGEOS2, ETALON1, and ETALON2 have spherical shapes, a perturbation model of solar radiation pressure, for example, can be simplified. As these satellites occupy altitudes greater than 5,000 km, the air drag effect is weak. Recently, the precisions of postfit residuals of LAGEOS1 and LAGEOS2 are as small as 1 cm (Sośnica et al. 2012). A precise modeling of perturbations and the precisions of estimation results are key points of geodetic parameter estimation problems. Thus, LAGEOS1, LAGEOS2, ETALON1, and ETALON2 are, arguably, the best tools for verifying the results of precise orbital and geodetic parameter estimation.
2.2 POD strategies
POD finds the state vector of an orbiting satellite at a specific time by using satellite tracking measurements and an estimation theory (Noomen 2001). In SLR data processing, POD is the essential procedure for geodetic parameter estimation. In this study, weeklybased POD was performed by the NASA/GSFC GEODYN II software using SLR CRD NP data of LAGEOS1, LAGEOS2, ETALON1, and ETALON2. SLR CRD NP data were obtained from an ftp server (ftp://cddis.gsfc.nasa.gov/pub/slr/data) by the crustal dynamics data information system (CDDIS) at NASA (Noll 2010). SLR observations from 24 ILRS stations, which were collected for 20 weeks from 7 January to 20 May, 2013, were used. Information about the ILRS stations and SLR NP observations for POD is displayed in Table 4. The NP number of LAGEOS is generally larger than that of ETALON, since the NP bin size of LAGEOS is shorter than that of ETALON. The NP bin size of LAGEOS is shorter than that of ETALON. The NP bin size of LAGEOS is 120 s while that of ETALON is 300 s. In Table 4, σ is the observationweighting sigma value of a station for GEODYN II input cards of POD. If σ>1 for a station, then the NPs of that station are underweighted by as much as the σvalue in the POD process. Therefore, ILRS stations for which 3 the crustal dynamics data information
σ =1 can be regarded as stations with a good tracking performance.Table 5 summarizes the model information of GEODYN II. The GRACE gravity model (GGM02C) for Earth gravity field modeling (Tapley et al. 2005) was used. The dimensions of the gravity field are limited to 30 because there is no difference between LAGEOS orbits using a degree of the gravity field above 30 (Sośnica et al. 2012). For the planetary ephemeris of the Sun, the Moon, or the planets in the solar system, the Jet Propulsion Laboratory (JPL) DE1403 that is derived from DE403 was ussed (Standish et al.1995). For atmospheric density modeling, the Jacchia model was applied (Jacchia 1971). The ITRF2005 SLR rescaled coordinates (Altamimi et al. 2007) and the IAU2000 model (Mathews et al. 2002) were used for station coordinates and the precession and nutationrelated values, respectively. The MendesPavlis model (Mendes et al. 2002, Mendes & Pavlis 2004) was used for tropospheric delay modeling, and the IERS Conventions 2003 (McCarthy & Petit 2004) and GOT00.2 (Ray 1999) were applied to account for Earth and ocean tides, respectively. The solar radiation pressure coefficient,
C_{R} , was set to a prior value of 1.13. For numerical integration, the 11^{th} Cowell’s method was used with a step size of 150 s for LAGEOS and 300 s for ETALON, respectively. A leastsquare batch filter was applied for parameter estimation, and a 3.5 sigmadata editing strategy was used for baddata rejection.2.3 Orbit quality assessment
For orbit quality assessment of SLRdedicated geodetic satellites such as LAGEOS and ETALON, the root mean square (RMS) value of postfit residuals is commonly used. In this study, the POD results of LAGEOS1, LAGEOS2, ETALON1, and ETALON2 were analyzed by a postfit residuals check. The total numbers of NP observations for 20 weeks were 25,287 and 23,484 for LAGEOS1 and LAGEOS2, and 2,731 and 2,379 for ETALON1 and ETALON2, respectively. After data editing, the numbers of NP observations used for POD processing decreased to 22,845 and 21,519 for LAGEOS1 and LAGEOS2 and to 2,504 and 2,200 for ETALON1 and ETALON2, respectively. Table 6 shows information about each weekly arc and the RMS values of postfit residuals of each satellite. The mean RMS values of LAGEOS1 and LAGEOS2 are 1.20 cm and 1.12 cm, respectively. Fig. 1 shows the RMS values of postfit residuals for LAGEOS1 and LAGEOS2 at each weekly arc. The values of xaxis indicate the first day of each arc. The mean RMS values of ETALON1 and ETALON2 are 1.02 cm and 1.11 cm, respectively. Fig. 2 shows the RMS values of postfit residuals for ETALON1 and ETALON2 at each weekly arc. The postfit residual is the final difference between the observed range and the computed range of the satellite after convergence. Therefore, it shows how well the determined orbit fits the measurements. The results of postfit residuals indicate that the precisions of POD results, in this study, are at a 1cm level. To achieve 1cm level precision, various geodetic parameters including satellite position and velocity, station coordinates, modeling coefficients of perturbations, and related values must be estimated very precisely. Moreover, the choice of the data editing and observation weighting of each station is a critical factor to obtain 1cm level orbits. In this study, all these factors are considered carefully, and precise orbits of 1cm level precision were finally obtained. In particular, the generation of cmlevel orbits of LAGEOS1 and LAGEOS2 is an essential part of ILRS AC data processing. Kim et al. (2012) summarized previous orbit precisions of LAGEOS and showed that the quality of LAGEOS orbits can reach a 1cm level. Recently, the precision of LAGEOS orbits has improved to be less than 1 cm (Sośnica et al. 2012). Therefore, in this study, the precision of POD results is important for ILRS AAC.
3. SOLUTIONS OF TRF AND EOPS
Weeklybased solutions of TRF and EOPs are one of the main products of ILRS ACs. Strategies to obtain solutions of TRF and EOPs for this study and four ACs are summarized in Table 7. Details of the strategies for generating TRF and EOPs of each AC are summarized in a description of ACs in CDDIS (ftp://cddis.gsfc.nasa.gov/slr/ products/ac/) and the socalled pos+eop product of ACs in CDDIS (ftp://cddis.gsfc.nasa.gov.slr/products/pos+eop/). Most ACs of ILRS employ the POD results of LAGEOS1, LAGEOS2, ETALON1, and ETALON2 to generate a weekly solution of TRF and a daily solution of EOPs. Each AC uses different editing and constraint strategies for SLR data processing and a combination of POD results from each satellite, respectively. Constraints mean that prior values (standard deviation) of TRF and EOPs are restricted within proper values, which are based on a requirement for each spacegeodetic technique. For SLR observations, ILRS recommends loosely constrained solution with a prior standard deviation on TRF and EOPs exceeding 1 m for consistency. Loosely constrained solution is based on the assumption that the uncertainty of a solution is large relative to a reference. The details of loosely constrained solutions are illustrated by Heflin et al. (1992), Blewitt (1998), Davies & Blewitt (2000), Bianco et al. (2003), and Coulot et al. (2010). For SLRbased solutions, loosely constrained approach is a standard strategy to combine solutions using various spacegeodetic techniques (Altamimi et al. 2007, 2011). In this study, we followed the strategy of AC and recommendations of ILRS to obtain solutions of TRF and EOPs using POD results of LAGEOS1, LAGEOS2, ETALON1, and ETALON2. Loosely constrained scheme with an a priori value (standard deviation) on both TRF and EOPs of 1 m was applied for solutions.
The stabilities of each station coordinate were analyzed to verify our TRF solution (KASITRFsolution). Eleven ILRS core sites, which are ILRS stations with a longterm tracking history and a stable data quality and continuity (http://ilrs.gsfc.nasa.gov/docs/ILRS_contribution_to_ITRF2008.pdf ), were used for verification by performing a stability analysis of KASITRFsolution. The eleven ILRS core sites are: 7080 (McDonald, TX, USA), 7090 (Yarragadee, Australia), 7105 (Greenbelt, MD, USA), 7110 (Monument Peak, CA, USA), 7501 (Hartebeesthoek, South Africa), 7810 (Zimmerwald, Switzerland), 7825 (Mount Stromlo, Australia), 7839 (Graz, Austria), 7840 (Herstmonceux, UK), 7941 (Matera, Italy), and 8834 (Wettzell, Germany). Table 4 shows that the observationweighting σ values of the 11 ILRS core sites are 1, which means that SLR NP observations of these stations show good performance. For precision assessment of our solution of EOPs (KASIEOPssolution), an external comparison to IERS EOP time series IERS 08 C04 results was made. Polar motion, denoted
X_{P} andY_{P} , and polar motion rates of each direction were estimated and evaluated using the standard deviation of each EOP.3.1 KASITRFsolution
For the KASITRFsolution, geocentric station coordinates (
X ,Y , andZ ) of 11 ILRS core sites were obtained from LAGEOS1, LAGEOS2, ETALON1, and ETALON2 POD results using SOLVE software. The performance of the KASITRFsolution can be checked by a stability analysis. The stability of TRF can be defined by standard deviation concepts. The stability of the directions of the station positions,X ,Y , andZ , are calculated as follows (Lejba & Schillak 2011):where
i is the number of a weekly arc, and is the mean value of theX_{i} direction. The stability ofY andZ are calculated similarly. The 3D stability is calculated as:The following steps are processed for a stability analysis . First, a TRF solution at each are is obtained in which the epoch occurs at the midpoint of a week; for example, from 7 to 13 January, the reference epoch occurs at noon on 10 January. Next, the state positions of solutions are converted to values at the epoch of the first week (i.e. noon at 10 January) using the station velocities of ITRF2005. Finally, the station positions at the same epoch are compared by stability analysis. Table 8 shows the stabilities of each direction (
S_{X} ,S_{Y} , andS_{Z} ) and the 3D stabilities (S ) of 11 ILRS core sites. As shown in Table 8, 3D stabilities of the KASITRF solution are distributed from 5.7 mm to 9.2 mm. Fig. 3 shows stabilities of each component for 11 ILRS core sites. The mean value of 3D stabilities is 7.0 mm. Schillak (2012) determined the coordinates of ILRS stations using NP observations of LAGEOS1 and LAGEOS2 from 1999 to 2008 and calculated their 3D stabilities. To validate our results, determined position stabilities of ILRS core sites by Schillak (2012) are presented in Table 8. The 3D stabilities of 8 stations from 2004 to 2008 have a mean value of 6.9 mm. The 3D stability value of each station in that study is displayed in Table 8. Fig. 4 shows the 3D stability differences between the KASITRFsolution and Schillak (2012) results. We see that the precisions of 3D stabilities of TRF from our research are consistent with those from previous research.3.2 KASIEOPssolution
For the KASIEOPssolution, polar motion
X_{P} ,Y_{P} , and polar motion rates were obtained from LAGEOS1, LAGEOS2, ETALON1, and ETALON2 POD results using SOLVE software. Fig. 5 shows daily polar motion from 7 January to 26 May, 2013. To assess our daily solution, the IERS 08 C04 time series were compared. Figs. 6 and 7 show the residuals of polar motion,X_{P} andY_{P} , with respect to IERS 08 C04 values, respectively. We see that the standard deviations of differences in polar motionX_{P} andY_{P} between the KASIEOPssolution and IERS 08 C04 are 0.754 milliarcseconds (mas) and 0.576 mas, respectively. Pavlis (2002) showed that the standard deviations ofX_{P} andY_{P} residuals with respect to IERS 08 C04 are 0.529 mas and 0.503 mas, respectively. We find that the precision of results in this study is similar to that in Pavlis (2002). The precision of EOPs with respect to IERS results depends on condition of constraints for EOPs solution. In general, IERS EOP solutions were calculated under a tight constraint. Therefore, they can be more precise than individual solutions such as the KASIEOPssolution and results of Pavlis (2002). Fig. 8 shows the polar motion rates ofX_{P} andY_{P} We see that polar motion rates ofX_{P} andY_{P} vary from 0.05 microarcseconds (μas) to 0.05 μas.4. CONCLUSIONS
In this study, we performed precise orbital and geodetic parameter estimation using SLR observations and validated results of POD and solutions of TRF and EOPs to prepare for ILRS AAC. We used SLR CRD NP observations of LAGEOS1, LAGEOS2, ETALON1, and ETALON2 for 20 weeks from 7 January to 20 May, 2013 and NASA/GSFC GEODYN II and SOLVE software. As a result of the verification of POD results, we obtained postfit residuals at a level of 1cm RMS for four satellites. Stability analysis was performed for validation of the KASITRFsolution, and results show that the mean 3D stability of coordinates of 11 ILRS core sites in the KASI TRFsolution has a precision level of 7.0 mm. This result is consistent with previous stability analyses of TRF. For precision assessment of the KASIEOPssolution, external comparisons with respect to IERS 08 C04 EOP series were performed. Results show that the precision of KASIEOPssolution is comparable to that of previous research. One of the most important products of ILRS AAC and AC is the 1cm level POD results of SLRdedicated geodetic satellites such as LAGEOS and ETALON and weeklybased solutions of TRF and EOPs. In conclusion, our results of precise orbital and geodetic parameter estimation using GEODYN II and SOLVE software constitute a significant achievement in the preparation of an ILRS AAC in the performance and results of SLR data processing.

[Table 1.] ILRS analysis centers (AC) (http://ilrs.gsfc.nasa.gov/science/analysisCenters/).

[Table 2.] ILRS associate analysis centers (AAC) (http://ilrs.gsfc.nasa.gov/science/analysisCenters/).

[Table 3.] Satellites of geodetic missions (http://ilrs.gsfc.nasa.gov/missions/satellite_missions).

[Table 4.] Information about ILRS stations and SLR normal points for precise orbit determination.

[Table 5.] Dynamic and measurement models for POD.

[Table 6.] Information about arcs and results of postfit residuals.

[Fig. 1.] The root mean square (RMS) values of postfit residuals (LAGEOS1, LAGEOS2).

[Fig. 2.] The root mean square (RMS) values of postfit residuals (ETALON1, ETALON2).

[Table 7.] Strategies for solutions of TRF and EOPs.

[Table 8.] Stabilities of the positions of ILRS core sites.

[Fig. 3.] Stabilities of KASITRFsolution for 11 ILRS core sites.

[Fig. 4.] 3D Stability differences between KASITRFsolution and previous study (Schillak 2012)

[Fig. 5.] Daily polar motion from KASIEOPssolution.

[Fig. 6.] Differences between KASIEOPssolution and IERS 08 C04 of XP.

[Fig. 7.] Differences between KASIEOPssolution and IERS 08 C04 of YP .

[Fig. 8.] Polar motion rates of KASIEOPssolution.