GOCE orbit predictions for SLR tracking
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- Jäggi, A., Bock, H. & Floberghagen, R. GPS Solut (2011) 15: 129. doi:10.1007/s10291-010-0176-6
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After a descent phase of about half a year, the Gravity field and steady-state Ocean Circulation Explorer (GOCE) reached the final orbital altitude of the first measurement and operational phase (MOP-1) in September 2009. Due to this very low orbital altitude and the inactive drag compensation during descent, the generation of reliable predictions of the GOCE trajectory turned out to be a major challenge even for short prediction intervals. As predictions of good quality are a prerequisite for frequent ranging from the tracking network of the International Laser Ranging Service (ILRS), Satellite Laser Ranging (SLR) data of GOCE was very sparse at mission start and made it difficult to independently calibrate and optimize the orbit determination based on data of the Global Positioning System (GPS). In addition to the GOCE orbit predictions provided by the European Space Agency (ESA), the Astronomical Institute of the University of Bern (AIUB) started providing predictions on July 22, 2009, as part of the Level 1b to Level 2 data processing performed at AIUB. The predictions based on the 12-h ultra-rapid products of the International GNSS Service (IGS) were originally intended to primarily serve the daylight passes in the early evening hours over Europe. The corresponding along-track prediction errors were often kept below 50 m during the descent phase and allowed for the first successful SLR tracking of GOCE over Europe on July 29, 2009, by the Zimmerwald observatory. Additional predictions based on the IGS 18-h ultra-rapid products are provided by AIUB since September 20, 2009, to further optimize the GOCE SLR tracking. In this article, the development of the GOCE prediction service at AIUB is presented, and the quality of the orbit predictions is assessed for periods with and without active drag compensation. The prediction quality is discussed as a function of the prediction interval, the quality of the input products for the GPS satellite orbits and clocks, and the availability of the GOCE GPS data. From the methodological point of view, different approaches for the treatment of the non-gravitational accelerations acting on the GOCE satellite are discussed and their impact on the prediction quality is assessed, in particular during the descent phase. Eventually, an outlook is given on the significance of GOCE SLR tracking to identify systematic errors in the GPS-based orbit determination, e.g., cross-track errors induced by mismodeled GOCE GPS phase center variations (PCVs).
KeywordsGOCEOrbit predictionNon-gravitational accelerationsDrag-free flightGPSSLR
The Gravity field and steady-state Ocean Circulation Explorer (GOCE) was launched on March 17, 2009, into a very low earth orbit (LEO). The first core explorer GOCE of the Living Planet Program of the European Space Agency (ESA) is intended to serve solid earth physics, oceanography, geodesy, and glaciology by measuring the stationary part of the earth’s gravity field with the highest possible accuracy and spatial resolution (Rummel et al. 2002). The core instrument of the mission is a three-axis gravity gradiometer for inferring the small-scale structures of the earth’s gravity field from in situ measured acceleration differences (Drinkwater et al. 2006). For the derivation of the long wavelength part of the earth’s gravity field and for orbit determination, the satellite is equipped with a dual-frequency Global Positioning System (GPS) receiver. At least two measurement and operational phases (MOP-1, MOP-2) of about 6 month duration each were originally planned to derive the geoid with 1-cm accuracy at a spatial resolution of 100 km (Johannessen et al. 2003). MOP-1 has started on September 29, 2009, at a mean spherical altitude of 259.56 km (254.9 km when referring to the mean semi-major axis). A drag-free control system is used to maintain the very low orbital altitude by compensating for atmospheric drag by onboard ion-thrusters.
The scientific data processing from Level 1b to Level 2 is performed by the High-level Processing Facility (HPF) of the European GOCE Gravity Consortium (Koop et al. 2006). Precise orbit determination (POD) based on measurements of the GPS receiver is an integral part of the HPF. A rapid science orbit (RSO) is derived at the Delft Institute of Earth Observation and Space Systems (DEOS) with a latency of less than 1 day but with relaxed accuracy requirements (Visser et al. 2009). A precise science orbit (PSO) is derived at the Astronomical Institute of the University of Bern (AIUB) with a latency of about 2 weeks and stringent accuracy requirements of about 2 cm 1-D root mean square (RMS) error (Bock et al. 2007). Satellite Laser Ranging (SLR) measurements collected by the tracking network of the International Laser Ranging Service (ILRS, Pearlman et al. 2002) serve as independent data to validate the quality of the orbit products. GOCE SLR tracking is performed with highest priority by the ILRS tracking network.
Due to the short tracking passes of only 3–4 min duration, orbit predictions of good quality are a prerequisite for frequent ranging from the ILRS tracking network to the GOCE satellite. Similar to other LEO satellites such as CHAMP (Schmidt et al. 2002), the extremely low orbital altitude of GOCE makes it a challenge to reliably predict the satellite trajectory even for short prediction intervals, in particular during periods without drag-free control. GOCE SLR tracking was thus very sparse in the first part of the descent phase at mission start and limited to very few stations observing visible twilight passes, e.g., Yarragadee in Australia and San Juan in Argentina. Stations observing daylight passes such as all European stations, however, were not able to track GOCE with the predictions available at that time. This situation initiated activities at AIUB to provide GOCE orbit predictions in addition to the predictions provided by ESA.
Section “GOCE orbit evolution” provides a short description of the evolution the GOCE orbital altitude. Based on real data, section “GOCE orbit prediction strategy” presents different strategies for predicting GOCE orbit positions. Section “Update rate of GOCE orbit predications” discusses the circumstances for the selected update rates of the AIUB predictions, which were originally intended to primarily serve the daylight passes in the early evening hours over Europe. Section “Impact of operational solutions on SLR tracking” demonstrates the impact of the AIUB predictions on the GOCE SLR tracking, and section “Significance of GOCE SLR tracking” outlines the importance of a continuous and dense SLR tracking for scientific analyses.
GOCE orbit evolution
A longer period of drag-free flight was initiated on 26 May (DOY 146) at an altitude of about 272.5 km with increased atmospheric density. In the course of this drag-free flight, on 9 June (DOY 160), various activities on the gradiometer calibration were initiated, e.g., the determination of the inverse calibration matrix (ICM) on 17–18 June (DOYs 168-169). As a consequence of these activities, the orbital altitude again increased as shown in Fig. 1. On 23 June (DOY 174), GOCE was switched back into the fine pointing mode for further descending to the final orbital altitude of 259.56 km. The GOCE ion engines started firing in open loop again on 13 September (DOY 256), and the satellite was brought in closed-loop drag-free flight on 14 September. The final orbital altitude of 259.56 km used for gravity field mapping during MOP-1 corresponds to a repeat cycle of 979 revolutions in 61 days.
GOCE orbit prediction strategy
Let us now describe the relevant aspects for the determination of LEO orbits from GPS data as they are implemented in a special version of the Bernese GPS Software (Dach et al. 2007). The same software version is currently used at AIUB to derive the GOCE PSO product and the orbit predictions for SLR tracking described in this article.
Pseudo-stochastic orbit modeling techniques as described by Jäggi et al. (2006) are used to realize the GOCE reduced-dynamic orbit determination. For the generation of the final PSO product (GOCE Level 2 Product Data Handbook 2009), which is delivered to the user community with a latency of 4 weeks, the 5-s GPS clock corrections (Bock et al. 2009) and the GPS final orbits from the Center of Orbit Determination in Europe (CODE, Dach et al. 2009), analysis center of the International GNSS Service (IGS, Dow et al. 2009) located at AIUB, are used to process the full amount of 1-s GPS data over an arclength of 30 h. The parameters of the reduced-dynamic orbit of the PSO product are the six initial osculating elements, three constant empirical accelerations acting over the entire arc in the radial, along-track, and cross-track directions, and (constrained) piecewise constant accelerations over 6 min acting in the same directions. No use is made of the GOCE common-mode accelerometer data, which implies that the piecewise constant accelerations mainly compensate the not explicitly modeled non-gravitational accelerations.
The same parametrization is used for the generation of the orbit predictions for SLR tracking. For the studies in this section, however, the GPS rapid orbits and the 30-s GPS rapid clock corrections of the previous day from the CODE analysis center are used to process 30-s sampled GPS data over an arclength of 24 h. Based on such an orbit (observed part), several strategies are studied for generating the GOCE orbit predictions by extrapolation.
Starting from the last state vector of the observed part of the orbit, the most straightforward prediction strategy consists of a pure orbit extrapolation based on the dynamic models and dynamic parameters used for the orbit determination of the observed part of the previous day. Using the previously described parametrization, this implies that the impact of the non-gravitational accelerations is only taken into account in a very crude way by three constant accelerations, i.e., only by a mean value.
A more refined but still simple treatment of non-gravitational accelerations may be realized by estimating once-per-revolution parameters. The positions obtained from the observed part of the previous day serve as pseudo-observations to initiate a new dynamic orbit determination with six initial osculating elements, three constant accelerations acting over the entire arc in the radial, along-track, and cross-track directions, and once-per-revolution periodic terms acting in the same directions. This fitted orbit is used for a pure orbit extrapolation based on the dynamic models and the dynamic orbit parameters estimated from the pseudo-observations. The once-per-revolution periodic parameters compensate for the largest part of the non-gravitational accelerations, i.e., not only for a mean value as in the case of the “straightforward” strategy but also for the main variation along the orbit.
Assessment of prediction strategies
The quality of the predictions decreases very rapidly with the length of the prediction interval. An extrapolation over 24 h increases the mean along-track errors to 1,089, 1,454, and 1,843 m for the three strategies. After 36 h, the along-track errors are as large as 2,574, 3,115, and 3,969 m. These numbers underline that a good prediction strategy is still helpful, but in order to keep the along-track errors small, a frequent update of the GOCE orbit predictions is of much greater importance.
Update rate of GOCE orbit predictions
The availability of GPS orbit and clock products in time and, most importantly, GOCE GPS data determine the update rates for the predictions computed at AIUB.
The IGS rapid (IGR) GPS orbit and clock products are not suitable for near real-time applications because of their latency. They are updated once per day and made available at 17 h, i.e., 17 h later than the last observations could contribute to the observed part of the GOCE orbit. The contribution from the CODE analysis center to the IGR, on the other hand, is available (in-house at AIUB) much earlier at about 7 h and would thus better serve the GOCE orbit predictions. However, a non-continuous distribution of the GOCE data from HPF’s central processing facility (CPF) to the single processing facilities (SPFs) makes this option not feasible either. Due to operational constraints, the data distribution is interrupted over night and the complete amount of GOCE GPS data of the previous day is available at AIUB only at about 10 h—too late for the generation of orbit predictions.
The IGS ultra-rapid (IGU) GPS orbit and clock products are of greater interest for the generation of GOCE predictions. They are updated four times per day and cover an interval of 48 h, where the first 24 h are estimated from real observations and the last 24 h are predicted orbit and clock information. Taking into account the latency of the GOCE GPS data, only the observed part of the IGU products can be used for the generation of the GOCE orbit predictions. The observed part of the 12-h IGU products, e.g., covers the interval from 12 h of the previous day to 12 h of the current day and is made available at 15 h. As the complete amount of GOCE GPS data of the same interval is made available to AIUB by the CPF at about 15.5 h, the GOCE orbit predictions can be submitted to the ILRS approximately half an hour later at about 16 h. This option was realized in a first step toward the establishment of the GOCE prediction service at AIUB. Unnecessary to say that the availability of the GOCE GPS data is crucial for a successful generation of the orbit predictions.
The left part of Fig. 6 shows an analogous analysis for a short interval out of the second drag-free flight period (DOYs 153-159, 2009) without much calibration activities (see section “GOCE orbit evolution”). It can be clearly seen that the drag compensation significantly improves the prediction quality as the non-gravitational forces are already compensated to a large extent by the IPA. The results shown for the descent phase thus represent a pessimistic assessment on what can be expected from the GOCE prediction service at AIUB during the MOPs.
Impact of operational solutions on SLR tracking
Due to the GOCE data downlink that takes place once-per-revolution, the GPS data is distributed in once-per-revolution batches to the SPFs. The bars in the background of Fig. 7 indicate the completeness of the GPS data when the generation of the GOCE orbit predictions has started. Bars going up to the top of Fig. 7 indicate that the observed part is completely covered by GPS data with none of the once-per-revolution files missing. If files are distributed with some latency, however, they cannot be taken into account for the orbit computation. As a consequence, the observed part is shorter than 24 h as indicated by the length of the bars in Fig. 7. The predictions are based on the full amount of GPS data for about half of the days of the 30-day period shown. For the other days, the correlation of the data availability with the prediction quality reveals (sometimes) quite striking coincidences, e.g., for DOYs 219 and 236. For other days, however, the prediction quality is not related with the data availability. On DOY 231, e.g., the GPS data availability was erroneously assumed to be complete and led to a degraded prediction quality (a re-computation revealed an achievable prediction quality of 40 instead of the reported 75 m). A similar operating error is also responsible for the inferior quality on DOY 221. In order to suppress such effects, which may determine whether SLR stations are able to successfully range to GOCE or not, time windows are meanwhile set automatically based on the actual availability of the GPS data. In addition, it was recognized that the observed part should rather be shortened by 6 min if the very last interval of piecewise constant accelerations is not fully covered with GPS observations. One weakly determined acceleration of the observed part may be sufficient to degrade the empirical acceleration model and propagate into the orbit extrapolation at every revolution (see section “Empirical strategy”).
Significance of GOCE SLR tracking
Traditionally, SLR data has played an important role for calibrating and optimizing the microwave-based POD of GNSS satellites (e.g., Urschl et al. 2007) and LEO satellites (e.g., Jäggi et al. 2006). For GPS-based LEO POD, the limiting factors are nowadays mainly the modeling of the phase center variations (PCVs) of the LEO GPS antennas (Jäggi et al. 2009). Neglected or mismodeled PCVs significantly deteriorate the computed LEO trajectories and, in particular, may shift the orbits in the cross-track direction up to several centimeters. As SLR measurements are mainly sensitive in the radial direction for most LEO satellites (due to their still “high” altitude), PCV-induced shifts in the cross-track direction could so far not be independently assessed (Jäggi et al. 2009).
Figure 10 shows that the number of SLR tracks is currently not yet equally distributed on both sides of the satellite. A further improvement in the coverage of the GOCE orbit with SLR data is therefore still desirable to facilitate a proper quality assessment of the GOCE PSO product. Corresponding investigations are currently performed for the PSO determination in the framework of the GOCE HPF and will be presented in the near future.
Satellite Laser Ranging data of GOCE was very sparse early in the mission, which made it difficult to independently calibrate and optimize the GPS-based orbit determination in the framework of the GOCE HPF. As orbit predictions of good quality are required for a successful SLR tracking, an effort was started on July 21, 2009 (DOY 202) to provide GOCE orbit predictions in addition to those from ESA as part of the Level 1b to Level 2 data processing at AIUB. Since September 20, 2009, the predictions are updated twice per day and are based on the 12- and 18-h IGU products. Due to the non-continuous distribution of the GOCE GPS data by HPF’s CPF, the update rates cannot be further increased. The new predictions have nevertheless significantly improved the GOCE SLR tracking. European SLR stations in particular could benefit from the predictions based on the 12-h IGU products due to very short prediction intervals for the evening passes. In combination with a reliable prediction strategy based on empirical accelerations estimated from GPS data of the observed part, the along-track errors for the European evening passes were often kept below 50 m during the descent phase. Thanks to the increased SLR data volume, it will be possible to independently assess the quality of the GOCE PSO product in the framework of the HPF.
This article is dedicated to Prof. Werner Gurtner, who passed away on October 24, 2009, after a long illness. W. Gurtner was the head of the Zimmerwald observatory since 1987 and chair of the ILRS Governing Board since 2002. His support and promotion of the activities described in this article are gratefully acknowledged. The study was performed in the framework of the GOCE High-level Processing Facility, which is funded by ESA.