Gravity field model adjustment from ERS-1 and TOPEX altimetry and SLR tracking using an analytical orbit perturbation theory

The JGM-2 gravity field model has been adjusted using 70 days of ERS-1 and 19 10-day repeat cycles of TOPEX/Poseidon SLR and single satellite altimeter crossover differences. In addition, dual satellite altimeter crossover differences between ERS-1 and TOPEX for the selected 70-day period of ERS-1 and TOPEX repeat cycle 18 have been used in the JGM-2 model adjustment. In the computation of the normal equations, use was made of the analytical Lagrange linear perturbation theory. The single satellite altimeter crossover difference rms was brought down from 15.2 to 14.1 cm for ERS-1 and from 10.6 to 10.5 cm for TOPEX. The dual satellite altimeter crossover difference rms was reduced from 17.7 to 16.9 cm. Furthermore, the weighted rms of fit of SLR measurements was brought down from 16.0 to 14.4 cm for ERS-1, and from 5.4 to 5.0 cm for TOPEX/Poseidon.     

SPOT-2 and TOPEX/Poseidon precise orbit determination from DORIS doppler tracking

The French earth observation satellite SPOT-2 has served as a testbed for precise orbit determination from DORIS doppler tracking in anticipation of the TOPEX/Poseidon mission. Using the most up-to-data gravity field model, JGM-2, a radial orbit accuracy of about 2–9 cm was achieved, with an rms of fit of the tracking data of about 0.64 mm/s. Furthermore, it was found that the coordinates of the ground stations can be determined with an accuracy of the order of 2–5 cm after removal of common rotations, and translations.

Using a slightly different model for atmospheric drag, but the same gravity model, precise orbits of TOPEX/Poseidon from DORIS tracking data were determined with a radial orbit accuracy of the order of 4–5 cm, which is far within the 13 cm mission requirement. This conclusion is based on the analysis of 1-day overlap of successive 11-day orbits, and the comparisons with orbits computed from satellite laser tracking (SLR) and from the combination of SLR and DORIS tracking. Results indicate a consistency between the different orbits of 1–4 cm, 4–20 cm, and 6–13 cm in the radial, cross-track, and along-track directions, respectively. The residual rms is about 4–5 cm for SLR data and 0.56 mm/s for DORIS tracking. These numbers are roughly twice as large as the system noise levels, reflecting the fact that there are still some modeling errors left.     

ERS-1 radial position refinement by dual crossover analysis with TOPEX/Poseidon

Achieving orbital accuracies in the radial direction for ERS-1 commensurate with those for TOPEX/Poseidon is of utmost importance for the integration of the two altimeter data sets. This paper outlines a procedure whereby the radial orbit error for ERS-1 is recovered as a time series expansion in the form of a finite Fourier series with additional terms for atmospheric drag, solar radiation pressure, and initial state vector mismodelling. Using a least squares collocation method with constraints derived from the JGM2 gravity field co-variance matrix, the radial error is recovered using both dual crossovers and ERS-1 single satellite crossovers. Aggregate arcs are then used to derive the ERS-1 orbit error over the repeat period of 35 days. The results are presented in the improvement of fit in the dual crossover, ERS-1 crossover and altimetry data sets as well as the recovery of an altimeter bias for the two satellites.     

Analysis of radial orbit errors of ERS-1, and the development of super-tailored gravity models

The altimetry mission of the future ESA remote sensing satellite ERS-1 requires very accurate orbit solutions, of which in particular the radial position component should have an accuracy of approximately 10 cm. This paper presents some investigations into the possibility of reducing the radial position error due to the earth's gravity field, which is by far the largest contributing error source.With a detailed harmonic analysis of the ERS-1 orbit a number of gravity field model terms are identified which produce the major radial orbit perturbations. These dominant terms are adjusted in a least-squares orbit determination and parameter estimation procedure using actual SEASAT laser tracking observations and altimeter height measurements. The initial gravity model is the NASA GEM-L2 model derived from satellite tracking data only, with an emphasis on LAGEOS data. The resulting super-tailored model yields a significantly improved radial accuracy relative to GEM-L2, but fails to reach the accuracy of the SEASAT-tailored model PGS-S4.Finally, the SEASAT altimeter residuals and the residuals of the cross-over differences are analyzed in the frequency domain by applying a special filtering technique which separates the major radial orbit error and geoid error contributions.     

Precise orbit determination and sea-surface topography from ERS-1

Results of ERS - 1 orbit refinement procedures for long-arcs are summarised with particular reference to gravity field modelling and sea-surface topography. Long arcs from the three day and thirty - five day repeat cycles have been used to refine the earth's gravity field constrained by the JGM- 2 covariance matrix and simultaneously to solve for the quasi - stationary sea - surface topography. Orbital computations are presented for arcs not included within the refinement process with improvements identified through rms of fit to laser, altimeter and single satellite crossover data. Additional results utilising dual crossovers with TOPEX / POSEIDON in a full dynamic process are also presented. In particular, reference is made to the relative altimeter biases between the respective satellites and the characteristics of the orbital adjustment through inclusion of dual crossover data.     

New improved orbit solutions for the ERS-1 and ERS-2 satellites

Improved orbit solutions of the European Remote Sensing Satellites ERS-1 and ERS-2 have been computed in the ITRF2005 terrestrial reference frame using the recent models based mainly on IERS Conventions 2003. These solutions cover the periods 3 August 1991 to 8 July 1996 for ERS-1, and 3 May 1995 to 4 July 2003 for ERS-2. For each satellite, the final orbit solution is based on a combination of three separate orbit solutions independently computed at the Delft Institute of Earth Observation and Space Systems (DEOS) of the Delft University of Technology (The Netherlands), the Navigation Support Office of the European Space Operations Centre (ESOC, Germany) and the Helmholtz Centre Potsdam GFZ German Research Centre for Geosciences (Germany) using three different software packages for precise orbit determination, but using the same models in the same terrestrial reference frame within the European Space Agency (ESA) project ‘Reprocessing of Altimeter Products for ERS (REAPER)’. Validation using radar altimeter data indicates that the new combined orbits of ERS-1 and ERS-2 computed by us are significantly more accurate, approaching the 2–3 cm level in radial direction, than previously available orbit solutions.     

Evaluation of JGM 2 geopotential errors from Geosat, TOPEX/Poseidon and ERS-1 crossover altimetry

World-ocean distribution of the crossover altimetry data from Geosat, TOPEX/Poseidon (T/P) and the ERS 1 missions have provided strong independent evidence that NASA's/CSR's JGM 2 geopotential model (70 × 70 in spherical harmonics) yields accurate radial ephemerides for these satellites. In testing the sea height crossover differences found from altimetry and JGM 2 orbits for these satellites, we have used the sea height differences themselves (of ascending minus descending passes averaged at each location over many exact repeat cycles) and the Lumped Latitude Coefficients (LLC) derived from them. For Geosat we find the geopotential-induced LLC errors (exclusive of non-gravitational and initial state discrepancies) mostly below 6 cm, for TOPEX the corresponding errors are usually below 2 cm, and for ERS 1 (35-day cycle) they are generally below 5 cm. In addition, we have found that these observations agree well overall with predictions of accuracy derived from the JGM 2 variance-covariance matrix; the corresponding projected LLC errors for Geosat, T/P, and ERS 1 are usually between 1 and 4 cm, 1 – 2 cm, and 1 – 4 cm, respectively (they depend on the filtering of long-periodic perturbations and on the order of the LLC). This agreement is especially impressive for ERS 1 since no data of any kind from this mission was used in forming JGM 2.

The observed crossover differences for Geosat, T/P and ERS 1 are 8, 3, and 11 cm (rms), respectively. These observations also agree well with prediction of accuracy derived from the JGM 2 variance-covariance matrix; the corresponding projected crossover errors for Geosat and T/P are 8 cm and 2.3 cm, respectively. The precision of our mean difference observations is about 3 cm for Geosat (approx. 24,000 observations), 1.5 cm for T/P (approx. 6,000 observations) and 5 cm for ERS 1 (approx. 44,000 observations). Thus, these “global” independent data should provide a valuable new source for improving geopotential models. Our results show the need for further correction of the low order JGM 2 geopotential as well as certain resonant orders for all 3 satellites.     

Towards development of a consistent orbit series for TOPEX,Jason-1, and Jason-2

The TOPEX/Poseidon, Jason-1 and Jason-2 set of altimeter data now provide a time series of synoptic observations of the ocean that span nearly 17 years from the launch of TOPEX in 1992. The analysis of the altimeter data including the use of altimetry to monitor the global change in mean sea level requires a stable, accurate, and consistent orbit reference over the entire time span. In this paper, we describe the recomputation of a time series of orbits that rely on a consistent set of reference frames and geophysical models. The recomputed orbits adhere to the IERS 2003 standards for ocean and earth tides, use updates to the ITRF2005 reference frame for both the SLR and DORIS stations, apply GRACE-derived models for modeling of the static and time-variable gravity, implement the University College London (UCL) radiation pressure model for Jason-1, use improved troposphere modeling for the DORIS data, and apply the GOT4.7 ocean tide model for both dynamical ocean tide modeling and for ocean loading. The new TOPEX orbits have a mean SLR fit of 1.79 cm compared to 2.21 cm for the MGDR-B orbits. These new TOPEX orbits agree radially with independent SLR/crossover orbits at 0.70 cm RMS, and the orbit accuracy is estimated at 1.5–2.0 cm RMS over the entire TOPEX time series. The recomputed Jason-1 orbits agree radially with the Jason-1 GDR-C orbits at 1.08 cm RMS. The GSFC SLR/DORIS dynamic and reduced-dynamic orbits for Jason-2 agree radially with independent orbits from the CNES and JPL at 0.70–1.06 cm RMS. Applying these new orbits, and using the latest altimeter corrections for TOPEX, Jason-1, and Jason-2 from September 1992 to May 2009, we find a global rate in mean sea level of 3.0 ± 0.4 mm/yr.     

Influence of time variable geopotential models on precise orbits of altimetry satellites,global and regional mean sea level trends

During the last decade a significant progress has been reached in the investigation of the gravity field of the Earth. Besides static, also time variable geopotential models have been recently created. In this paper we investigate the impact of the recent time variable geopotential models on altimetry satellite orbits and such altimetry products based on these orbits, as global and regional mean sea level trends. We show that the modeling of time variable gravity improves the orbit solutions, at least for the GRACE period where time variable gravity is sufficiently accurately observed by this mission. Our analysis includes six geopotential models jointly developed by GFZ German Research Centre for Geosciences and Space Geodesy Research Group (CNES/GRGS) Toulouse: the stationary model EIGEN-GL04S, a stationary version of EIGEN-6S (EIGEN-6S_stat), a corrected version of EIGEN-6S and three enhanced versions of EIGEN-6S called EIGEN-6S2, EIGEN-6S2A and EIGEN-6S2B. By “stationary” we mean “containing periodic parameters such as annual and semi-annual variations, but no secular (drift) terms”. We computed precise orbits for the radar altimetry satellites ERS-1, ERS-2, TOPEX/Poseidon, and Envisat over 20 years between 1991 and 2011. The orbit, single-mission and multi-mission altimetry crossover analyses show that the time variable models EIGEN-6S_corrected, EIGEN-6S2 and its two precursors EIGEN-6S2A/B perform notably better than the stationary models for the GRACE period from 2003 onwards. Thus, using EIGEN-6S2 and EIGEN-6S2A/B we have got 3.6% smaller root mean square fits of satellite laser ranging observations for Envisat, as when using EIGEN-GL04S. However, for the pre-GRACE period 1991–2003, the stationary geopotential models EIGEN-GL04S and EIGEN-6S_stat as well as EIGEN-6S2 having no drift terms for degree 3–50 at this time interval perform superior compared to EIGEN-6S_correct and EIGEN-6S2A/B which contain drifts for this period. We found, that the time variable geopotential models have a low (0.1–0.2 mm/yr) impact on our results for the global mean sea level trend. However, we found strong East/West differences up to 3 mm/yr in the regional mean sea level trends when using orbits of all four satellites based on time variable and stationary geopotential models. We show that these differences are related to the relative drifts of the centers-of-origin between the orbit solutions based on the time variable and stationary geopotential models. From the results of our detailed study, we conclude that the final version of the time variable gravity field model EIGEN-6S2 performs best for the four satellites tested. This model provides the most reliable and mission-consistent sea level estimates for the whole time period from 1992 to 2010. This model is of maximum spherical harmonic degree and order 260 and contains time series for drifts as well as annual and semiannual variations of the spherical harmonic coefficients for degree 2–50.     

ERS-1 and ERS-2 operational and precise orbit determination

This paper presents the European Space Operations Centre's orbit determination and prediction systems for the ERS-1 mission. The routine operational orbit determination and prediction subsystem is discussed briefly, and statistics of the accuracy compared to the requirements are given. The precise orbit determination subsystem is then described, and the accuracy of its results are compared to those of the operational orbit system and to the D-PAF preliminary orbit solutions. Some geophysical results from the altimeter data, processed in these orbit determinations, are also presented. The ESOC/OAD ‘ERS-1 Orbit Report’ is introduced as a document providing this information on a monthly basis. Finally, this paper describes how the experience gained with the precise orbit determination will be exploited to further improve the accuracy of the routine system that will be used for ERS-2, and provides an estimate of this accuracy.     

GSFC DORIS contribution to ITRF2008

The NASA GSFC DORIS analysis center has provided weekly DORIS solutions from November 1992 to January 2009 (839 SINEX files) of station positions and Earth Orientation Parameters for inclusion in the DORIS contribution to ITRF2008. The NASA GSFC GEODYN orbit determination software was used to process the orbits and produce the normal equations. The weekly SINEX gscwd10 submissions included DORIS data from Envisat, TOPEX/Poseidon, SPOT-2, SPOT-3, SPOT-4, SPOT-5. The orbits were mostly seven days in length (except for weeks with data gaps or maneuvers). The processing used the GRACE-derived EIGEN-GL04S1 gravity model, updated modeling for time-variable gravity, the GOT4.7 ocean tide model and tuned satellite-specific macromodels for SPOT-2, SPOT-3, SPOT-4, SPOT-5 and TOPEX/Poseidon. The University College London (UCL) radiation pressure model for Envisat improves nonconservative force modeling for this satellite, reducing the median residual empirical daily along-track accelerations from 3.75 × 10⁻⁹ m/s² with the a priori macromodel to 0.99 × 10⁻⁹ m/s² with the UCL model. For the SPOT and Envisat DORIS satellite orbits from 2003 to 2008, we obtain average RMS overlaps of 0.8–0.9 cm in the radial direction, 2.1–3.4 cm cross-track, and 1.7–2.3 cm along-track. The RMS orbit differences between Envisat DORIS-only and SLR & DORIS orbits are 1.1 cm radially, 6.4 cm along-track and 3.7 cm cross-track and are characterized by systematic along-track mean offsets due to the Envisat DORIS system time bias of ±5–10 μs. We obtain a good agreement between the geometrically-determined geocenter parameters and geocenter parameters determined dynamically from analysis of the degree one terms of the geopotential. The intrinsic RMS weekly position repeatability with respect to the IDS-3 combination ranges from 2.5 to 3.0 cm in 1993–1994 to 1.5 cm in 2007–2008.     

Generating precise and homogeneous orbits for Jason-1 and Jason-2

Driven by the GMES (Global Monitoring for Environment and Security) and GGOS (Global Geodetic Observing System) initiatives the user community has a strong demand for high-quality altimetry products. In order to derive such high-quality altimetry products, precise orbits for the altimetry satellites are a necessity. With the launch of the TOPEX/Poseidon mission in 1992 a still on-going time series of high-accuracy altimetry measurements of ocean topography started, continued by the altimetry missions Jason-1 in 2001 and Jason-2/OSTM in 2008. This paper contributes to the on-going orbit reprocessing carried out by several groups and presents the efforts of the Navigation Support Office at ESA/ESOC using its NAPEOS software for the generation of precise and homogeneous orbits referring to the same reference frame for the altimetry satellites Jason-1 and Jason-2. Data of all three tracking instruments on-board the satellites (beside the altimeter), i.e. GPS, DORIS, and SLR measurements, were used in a combined data analysis. About 7 years of Jason-1 data and more than 1 year of Jason-2 data were processed. Our processing strategy is close to the GDR-C standards. However, we estimated slightly different scaling factors for the solar radiation pressure model of 0.96 and 0.98 for Jason-1 and Jason-2, respectively. We used 30 s sampled GPS data and introduced 30 s satellite clocks stemming from ESOC’s reprocessing of the combined GPS/GLONASS IGS solution. We present the orbit determination results, focusing on the benefits of adding GPS data to the solution. The fully combined solution was found to give the best orbit results. We reach a post-fit RMS of the GPS phase observation residuals of 6 mm for Jason-1 and 7 mm for Jason-2. The DORIS post-fit residuals clearly benefit from using GPS data in addition, as the DORIS data editing improves. The DORIS observation RMS for the fully combined solution is with 3.5 mm and 3.4 mm, respectively, 0.3 mm better than for the DORIS-SLR solution. Our orbit solution agrees well with external solutions from other analysis centers, as CNES, LCA, and JPL. The orbit differences between our fully combined orbits and the CNES GDR-C orbits are of about 0.8 cm for Jason-1 and at 0.9 cm for Jason-2 in the radial direction. In the cross-track component we observe a clear improvement when adding GPS data to the POD process. The 3D-RMS of the orbit differences reveals a good orbit consistency at 2.7 cm and 2.9 cm for Jason-1 and Jason-2. Our resulting orbit series for both Jason satellites refer to the ITRF2005 reference frame and are provided in sp3 file format on our ftp server.     

Precision orbit determination for TOPEX/Poseidon using TDRSS doppler tracking data

Precision orbit determination on the TOPEX/Poseidon (T/P) altimeter satellite is now being routinely achieved with sub-5cm radial and sub-15 cm total positioning accuracy using state-of-the-art modeling with precision tracking provided by a combination of: (a) global Satellite Laser Ranging (SLR) and Doppler Orbitography and Radiopositioning Integrated by Satellite (DORIS), or (b) the Global Positioning System (GPS) Constellation which provides pseudo-range and carrier phase observations. The geostationary Tracking and Data Relay Satellite System (TDRSS) satellites are providing the operational tracking and communication support for this mission. The TDRSS Doppler data are of high precision (0.3 mm/s nominal noise levels). Unlike other satellite missions supported operationally by TDRSS, T/P has high quality independent tracking which enables absolute orbit accuracy assessments. In addition, the T/P satellite provides extensive geometry for positioning a satellite at geostationary altitude, and thus the TDRSS-T/P data provides an excellent means for determining the TDRS orbits. Arc lengths of 7 and 10 days with varying degrees of T/P spacecraft attitude complexity are studied. Sub-meter T/P total positioning error is achieved when using the TDRSS range-rate data, with radial orbit errors of 10.6 cm and 15.5 cm RMS for the two arcs studied. Current limitations in the TDRSS precision orbit determination capability include mismodeling of numerous TDRSS satellite-specific dynamic and electronic effects, and in the inadequate treatment of the propagation delay and bending arising from the wet troposphere and ionosphere.     

Preliminary study of differential force modelling on ERS-1 and ERS-2

The two near identical satellites ERS-1 and ERS-2 are orbiting the Earth in the same orbit and same orbital plane with ERS-1 some thirty-two minutes in the lead. If their altimetric datasets are differenced along the repeating ground-track any fixed geographically correlated signature will cancel. The residual signature of this differenced dataset will therefore arise from imprecise corrections to the altimetric dataset but more significantly from temporal variations in the forces affecting both satellites; in particular luni-solar attraction and aerodynamic force modelling. This study presents preliminary results of differential force modelling on the satellites with an emphasis on the aerodynamic effects.     

Precision orbit determination performance for CryoSat-2

In this paper we discuss our efforts to perform precision orbit determination (POD) of CryoSat-2 which depends on Doppler and satellite laser ranging tracking data. A dynamic orbit model is set-up and the residuals between the model and the tracking data is evaluated. The average r.m.s. of the 10?s averaged Doppler tracking pass residuals is approximately 0.39?mm/s; and the average of the laser tracking pass residuals becomes 1.42?cm. There are a number of other tests to verify the quality of the orbit solution, we compare our computed orbits against three independent external trajectories provided by the CNES. The CNES products are part of the CryoSat-2 products distributed by ESA. The radial differences of our solution relative to the CNES precision orbits shows an average r.m.s. of 1.25?cm between Jun-2010 and Apr-2017. The SIRAL altimeter crossover difference statistics demonstrate that the quality of our orbit solution is comparable to that of the POE solution computed by the CNES. In this paper we will discuss three important changes in our POD activities that have brought the orbit performance to this level. The improvements concern the way we implement temporal gravity accelerations observed by GRACE; the implementation of ITRF2014 coordinates and velocities for the DORIS beacons and the SLR tracking sites. We also discuss an adjustment of the SLR retroreflector position within the satellite reference frame. An unexpected result is that we find a systematic difference between the median of the 10 s Doppler tracking residuals which displays a statistically significant pattern in the South Atlantic Anomaly (SSA) area where the median of the velocity residuals varies in the range of ?0.15 to +0.15?mm/s.     

Improvement of the SLR Borowiec station position in the global network ITRF91

This paper describes briefly two station coordinates solutions, the first one computed at Space Research Centre (SRC) using tracking data from Lageos satellite, and the second one computed at European Space Operations Centre (ESOC) using tracking data from Lageos 1, ERS-1 and TOPEX/Poseidon in a multi-arc solution. In particular the solution computed for the Borowiec station in ITRF91 system is described extensively. The Borowiec station position was estimated simultaneousely, considering or not the existence of range biases, with other geophysical parameters such as: daily polar motion parameters x_p, y_p, ocean tide coefficients, earth gravitational constant GM, etc.     

Derniers resultats de calcul d'orbite SPOT et TOPEX/POSEIDON obtenus avec DORIS

DORIS is a tracking system developed by CNES to support precise orbit computation of the US-French TOPEX/POSEIDON project. Moreover DORIS data are currently processed to compute SPOT2 and SPOT3 orbits. Although the SPOT satellites are at 800 km altitudes, their orbits reach the decimetric level, to be compared to the 3–4 cm RMS on the T/P radial component.For each type of orbit, there is an adaptive period of a few months which is used for improving the precision. The paper describes what has been done to reduce some items in the total error budget. The latest results will be presented as well as the criteria which are settled to characterize the improvements.Finally, the future developments of DORIS and the potential projects flowing DORIS will be outlined such as ENVISAT and TOPEX/POSEIDON Follow On.     

Impact of ITRS 2014 realizations on altimeter satellite precise orbit determination

This paper evaluates orbit accuracy and systematic error for altimeter satellite precise orbit determination on TOPEX, Jason-1, Jason-2 and Jason-3 by comparing the use of four SLR/DORIS station complements from the International Terrestrial Reference System (ITRS) 2014 realizations with those based on ITRF2008. The new Terrestrial Reference Frame 2014 (TRF2014) station complements include ITRS realizations from the Institut National de l’Information Géographique et Forestière (IGN) ITRF2014, the Jet Propulsion Laboratory (JPL) JTRF2014, the Deutsche Geodätisches Forschungsinstitut (DGFI) DTRF2014, and the DORIS extension to ITRF2014 for Precise Orbit Determination, DPOD2014. The largest source of error stems from ITRF2008 station position extrapolation past the 2009 solution end time. The TRF2014 SLR/DORIS complement impact on the ITRF2008 orbit is only 1–2 mm RMS radial difference between 1992–2009, and increases after 2009, up to 5 mm RMS radial difference in 2016. Residual analysis shows that station position extrapolation error past the solution span becomes evident even after two years, and will contribute to about 3–4 mm radial orbit error after seven years. Crossover data show the DTRF2014 orbits are the most accurate for the TOPEX and Jason-2 test periods, and the JTRF2014 orbits for the Jason-1 period. However for the 2016 Jason-3 test period only the DPOD2014-based orbits show a strong and statistically significant margin of improvement. The positive results with DTRF2014 suggest the new approach to correct station positions or normal equations for non-tidal loading before combination is beneficial. We did not find any compelling POD advantage in using non-linear over linear station velocity models in our SLR & DORIS orbit tests on the Jason satellites. The JTRF2014 proof-of-concept ITRS realization demonstrates the need for improved SLR+DORIS orbit centering when compared to the Ries (2013) CM annual model. Orbit centering error is seen as an annual radial signal of 0.4 mm amplitude with the CM model. The unmodeled CM signals show roughly a 1.8 mm peak-to-peak annual variation in the orbit radial component. We find the TRF network stability pertinent to POD can be defined only by examination of the orbit-specific tracking network time series. Drift stability between the ITRF2008 and the other TRF2014-based orbits is very high, the relative mean radial drift error over water is no larger than 0.04 mm/year over 1993–2015. Analyses also show TRF induced orbit error meets current altimeter rate accuracy goals for global and regional sea level estimation.     

基于自适应滤波的编队卫星实时相对定轨

提出基于自适应滤波的编队卫星实时相对定轨算法,利用2005-12-09—10两颗GRACE（Gravity Recovery and Climate Experiment）卫星的GPS（Global Positioning System）实测数据进行实时相对定轨试验计算,采用JPL（Jet Propulsion Laboratory）轨道对试验结果外部检核,结果表明:①自适应滤波相对定轨通过自适应因子,可以较好地平衡编队卫星的观测信息和相对动力学信息,其相对定轨结果精度优于Kalman滤波相对定轨结果;②自适应滤波相对定轨结果随着星间基线缩短而精度提高;③两颗GRACE卫星采用单频伪距和广播星历进行自适应滤波相对定轨,可以得到精度优于6cm的星间基线。