Satellite Laser Ranging Observations Research Articles

The challenge of precise orbit determination for STSAT-2C using extremely sparse SLR data

The Science and Technology Satellite (STSAT)-2C is the first Korean satellite equipped with a laser retro-reflector array for satellite laser ranging (SLR). SLR is the only on-board tracking source for precise orbit determination (POD) of STSAT-2C. However, POD for the STSAT-2C is a challenging issue, as the laser measurements of the satellite are extremely sparse, largely due to the inaccurate two-line element (TLE)-based orbit predictions used by the SLR tracking stations. In this study, POD for the STSAT-2C using extremely sparse SLR data is successfully implemented, and new laser-based orbit predictions are obtained. The NASA/GSFC GEODYN II software and seven-day arcs are used for the SLR data processing of two years of normal points from March 2013 to May 2015. To compensate for the extremely sparse laser tracking, the number of estimation parameters are minimized, and only the atmospheric drag coefficients are estimated with various intervals. The POD results show that the weighted root mean square (RMS) post-fit residuals are less than 10m, and the 3D day boundaries vary from 30m to 3km. The average four-day orbit overlaps are less than 20/330/20m for the radial/along-track/cross-track components. The quality of the new laser-based prediction is verified by SLR observations, and the SLR residuals show better results than those of previous TLE-based predictions. This study demonstrates that POD for the STSAT-2C can be successfully achieved against extreme sparseness of SLR data, and the results can deliver more accurate predictions.

Orbit Determination Using SLR Data for STSAT-2C: Short-arc Analysis

In this study, we present the results of orbit determination (OD) using satellite laser ranging (SLR) data for the Science and Technology Satellite (STSAT)-2C by a short-arc analysis. For SLR data processing, the NASA/GSFC GEODYN II software with one year (2013/04 - 2014/04) of normal point observations is used. As there is only an extremely small quantity of SLR observations of STSAT-2C and they are sparsely distribution, the selection of the arc length and the estimation intervals for the atmospheric drag coefficients and the empirical acceleration parameters was made on an arc-to-arc basis. For orbit quality assessment, the post-fit residuals of each short-arc and orbit overlaps of arcs are investigated. The OD results show that the weighted root mean square post-fit residuals of short-arcs are less than 1 cm, and the average 1-day orbit overlaps are superior to 50/600/900 m for the radial/cross-track/along-track components. These results demonstrate that OD for STSAT-2C was successfully achieved with cm-level range precision. However its orbit quality did not reach the same level due to the availability of few and sparse measurement conditions. From a mission analysis viewpoint, obtaining the results of OD for STSAT-2C is significant for generating enhanced orbit predictions for more frequent tracking.

LAGEOS Sensitivity to Ocean Tides

Satellite Laser Ranging (SLR) to LAGEOS has a remarkable contribution to high-precise geodesy and geodynamics through deriving and validating various global geophysical models. This paper validates ocean tide models based on the analysis of satellite altimetry data, coastal tide gauges, and hydrodynamic data, i.e., CSR3.0, TOPEX4.0, CSR4.0A, FES2004, GOT00.2, and the CSRC Schwiderski model. LAGEOS orbits and SLR observation residuals from solutions based on different ocean tide models are compared and examined. It is found that LAGEOS orbits are sensitive to tidal waves larger than 5 mm. The analysis of the aliasing periods of LAGEOS orbits and tidal waves reveals that, in particular, the tidal constituent S2 is not well established in the recent ocean tide models. Some of the models introduce spurious peaks to empirical orbit parameters, which can be associated with S2, Sa, and K2 tidal constituents, and, as a consequence, can be propagated to fundamental parameters derived from LAGEOS observations.

Time variable Earth’s gravity field from SLR satellites

The time variable Earth’s gravity field contains information about the mass transport within the system Earth, i.e., the relationship between mass variations in the atmosphere, oceans, land hydrology, and ice sheets. For many years, satellite laser ranging (SLR) observations to geodetic satellites have provided valuable information of the low-degree coefficients of the Earth’s gravity field. Today, the Gravity Recovery and Climate Experiment (GRACE) mission is the major source of information for the time variable field of a high spatial resolution. We recover the low-degree coefficients of the time variable Earth’s gravity field using SLR observations up to nine geodetic satellites: LAGEOS-1, LAGEOS-2, Starlette, Stella, AJISAI, LARES, Larets, BLITS, and Beacon-C. We estimate monthly gravity field coefficients up to degree and order 10/10 for the time span 2003–2013 and we compare the results with the GRACE-derived gravity field coefficients. We show that not only degree-2 gravity field coefficients can be well determined from SLR, but also other coefficients up to degree 10 using the combination of short 1-day arcs for low orbiting satellites and 10-day arcs for LAGEOS-1/2. In this way, LAGEOS-1/2 allow recovering zonal terms, which are associated with long-term satellite orbit perturbations, whereas the tesseral and sectorial terms benefit most from low orbiting satellites, whose orbit modeling deficiencies are minimized due to short 1-day arcs. The amplitudes of the annual signal in the low-degree gravity field coefficients derived from SLR agree with GRACE K-band results at a level of 77 %. This implies that SLR has a great potential to fill the gap between the current GRACE and the future GRACE Follow-On mission for recovering of the seasonal variations and secular trends of the longest wavelengths in gravity field, which are associated with the large-scale mass transport in the system Earth.

Second-degree Stokes coefficients from multi-satellite SLR

The long wavelength part of the Earth’s gravity field can be determined, with varying accuracy, from satellite laser ranging (SLR). In this study, we investigate the combination of up to ten geodetic SLR satellites using iterative variance component estimation. SLR observations to different satellites are combined in order to identify the impact of each satellite on the estimated Stokes coefficients. The combination of satellite-specific weekly or monthly arcs allows to reduce parameter correlations of the single-satellite solutions and leads to alternative estimates of the second-degree Stokes coefficients. This alternative time series might be helpful for assessing the uncertainty in the impact of the low-degree Stokes coefficients on geophysical investigations. In order to validate the obtained time series of second-degree Stokes coefficients, a comparison with the SLR RL05 time series of the Center of Space Research (CSR) is done. This investigation shows that all time series are comparable to the CSR time series. The precision of the weekly/monthly $$C_{21}$$ and $$S_{21}$$ coefficients is analyzed by comparing mass-related equatorial excitation functions $$\chi ^{\text {mass}}_{1,2}$$ with geophysical model results and reduced geodetic excitation functions. In case of $$\chi ^{\text {mass}}_{1}$$ , the annual amplitude and phase of the DGFI solution agrees better with three of four geophysical model combinations than other time series. In case of $$\chi ^{\text {mass}}_{2}$$ , all time series agree very well to each other. The impact of $$C_{20}$$ on the ice mass trend estimates for Antarctica are compared based on CSR GRACE RL05 solutions, in which different monthly $$C_{20}$$ time series are used for replacing. We found differences in the long-term Antarctic ice loss of $$12.3$$ Gt/year between the GRACE solutions induced by the different $$C_{20}$$ SLR time series of CSR and DGFI, which is about 13 % of the total ice loss of Antarctica. This result shows that Antarctic ice mass loss quantifications must be carefully interpreted.

Satellite laser ranging to GPS and GLONASS

Satellite laser ranging (SLR) to the satellites of the global navigation satellite systems (GNSS) provides substantial and valuable information about the accuracy and quality of GNSS orbits and allows for the SLR-GNSS co-location in space. In the framework of the NAVSTAR-SLR experiment two GPS satellites of Block-IIA were equipped with laser retroreflector arrays (LRAs), whereas all satellites of the GLONASS system are equipped with LRAs in an operational mode. We summarize the outcome of the NAVSTAR-SLR experiment by processing 20 years of SLR observations to GPS and 12 years of SLR observations to GLONASS satellites using the reprocessed microwave orbits provided by the center for orbit determination in Europe (CODE). The dependency of the SLR residuals on the size, shape, and number of corner cubes in LRAs is studied. We show that the mean SLR residuals and the RMS of residuals depend on the coating of the LRAs and the block or type of GNSS satellites. The SLR mean residuals are also a function of the equipment used at SLR stations including the single-photon and multi-photon detection modes. We also show that the SLR observations to GNSS satellites are important to validate GNSS orbits and to assess deficiencies in the solar radiation pressure models. We found that the satellite signature effect, which is defined as a spread of optical pulse signals due to reflection from multiple reflectors, causes the variations of mean SLR residuals of up to 15 mm between the observations at nadir angles of 0 $$^{\circ }$$ and 14 $$^{\circ }$$ . in case of multi-photon SLR stations. For single-photon SLR stations this effect does not exceed 1 mm. When using the new empirical CODE orbit model (ECOM), the SLR mean residual falls into the range 0.1–1.8 mm for high-performing single-photon SLR stations observing GLONASS-M satellites with uncoated corner cubes. For best-performing multi-photon stations the mean SLR residuals are between $$-12.2$$ and $$-25.6$$ mm due to the satellite signature effect.

Separation of atmospheric, oceanic and hydrological polar motion excitation mechanisms based on a combination of geometric and gravimetric space observations

The goal of our study is to determine accurate time series of geophysical Earth rotation excitations to learn more about global dynamic processes in the Earth system. For this purpose, we developed an adjustment model which allows to combine precise observations from space geodetic observation systems, such as Satellite Laser Ranging (SLR), Global Navigation Satellite Systems, Very Long Baseline Interferometry, Doppler Orbit determination and Radiopositioning Integrated on Satellite, satellite altimetry and satellite gravimetry in order to separate geophysical excitation mechanisms of Earth rotation. Three polar motion time series are applied to derive the polar motion excitation functions (integral effect). Furthermore we use five time variable gravity field solutions from Gravity Recovery and Climate Experiment to determine not only the integral mass effect but also the oceanic and hydrological mass effects by applying suitable filter techniques and a land–ocean mask. For comparison the integral mass effect is also derived from degree 2 potential coefficients that are estimated from SLR observations. The oceanic mass effect is also determined from sea level anomalies observed by satellite altimetry by reducing the steric sea level anomalies derived from temperature and salinity fields of the oceans. Due to the combination of all geodetic estimated excitations the weaknesses of the individual processing strategies can be reduced and the technique-specific strengths can be accounted for. The formal errors of the adjusted geodetic solutions are smaller than the RMS differences of the geophysical model solutions. The improved excitation time series can be used to improve the geophysical modeling.

Precise orbit determination using the batch filter based on particle filtering with genetic resampling approach

In this study, genetic resampling (GRS) approach is utilized for precise orbit determination (POD) using the batch filter based on particle filtering (PF). Two genetic operations, which are arithmetic crossover and residual mutation, are used for GRS of the batch filter based on PF (PF batch filter). For POD, Laser-ranging Precise Orbit Determination System (LPODS) and satellite laser ranging (SLR) observations of the CHAMP satellite are used. Monte Carlo trials for POD are performed by one hundred times. The characteristics of the POD results by PF batch filter with GRS are compared with those of a PF batch filter with minimum residual resampling (MRRS). The post-fit residual, 3D error by external orbit comparison, and POD repeatability are analyzed for orbit quality assessments. The POD results are externally checked by NASA JPL’s orbits using totally different software, measurements, and techniques. For post-fit residuals and 3D errors, both MRRS and GRS give accurate estimation results whose mean root mean square (RMS) values are at a level of 5cm and 10–13cm, respectively. The mean radial orbit errors of both methods are at a level of 5cm. For POD repeatability represented as the standard deviations of post-fit residuals and 3D errors by repetitive PODs, however, GRS yields 25% and 13% more robust estimation results than MRRS for post-fit residual and 3D error, respectively. This study shows that PF batch filter with GRS approach using genetic operations is superior to PF batch filter with MRRS in terms of robustness in POD with SLR observations.

Galileo orbit determination using combined GNSS and SLR observations

The first two Galileo In-Orbit Validation satellites were launched in October 2011 and started continuous signal transmission on all frequencies in early 2012. Both satellites are equipped with two different types of clocks, namely rubidium clocks and hydrogen masers. Based on two test periods, the quality of the Galileo orbit determination based on Global Navigation Satellite System (GNSS) and Satellite Laser Ranging (SLR) observations is assessed. The estimated satellite clock parameters are used as quality indicator for the orbits: A bump at orbital periods in the Allan deviation indicates systematic errors in the GNSS-only orbit determination. These errors almost vanish if SLR observations are considered in addition. As the internal consistency is degraded by the combination, the offset of the SLR reflector is shifted by +5 cm, resulting in an improved orbit consistency as well as accuracy. Another approach to reduce the systematic errors of the GNSS-only orbit determination employs constraints for the clock estimates with respect to a linear model. In general, one decimeter orbit accuracy could be achieved.

Precise Orbital and Geodetic Parameter Estimation using SLR Observations for ILRS AAC

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 LAGEOS-1, LAGEOS-2, ETALON-1, and ETALON-2 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 weekly-based 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 post-fit 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 post-fit residuals show that the RMS of the orbits of LAGEOS-1 and LAGEOS-2 are 1.20 and 1.12 cm, and those of ETALON-1 and ETALON-2 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 <TEX>$X_P$</TEX> and <TEX>$Y_P$</TEX> 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.

Recent Results for the Arabian Plate Motion Using Satellite Laser Ranging Observations of Riyadh SLR Station to LAGEOS-1 and LAGEOS-2 Satellites

Saudi Arabia Laser Ranging Observatory (SALRO-7832) has been established in 1995 and is situated in the Arabian tectonic plate which is countering a north east motion. Laser ranging observations of about 20 global SLR stations to LAGEOS-1 and LAGEOS-2 satellites collected for 14 years (1996–2009) have been used to determine Riyadh SLR station positions and velocity. The NASA Goddard’s GEODYN-II orbital software has been used to perform orbit determination of these two satellites. The computations were performed on the basis of 114 monthly arcs of observations with the total number of normal points of 33,708 and 40,168 for LAGEOS-1 and LAGEOS-2, respectively. The geocentric coordinates were computed and then transformed to the topocentric North, East and vertical components in reference to the ITRF2008 terrestrial reference frame. The range biases of the Riyadh SLR station in the whole period of study were 2.5 and 2.0 mm with long-term bias stability 7.5 and 7.2 mm for LAGEOS-1 and LAGEOS-2 satellites, respectively. The orbital RMS of fit for all stations was equal to 16.4 mm for the whole period. The stability of the time series positions in form of RMS of the X, Y, Z component residuals w.r.t. a linear trend for Riyadh SLR station were 10.1, 9.3, and 9.0 mm, respectively. 3D deviation from ITRF2008 position was equal to 4.5 mm. The velocities were 29.1 ± 0.2, 31.6 ± 0.2, and 1.9 ± 0.3 mm/year in the North, East and vertical directions, respectively, with a horizontal and 3D velocity 42.9 ± 0.2 mm/year and azimuth 47.4 ± 0.8 arc degrees. The central part of the Arabian tectonic plate motion was precisely determined from the Riyadh SLR data and the results showed a good agreement with ITRF2008 velocity, geological model NNR NUVEL1A and with recent GPS estimates. This paper includes a full discussion of the results of Riyadh SLR station collected over 14 years of activity and gives the absolute movement of the central part of the Arabian tectonic plate (velocity and azimuth).

Spin parameters of Low Earth Orbiting satellites Larets and Stella determined from Satellite Laser Ranging data

Satellite Laser Ranging (SLR) measurements contain information about the spin parameters of the fully passive, geodetic satellites. In this paper we spectrally analyze the SLR data of 5 geodetic satellites placed on the Low Earth Orbits: GFZ-1, WESTPAC, Larets, Starlette, Stella, and successfully retrieve the frequency signal from Larets and Stella only. The obtained signals indicate an exponential increase of the spin period of Larets: T=0.860499·exp(0.0197066·D) [s], and Stella: T=13.5582·exp(0.00431232·D) [s], where D is in days since launch. The initial spin periods calculated from the first month of the SLR observations are: Larets: Tinitial=0.8239s, Stella: Tinitial=13.2048s. Analysis of the apparent effects indicates the counter-clockwise spin direction of the satellites. The twice more heavy Stella lost its rotational energy more than four times slower than Larets. Fitting the spin model to the observed spin trends allows determination of the spin axis orientation evolution for Larets and Stella before their rotational period becomes equal to the orbital period.

Time‐variable gravity signal in Greenland revealed by high‐low satellite‐to‐satellite tracking

In the event of a termination of the Gravity Recovery and Climate Experiment (GRACE) mission before the launch of GRACE Follow‐On (due for launch in 2017), high‐low satellite‐to‐satellite tracking (hl‐SST) will be the only dedicated observing system with global coverage available to measure the time‐variable gravity field (TVG) on a monthly or even shorter time scale. Until recently, hl‐SST TVG observations were of poor quality and hardly improved the performance of Satellite Laser Ranging observations. To date, they have been of only very limited usefulness to geophysical or environmental investigations. In this paper, we apply a thorough reprocessing strategy and a dedicated Kalman filter to Challenging Minisatellite Payload (CHAMP) data to demonstrate that it is possible to derive the very long‐wavelength TVG features down to spatial scales of approximately 2000 km at the annual frequency and for multi‐year trends. The results are validated against GRACE data and surface height changes from long‐term GPS ground stations in Greenland. We find that the quality of the CHAMP solutions is sufficient to derive long‐term trends and annual amplitudes of mass change over Greenland. We conclude that hl‐SST is a viable source of information for TVG and can serve to some extent to bridge a possible gap between the end‐of‐life of GRACE and the availability of GRACE Follow‐On.

Preliminary Products of Precise Orbit Determination Using Satellite Laser Ranging Observations for ILRS AAC

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 LAGEOS-1, LAGEOS-2, ETALON-1, and ETALON-2, the NASA/GSFC GEODYN II software are utilized for POD. Weekly-based orbit determination strategy is applied to process SLR observations and the post-fit 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 post-fit 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 post-fit residuals. The post-fit residuals results show that the precisions of the orbits of LAGEOS-1 and LAGEOS-2 are 0.9 and 1.3 cm, and those of ETALON-1 and ETALON-2 are 2.5 and 1.9 cm, respectively. The orbit assessment results by ILRS CPF show that the radial accuracies of LAGEOS-1 and LAGEOS-2 are 4.0 cm and 5.3 cm, and the radial accuracies of ETALON-1 and ETALON-2 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.

Combination of GNSS and SLR observations using satellite co-locations

Satellite Laser Ranging (SLR) observations to Global Navigation Satellite System (GNSS) satellites may be used for several purposes. On one hand, the range measurement may be used as an independent validation for satellite orbits derived solely from GNSS microwave observations. On the other hand, both observation types may be analyzed together to generate a combined orbit. The latter procedure implies that one common set of orbit parameters is estimated from GNSS and SLR data. We performed such a combined processing of GNSS and SLR using the data of the year 2008. During this period, two GPS and four GLONASS satellites could be used as satellite co-locations. We focus on the general procedure for this type of combined processing and the impact on the terrestrial reference frame (including scale and geocenter), the GNSS satellite antenna offsets (SAO) and the SLR range biases. We show that the combination using only satellite co-locations as connection between GNSS and SLR is possible and allows the estimation of SLR station coordinates at the level of 1–2 cm. The SLR observations to GNSS satellites provide the scale allowing the estimation of GNSS SAO without relying on the scale of any a priori terrestrial reference frame. We show that the necessity to estimate SLR range biases does not prohibit the estimation of GNSS SAO. A good distribution of SLR observations allows a common estimation of the two parameter types. The estimated corrections for the GNSS SAO are 119 mm and −13 mm on average for the GPS and GLONASS satellites, respectively. The resulting SLR range biases suggest that it might be sufficient to estimate one parameter per station representing a range bias common to all GNSS satellites. The estimated biases are in the range of a few centimeters up to 5 cm. Scale differences of 0.9 ppb are seen between GNSS and SLR.

South American SLR stations monitoring ground displacement caused by the M8.8 Chilean earthquake of 2010

The M8.8 Chilean earthquake of February 27, 2010 caused a large surface displacement near its epicenter. Satellite Laser Ranging (SLR) station 7405, cooperatively operated by Germany and Chile about 130 km from the epicenter was affected by the earthquake. Another SLR station, No. 7406, operated jointly by the National Astronomical Observatories of the Chinese Academy of Sciences and San Juan University of Argentina, was about 600 km from the epicenter. Combining the observations of these two SLR stations with global SLR station observations, we calculate the geocentric coordinates of the two stations based on ITRF2000. The results show that the coordinates of the two stations have changed by varying degrees. SLR-7405 moved substantially towards the southwest with displacements of about 3.11, 0.52 and 0.49 m in X, Y, Z directions; the corresponding displacements for SLR-7406 are about 0.02, 0.03 and 0.02 m. This solution, as an independent result derived from SLR observations, could provide an essential external check for other positioning techniques such as GPS.

Improved kHz-SLR tracking techniques and orbit quality analysis for LEO missions

Satellite gravity field missions such as CHAMP, GRACE and GOCE are designed as low Earth orbiting spacecraft (LEO) with orbit heights of about 250–500 km. The challenging mission objectives require a very precise knowledge of the satellite orbit position in space. For these missions precise orbit information is typically provided by GPS satellite-to-satellite tracking (SST) observations supported by satellite laser ranging (SLR). The role of SLR is primarily devoted to serve as an independent tracking instrument used to calibrate and validate the on-board GPS flight receiver. However, the very limited visibility of LEOs from SLR ground stations together with the accordingly high angular rates necessary for the laser mounting to follow the satellite make it more difficult to track LEO missions. At the Observatory Graz–Lustbühel, the Space Research Institute of the Austrian Academy of Sciences operates a very novel SLR facility which was continuously upgraded during the recent years, and is today the only station worldwide capable to operate at kHz-firing rates. The activities presented here focus on a number of hardware upgrades and methodical improvements at the SLR station Graz aiming for a faster and more reliable target acquisition. These include upgrades of laser tracking algorithms as well as a redesign of the laser detection package in particular for LEO spacecraft. These improvements allow an extension of the measurement durations and thus increase the number of observations per pass. As a result we are able to raise the normal point accuracy as well as the overall system performance for LEO tracking. Improvements of the pointing accuracy and the range gate control system lead to a data quantity raise of about 5%. Another task addresses both a geometric and dynamic arc comparison of SLR derived orbits with GPS SST orbit solutions. In the case of CHAMP, the resulting one-way SLR range residuals are in the order of a few centimetres. This allows to draw conclusions on the accuracy of orbit solutions. In order to evaluate the performance of this technique for the upcoming GOCE mission, investigations are carried out in an analogous manner based on simulated GOCE SLR observations. In this study, it is demonstrated that satellite laser ranging, in particular with high-rate tracking capabilities and low orbit optimizations, offers a valuable tool for orbit validation purposes.

Interannual variability of low-degree gravitational change, 1980?2002

Time variations in the Earth's gravity field at periods longer than 1 year, for degree-two spherical harmonics, DC21, DS21, and DC20, are estimated from accurately measured Earth rotational variations. These are compared with predictions of atmospheric, oceanic, and hydrologic models, and with independent satellite laser ranging (SLR) results. There is remarkably good agreement between Earth rotation and model predic- tions of DC21 and DS21 over a 22-year period. After decadal signals are removed, Earth-rotation-derived interannual DC20 variations are dominated by a strong oscillation of period about 5.6 years, probably due to uncertainties in wind and ocean current estimates. The model-predicted DC20 agrees reasonably well with SLR observations during the 22-year period, with the excep- tion of the recent anomaly since 1997/1998.

The impact of accelerometry on CHAMP orbit determination

The contribution of the STAR accelerometer to the CHAMP orbit precision is evaluated and quantified by means of the following results: orbital fit to the satellite laser ranging (SLR) observations, GPS reduced-dynamic vs SLR dynamic orbit comparisons, and comparison of the measured to the modeled non-gravitational accelerations (atmospheric drag in particular). In each of the four test periods in 2001, five CHAMP arcs of 2 days' length were analyzed. The mean RMS-of-fit of the SLR observations of the orbits computed with STAR data or the non-gravitational force model were 11 and 24 cm, respectively. If the accelerometer calibration parameters are not known at least at the few percent level, the SLR orbit fit deteriorates. This was tested by applying a 10% error to the along-track scale factor of the accelerometer, which increased the SLR RMS-of-fit on average to 17 cm. Reference orbits were computed employing the reduced-dynamic technique with GPS tracking data. This technique yields the most accurate orbit positions thanks to the estimation of a large number of empirical accelerations, which compensate for dynamic modeling errors. Comparison of the SLR orbits, computed with STAR data or the non-gravitational force model, to the GPS-based orbits showed that the SLR orbits employing accelerometer observations are twice as accurate. Finally, comparison of measured to modeled accelerations showed that the level of geomagnetic activity is highly correlated with the atmospheric drag model error, and that the largest errors occur around the geomagnetic poles.

Application of ERS-2 prare data for orbit determination and gravity field and station coordinate estimation

Three and a half years of ERS-2 PRARE ( Precise Range and Range-rate Equipment) observations covering May 1995 – December 1998 have been analyzed for use in ERS-2 orbit determination, gravity field modeling and station coordinate estimation. Including PRARE data in the ERS-2 orbit computation results in significantly more precise and stable orbits. The estimated resulting orbit accuracy is below 5 cm, and seems to approach the TOPEX/POSEIDON orbit accuracy level. The improved orbits result in more accurate dynamic sea surface topography modeling. In addition, it can be shown that the PRARE data contain important information for reducing the gravity field induced ERS orbit error. PRARE data have been used successfully in addition to SLR ( Satellite Laser Ranging) observations and radar altimeter crossover differences to reduce the gravity field induced ERS-2 orbit errors. Finally, time series of PRARE station coordinate solutions were produced resulting in realistic velocity estimates. For the stations not located close to plate boundaries excellent agreement was found with predicted velocities using either the NUVEL-1a model or the ITRF'94 solution. Special attention was paid to the Neumayer station which is located on an ice sheet. Clear tidal components could be observed in the motion of this station derived from the tracking observations. The analysis of PRARE data has proven PRARE's ability for improved orbit determination, gravity field modeling and station coordinate estimation.