Available online at www.sciencedirect.com

www.elsevier.com/locate/asr

Advances in Space Research 50 (2012) 260–271

Inter-agency comparison of TanDEM-X baseline solutions

A. Jaggi a,⇑, O. Montenbruck b, Y. Moon c, M. Wermuth b, R. Konig c, G. Michalak c,H. Bock a, D. Bodenmann a

a Astronomical Institute, University of Bern, Sidlerstrasse 5, CH-3012 Bern, Switzerlandb Deutsches Zentrum fur Luft- und Raumfahrt, Oberpfaffenhofen, Germany

c German Research Centre for Geosciences, Potsdam, Germany

Received 21 December 2011; received in revised form 23 March 2012; accepted 24 March 2012Available online 3 April 2012

Abstract

TanDEM-X (TerraSAR-X add-on for Digital Elevation Measurement) is the first Synthetic Aperture Radar (SAR) mission usingclose formation flying for bistatic SAR interferometry. The primary goal of the mission is to generate a global digital elevation model(DEM) with 2 m height precision and 10 m ground resolution from the configurable SAR interferometer with space baselines of a fewhundred meters. As a key mission requirement for the interferometric SAR processing, the relative position, or baseline vector, of the twosatellites must be determined with an accuracy of 1 mm (1D RMS) from GPS measurements collected by the onboard receivers. Theoperational baseline products for the TanDEM-X mission are routinely generated by the German Research Center for Geosciences(GFZ) and the German Space Operations Center (DLR/GSOC) using different software packages (EPOS/BSW, GHOST) and analysisstrategies. For a further independent performance assessment, TanDEM-X baseline solutions are generated at the Astronomical Instituteof the University of Bern (AIUB) on a best effort basis using the Bernese Software (BSW).

Dual-frequency baseline solutions are compared for a 1-month test period in January 2011. Differences of reduced-dynamic baselinesolutions exhibit a representative standard deviation (STD) of 1 mm outside maneuver periods, while biases are below 1 mm in all direc-tions. The achieved baseline determination performance is close to the mission specification, but independent SAR calibration data takesacquired over areas with a well known DEM from previous missions will be required to fully meet the 1 mm 1D RMS target. Besides theoperational solutions, single-frequency baseline solutions are tested. They benefit from a more robust ambiguity fixing and show aslightly better agreement of below 1 mm STD, but are potentially affected by errors caused by an incomplete compensation of differentialionospheric path delays.� 2012 COSPAR. Published by Elsevier Ltd. All rights reserved.

Keywords: TanDEM-X; Precise baseline determination (PBD); Inter-agency baseline comparison; Ambiguity fixing; GPS; SAR

1. Introduction

Spaceborne Synthetic Aperture Radar (SAR) is a wellestablished remote sensing technique, which enables a glo-bal monitoring of the Earth irrespective of weather condi-

0273-1177/$36.00 � 2012 COSPAR. Published by Elsevier Ltd. All rights rese

http://dx.doi.org/10.1016/j.asr.2012.03.027

⇑ Corresponding author. Tel.: +41 31 6318596; fax: +41 31 6313869.E-mail addresses: adrian.jaeggi@aiub.unibe.ch (A. Jaggi), Oliver.

Montenbruck@dlr.de (O. Montenbruck), moon@gfz-potsdam.de(Y. Moon), Martin.Wermuth@dlr.de (M. Wermuth), rolf.koenig@gfz-potsdam.de (R. Konig), michalak@gfz-potsdam.de (G. Michalak),heike.bock@aiub.unibe.ch (H. Bock), dominik.bodenmann@students.unibe.ch (D. Bodenmann).

tions. Beyond standalone, single-SAR applications (e.g.,Freeman et al., 1996), added value can be gained by aphase coherent combination of two SAR interferogramsof the same area. Temporal variations such as tectonicmotion or subsidence can, e.g., be studied by repeat passinterferometry. On the other hand, height informationcan be derived through simultaneous observations fromSAR instruments at slightly different locations. In bistaticSAR interferometry radar pulses are transmitted by a sin-gle illuminator but concurrently received by two antennas.The achievable resolution depends on the antenna separa-tion which is limited by the physical spacecraft dimension

rved.

A. Jaggi et al. / Advances in Space Research 50 (2012) 260–271 261

in a single satellite mission. To overcome this limitation,formation flying satellites may be used as an alternative(Krieger et al., 2010). In the German TanDEM-X (Terra-SAR-X add-on for Digital Elevation Measurement) mis-sion, two spacecraft establish the first configurable SARinterferometer with baselines of a few hundred meters(Krieger et al., 2007). The mission consists of two almostidentical satellites, TerraSAR-X (launched on 15 June,2007) and TanDEM-X (launched on 21 June, 2010) withhighly flexible X-band SAR instruments, which are con-trolled from ground to stay in a safe relative orbit withthe desired inter-orbit (out-of-plane) separation duringdata collection (Montenbruck et al., 2008). The primarymission goal consists of the generation of a global digitalelevation model (DEM) with 2 m height precision and10 m ground resolution. To cover the entire surface ofthe Earth, the satellites fly in formation in sun-synchronousorbits at an altitude of 514 km and operate in parallel for anominal duration of three years (until termination of theTerraSAR-X mission).

For interferometric processing, the phase differencecaused by the different distances of the receiving antennasfrom the target site must be compensated. To this end,the relative position, or baseline vector, of the two space-craft is measured with high accuracy using differential car-rier phase measurements of the Global Positioning System(GPS). In view of the X-band wavelength of about 3 cm,even small errors in the line-of-sight component of thebaseline vector would not only result in a considerableheight error, but also in an undesirable tilt and shift ofthe derived DEM. A 1 mm (1D RMS) accuracy require-ment has therefore been established for the GPS based pre-cise baseline determination (PBD) process (TanDEM-XMission Requirements Document, 2007). As a rule ofthumb, a baseline error of 1 mm in line of sight translatesinto a DEM height error of 1 m (Wermuth et al., 2011).

To meet this challenging specification, the TerraSAR-Xand TanDEM-X satellites are both equipped with a geo-detic grade GPS receiver (Rothacher et al., 2007) contrib-uted by the German Research Center for Geosciences(GFZ). The receivers support tracking of the coarse &acquisition (C/A) code on the L1 frequency as well assemi-codeless tracking of the encrypted P(Y)-code on L1and L2. Representative values of the receiver tracking noiseover the relevant range of signal levels amount to 10–30 cmand 0.5–1 mm for the 10 s code and phase measurements,respectively (Montenbruck et al., 2006). To minimize theimpact of multipath, the receivers are operated with cho-kering antennas.

Given the high importance of the accurate baseline solu-tions for the interferometric SAR processing, independentbaseline solutions are routinely generated by both GFZand the German Space Operations Center (DLR/GSOC)within the TanDEM-X project. This setup allows across-comparison for error detection as well as a weightedaveraging to reduce the overall variance of the combinedproduct (Montenbruck et al., 2010). For a further indepen-

dent performance assessment, the TanDEM-X baselinesare additionally computed by the Astronomical Instituteof the University of Bern (AIUB) on a best effort basis.Dual- and single-frequency baseline solutions computedby all three agencies are compared in this study for a 1-month test period in January 2011.

Section 2 introduces the methods for PBD at the threeinstitutions. Section 3 presents the auxiliary input productsrequired for PBD. A detailed inter-agency comparison ofTanDEM-X baseline solutions is performed in Section 4,which also discusses alternative solution strategies.

2. Methods for precise baseline determination

Different software packages and processing strategiesare implemented at GFZ and DLR to generate the opera-tional baseline products, and at AIUB to generate solu-tions on a best effort basis. This section gives an overviewof the relevant processing details for PBD at all three insti-tutions. A short summary of the measurement anddynamic models used is provided in Table 1.

2.1. AIUB approach

The baseline solutions computed at AIUB are generatedwith a special version of the Bernese Software (BSW, Dachet al., 2007). The same software version is currently used atAIUB to derive the GOCE precise science orbit product(Bock et al., 2011) in the context of the High-level Process-ing Facility of the European GOCE Gravity Consortium(HPF, Koop et al., 2006), and has been used for variousstudies on precise orbit determination (POD) of low Earthorbiting satellites (e.g., Jaggi et al., 2009b) and subsequentgravity field recovery (e.g., Jaggi et al., 2011).

The baseline solutions are generated by a procedureoriginally developed by Jaggi et al. (2007) using data fromthe GRACE mission (Tapley et al., 2004b) and laterextended to the TanDEM-X processing. The positions ofone satellite (TerraSAR-X) are kept fixed to a reduced-dynamic single-satellite solution established in a batchleast-squares estimation process, which is essentially basedon 30 s zero-difference (ZD) ionosphere-free GPS carrierphase data only. The reduced-dynamic (or kinematic) orbitparameters of the other satellite (TanDEM-X) are esti-mated in a batch least-squares estimation process as well,which is based on 30 s (or 10 s) double-difference (DD) ion-osphere-free GPS carrier phase data with DD ambiguitiesresolved to their integer values. In the dual-frequency pro-cessing the Melbourne-Wubbena linear combination isanalyzed first to resolve the wide-lane ambiguities, whichare subsequently introduced as known to resolve the nar-row-lane ambiguities simultaneously with the reduced-dynamic (or kinematic) baseline determination. For sin-gle-frequency PBD the L1 carrier phase ambiguities aredirectly fixed to their integer values.

For ZD and DD reduced-dynamic POD and PBD, sixinitial osculating elements are estimated per satellite and

Table 1Summary of the measurement and dynamic models employed for PBD.

Item AIUB (BSW) GFZ (BSW) DLR (GHOST)

GPS measurement model Double-difference ionosphere-freephase; 30 s/10 s sampling; igs05.atxa

phase center offsets and variations oftransmitter and receiver antennas;CODE final GPS orbits and 30 s/10 sclocks

Double-difference ionosphere-freephase; 30 s sampling; igs05.atx phasecenter offsets and variations oftransmitter and receiver antennas;CODE final GPS orbit and 30 sclocks

L1 and/or L2 single-difference codeand phase, 10 s sampling; igs05.atxphase center offsets and variations oftransmitter and receiver antennas;CODE final GPS orbits and 10 sclocks; differential ionospheric pathdelays

Gravitational forces EIGEN-5Cb gravity (120� 120);solid-earth, pole and ocean tides(IERS2003e, CSR 3.0g); luni-solar-planetary gravity (DE-405j)

EIGEN-GL04Sc gravity; solid-earth,pole and ocean tides (IERS1996f,CSR Ch); luni-solar-planetary gravity(DE-200k)

GGM01 d gravity (100� 100); solid-earth, pole and ocean tides(IERS2003, TOPEX_3.0i); luni-solargravity (analytical ephemerides)

Non-gravitational forces No drag and radiation force model;pseudo-stochastic RAO accelerationsat 6-min intervals; maneuvers(additional set of pulses)

No drag and radiation force model;pseudo-stochastic RAO pulses at 6-min intervals; maneuvers (additionalset of pulses)

Jacchia-Gilll density model;solarradiation pressure; empirical RAOaccelerations (exponentiallycorrelated); maneuvers (constantthrust arc)

Reference frames ITRF2005 m/IGS05 reference frame;IERS2003 reference frametransformations;CODE final ERPs;s/c attitude dual star trackers

ITRF2005/IGS05 reference frame;IERS2003 reference frametransformations;CODE final ERPs;s/c attitude single star tracker

ITRF2005/IGS05 reference frame;IERS1996 reference frametransformations;CODE final ERPs;s/c attitude dual star trackers

Estimation Batch least-squares Batch least-squares Extended Kalman filter/smoother

a Schmid et al. (2007).b Forste et al. (2008b).c Forste et al. (2008a).d Tapley et al. (2004a).e McCarthy et al. (2003).f McCarthy (1996).g UT/CSR Ocean Tide Models (1997).h UT/CSR Ocean Tide Models (1995).i UT/CSR Ocean Tide Models (2001).j Standish (1998).

k Standish (1990).l Gill (1971).

m Altamimi et al. (2007).

262 A. Jaggi et al. / Advances in Space Research 50 (2012) 260–271

24 h orbital arc, additional constant empirical accelerationsare set up per satellite in the radial (R), along-track (A),and out-of-plane (O) directions acting over the entire time-span of the orbital arcs, and, on top, piecewise constantempirical accelerations acting in the same directions over6-min intervals (Jaggi et al., 2006). The latter parametersare characterized by a priori variances constraining themto zero (absolute constraining). For DD PBD the entireset of TanDEM-X empirical accelerations is in additiontightly constrained to the TerraSAR-X estimates fromZD POD (relative constraining).

2.2. DLR approach

TerraSAR-X and TanDEM-X POD and PBD is rou-tinely performed at GSOC/DLR using the GPS High-pre-cision Orbit determination Software Tools (GHOST,Wermuth et al., 2010). The package contains various mod-ules for precise orbit and baseline determination and isjointly used for the operational processing and offline anal-yses. Products used for this study have been reprocessed tomatch the latest processing standards and do not fullymatch the routine mission products.

The reduced-dynamic baseline solutions are generatedby a procedure originally developed by Kroes et al.(2005) using data from the GRACE mission and laterextended to the TanDEM-X processing (Montenbrucket al., 2010). The positions of one satellite (TerraSAR-X)are kept fixed to a reduced-dynamic single-satellite solutionestablished in a batch least-squares estimation processbased on ZD ionosphere-free GPS code and carrier phasedata. The reduced-dynamic orbit parameters of the othersatellite (TanDEM-X) are estimated by an extended Kal-man filter/smoother using single-difference (SD) iono-sphere-free GPS code and carrier phase observations.Intermediate DD ambiguities are formed from the esti-mated SD ambiguities and resolved to their integer valuesby the Least-squares AMbiguity Decorrelation Adjustmentmethod (LAMBDA, Teunissen, 1995) to constrain the SDambiguities by a pseudo-measurement update. Followingsuccessful ambiguity fixing, kinematic relative positionsmay, furthermore, be computed from the DD carrier phaseobservations.

The Filter for Relative Navigation of Spacecraft(FRNS, Kroes, 2006) used for the PBD estimates theinstantaneous relative position and velocity, differential

A. Jaggi et al. / Advances in Space Research 50 (2012) 260–271 263

drag and radiation pressure coefficients, empirical accelera-tions and the relative clock offset at each measurementepoch. In addition, ionospheric path delays and indepen-dent L1 and L2 carrier phase ambiguities are estimatedfor each tracked channel in the dual-frequency processing.For single-frequency processing, only a single vertical pathdelay parameter (common to all observed satellites) andthe channel-wise L1 phase ambiguities are estimated(Montenbruck et al., 2011).

2.3. GFZ approach

GFZ is running two different software tools for generat-ing baseline solutions, the BSW and the in-house EarthParameter and Orbit System (EPOS). The basic featuresof EPOS are described in Zhu et al. (2004). Products usedfor this study have been reprocessed with both softwarepackages to match the latest processing standards and donot fully match the routine mission products.

The GFZ routine baseline product is based on the BSW5.0 with some modifications and extensions implemented atGFZ for the purpose of the operational TanDEM-X base-line processing. The GFZ BSW POD and PBD solutionsare based on a reduced-dynamic batch processing schemeclosely matching the AIUB approach described in Sec-tion 2.1. Differences to the AIUB approach are mainlyrelated to the different software versions used at the twoinstitutions. For both POD and PBD, e.g., empirical forcesare modeled as instantaneous velocity changes in theradial, along-track, and out-of-plane direction using a sim-ilar constraining philosophy as for the AIUB approach.

The GFZ EPOS solution is also based on a reduced-dynamic approach, but consequently using ZD iono-sphere-free code and phase data. As opposed to the relativeapproach of the BSW, a multi-satellite POD approach isfollowed with EPOS. The estimated parameters are initialstates of both satellites, scaling factors of the solar radiationpressure model, empirical accelerations in the radial, along-track, and out-of-plane direction at 6-min intervals. Addi-tionally the empirical accelerations are highly constrainedto result in almost identical values for both satellites. Ambi-guity fixing is realized by constraining corresponding linearcombinations of appropriate four ZD ionosphere-freeambiguities. The side constraints are obtained by fixingthe DD wide-lane and narrow-lane ambiguities to their inte-ger values and computing the floating DD ionosphere-freelinear combination. The side constraints are applied onceon cleaned data at the end of the iterative screening proce-dure. EPOS solutions are computed in batches of 12 h.

Table 2GPS antenna position in the spacecraft body system relative to the center-of-g

Spacecraft Antenna X (mm) Y (mm)

TerraSAR-X POD main +1588.5 �16.7TanDEM-X POD aux +1200.0 �17.7

If not stated differently GFZ BSW baseline solutions aredenoted by “GFZ” in this article.

3. Input products

3.1. Antenna offsets

The coordinates of the POD antennas with respect tothe center-of-gravity (CoG) in the respective satellite-fixedsystems are summarized in Table 2. Additional phase cen-ter offsets of the antenna/chokering combination of thePOD antennas with respect to the antenna reference points(ARP) are documented by Montenbruck et al. (2009). Theyare given in an antenna-fixed system and are consistentlyused for this study by all three agencies. Definitions ofthe underlying satellite- and antenna-fixed coordinate sys-tems may be found, e.g., in Montenbruck et al. (2009),Jaggi et al. (2009b).

Additional phase center variations (PCVs) of the PODantennas have been derived individually by all three agen-cies for each satellite for the ionosphere-free linear com-bination (see next section) in a stacking approach basedon ZD GPS carrier phase residuals. The patterns havebeen derived as part of the POD process, either relativeto the ground calibration such as performed at GFZand at DLR, or relative to zero as performed at AIUB.PCVs primarily serve the final single-satellite orbit deter-mination based on ZD GPS data, but they are also usedat AIUB for nominal PBD based on DD GPS data (seeSection 2). For study purposes, differential PCVs havealso been estimated at AIUB as part of the parameterestimation process (direct approach) from DD dual-fre-quency and single-frequency ambiguity-fixed GPS data,respectively (Jaggi et al., 2009b). The use of differentialpatterns is of particular interest for single-frequencyPBD, because single-satellite patterns cannot be derivedas part of the POD process. At DLR, differential phasepattern corrections (relative to the ground calibration)for the single-frequency processing have been derived ina stacking approach based on post-measurement updateSD carrier phase residuals computed in the baselinedetermination. Other than in the POD based residualsstacking, only one iteration is required in the PBD pro-cessing thanks to the use of ambiguity-fixed carrier phasemeasurements. Application of the differential patternsyields a small benefit for the reduced-dynamic PBD butresults in a substantially reduced noise level of the kine-matic baseline determination as will be shown inSection 4.1.2.

ravity (CoG) for TerraSAR-X and TanDEM-X in January, 2011.

Z (mm) Boresight (+z) Azimuth (+y)

�1065.4 (0,0,�1) (0,�1,0)�1069.0 (0,0,�1) (�1,0,0)

264 A. Jaggi et al. / Advances in Space Research 50 (2012) 260–271

3.2. GPS observations

The Integrated GPS and Occultation Receiver (IGOR)onboard TerraSAR-X and TanDEM-X provides C/A,P1, and P2 code measurements together with the corre-sponding carrier phase observations. Consequently, twotypes of carrier phase measurements are available on thefirst frequency, which are subsequently denoted as L1(C)and L1(P). Baseline solutions may thus be generated byeither using ionosphere-free GPS observations based onL1(C) and L2(P) data, or based on L1(P) and L2(P) data.Following the experience with BlackJack receivers onGRACE, L1(C) data are preferred because of their slightlylower noise level (Jaggi et al., 2009a).

The IGOR receivers on TanDEM-X and TerraSAR-Xoperate on crystal oscillators that are nominally steeredto GPS time with sub-microsecond accuracy based on thereceiver-internal navigation solution. During radio-occul-tation measurements (performed on TerraSAR-X), how-ever, the clock steering is temporarily disabled and clockoffsets on the level of several microseconds may be encoun-tered. Given the high orbital velocity, even a 1 ls timinginconsistency would result in a phase modeling error ofup to 8 mm. While the reduced-dynamic PBD processingoffers a certain level of robustness against such errors, thekinematic baseline processing is particularly sensitive andresults in along-track errors proportional to the timing off-set between the receivers. In the DLR processing chain aclock-offset correction and an extrapolation to integer sec-onds of GPS time is therefore performed on the raw obser-vations prior to use in the PBD. Asynchronicities in themeasurement epochs of the TanDEM-X and TerraSAR-X GPS observations are presently neglected in the GFZand AIUB processing using the BSW.

3.3. Attitude data

Attitude information of the spacecraft is based on thestar camera data provided as part of the house-keepingtelemetry. Each s/c is equipped with three star cameraspointing in different directions and an optimal combinationof the available star camera quaternions is routinely per-formed at DLR (Kahle et al., 2007) to obtain a combinedattitude product for POD and PBD purposes with a typical3D accuracy of 0.01� ð1rÞ. At GFZ the spacecraft orienta-tion is derived from attitude quaternions of only one singlestar camera, which slightly degrades the performanceabout the boresight axis but has no relevant impact onthe baseline processing. At a CoG-to-antenna distance ofbelow 2 m, a 0.01� attitude error introduces a modelingerror of 0.3 mm, which is well below the ionosphere-freecarrier phase noise.

3.4. Maneuver handling

The TanDEM-X satellite performs pairs of thrusts inflight and anti-flight direction to maintain a predefined

relative eccentricity vector with respect to TerraSAR-X.The formation-keeping maneuvers are performed with80 mN cold-gas thrusters and impose a Dv of a few mm/sat a typical duration of about one minute. In addition,orbit-keeping maneuvers of several cm/s are performedabout once per week (depending on atmospheric condi-tions) with dedicated 1 N thrusters to maintain a specifiedrepeat ground-track (Kahle et al., 2011). Both types ofmaneuvers need to be considered in the operational orbitdetermination process to obtain continuous and accurateorbit and baseline products.

In the BSW and EPOS software, orbit maneuvers aretreated as a series of instantaneous velocity changes(pulses) at specified epochs in the radial, along-track, andout-of-plane direction. The epochs match known times atwhich the maneuvers were commanded. As part of thePOD and PBD process, respectively, the Dv’s in each axisare estimated for each maneuver as additional parametersin the least-squares adjustment.

Within the GHOST software, orbit maneuvers are trea-ted as constant thrust arcs of specified (known) burn starttime and duration and parameterized by a total velocityincrement in radial, along-track, and out-of-plane direc-tion. As part of the POD process for TerraSAR-X andTanDEM-X, the Dv’s in each axis are estimated for eachmaneuver with high precision in a least-squares adjust-ment. Within the subsequent baseline determination, thePOD estimate is used as a priori value when propagatingthe relative state between measurement epochs. Remainingdiscrepancies between the assumed and real thrust are com-pensated through supplementary process noise for the rel-ative position and velocity.

3.5. GPS satellite orbits and clocks

The final GPS orbits from the Center for Orbit Determi-nation in Europe (CODE, Dach et al., 2009) are used toprocess the ZD (all institutions), SD (DLR only), andDD (AIUB and GFZ with the BSW) GPS data from theTanDEM-X mission. High-rate GPS satellite clock correc-tions from CODE (Bock et al., 2009) are used for the ZDprocessing by all institutions. GFZ EPOS solutions arebased on an independent set of GPS orbits and clock cor-rections computed at GFZ.

4. Inter-agency comparisons

Reduced-dynamic ambiguity-fixed baseline solutions ofJanuary 2011 computed by the three agencies are comparedin this section. The AIUB and GFZ solutions are based onthe BSW, the DLR solutions are based on the GHOSTsoftware (see Sections 2.1–2.3). Days with orbit-keepingmaneuvers simultaneously performed on TerraSAR-Xand TanDEM-X (January 6, 19, 28) are excluded fromthe comparison. Section 4.1 presents the comparisons forthe nominal dual-frequency baseline solutions, single-fre-quency baseline solutions are compared in Section 4.2.

1 6 11 16 21 26 310

1

2

3

Rad

ial (

mm

)

1 6 11 16 21 26 310

1

2

3

Alo

ng−t

rack

(mm

)1 6 11 16 21 26 31

0

1

2

3

Out

-of-p

lane

(mm

)

January 2011

Fig. 1. Daily standard deviations of inter-agency dual-frequency baselinecomparisons. Empty bars indicate the statistics for entire 24 h arcs,colored bars exclude maneuver periods (in blue: GFZ-DLR, in green:GFZ-AIUB, in red: AIUB-DLR). (For interpretation of the references tocolor in this figure legend, the reader is referred to the web version of thisarticle.)

Table 3Median values (mm) of the daily standard deviations of dual-frequencybaseline comparisons without (with) considering maneuver intervals.

Comparison Radial Along-track Out-of-plane

GFZ – DLR 0.5 (0.7) 0.8 (1.4) 0.8 (0.9)GFZ – AIUB 0.4 (0.7) 0.9 (1.7) 1.0 (1.1)AIUB – DLR 0.5 (0.8) 0.9 (1.2) 1.0 (1.1)

A. Jaggi et al. / Advances in Space Research 50 (2012) 260–271 265

4.1. Dual-frequency solutions

Fig. 1 shows the daily standard deviations (STDs) of theinter-agency baseline comparisons based on L1(C) andL2(P) ionosphere-free GPS carrier phase observations.Empty bars indicate the statistics for the entire 24 h arcs(including maneuver periods) and characterize the capabil-ity of the three agencies to handle the frequent TanDEM-Xformation-keeping maneuvers, which occur in pairs ofburns separated by half of an orbital revolution. Filledbars, on the other hand, exclude time intervals for eachday starting 20 min before the first maneuver and ending20 min after the second maneuver, i.e., a total of about1.5 h of data is excluded, which allows consistency outsidethe maneuver periods to be assessed. Median values of thedaily STDs shown in Fig. 1 are provided in Table 3. Notethat the median values involving the AIUB solutions woulddegrade by at maximum 0.1 mm when using the gravityfield model EIGEN-2 (Reigber et al., 2003) from the pre-GRACE era for PBD at AIUB, i.e., the STDs reportedin Table 3 are still representative in the presence of signif-icant force mismodeling because of the estimation ofempirical orbit parameters.

Excluding maneuver time periods, Fig. 1 shows analmost constant consistency level between AIUB andDLR with STDs of about 0.5, 0.9, and 1.0 mm in theradial, along-track, and out-of-plane components, respec-tively. Apart from the out-of-plane component, the com-parisons between GFZ and the other agencies reveal aslightly larger variability for the radial and along-trackcomponent, e.g., about 0.24 instead of 0.09 mm variabilityfor the along-track component, but with almost identicaloverall STDs (see Table 3). The origin of the larger varia-tion is still under investigation. Fig. 1 (center) shows thatfor certain periods the along-track agreement betweenGFZ and DLR is excellent and stable with a STD of about0.6 mm, e.g., for mid January. The out-of-plane compari-son between AIUB and the other agencies shows an agree-ment of about 1 mm, which is caused by a prominent once-per-rev variability in the out-of-plane direction. The originof this variation has not yet been resolved. No effect of thiskind is seen between the GFZ and DLR baseline solutions,which show an agreement of about 0.8 mm.

When including maneuver time periods in the compari-son of the solutions, a significant increase of the STD (upto a factor of two over 24 h) can be observed for the base-line difference in the radial and along-track direction(Fig. 1, Table 3). The STD of the out-of-plane differencesand the mean bias in all axes, on the other hand, is hardlyaffected by the maneuver periods. Larger discrepancies areobserved, e.g., on 3 and 14 January due to the DLR andAIUB solution, respectively. In the latter case a ratherunfavorable occurrence of a formation-keeping maneuverjust 4 min after the beginning of the orbital arc is responsi-ble for the observed degradation.

Fig. 2 and Table 4 show biases of about 1 mm at maxi-mum between all agencies. Smallest biases of 0.1–0.2 mm

occur for the radial direction. Tight relative constraintsimposed on the empirical accelerations in the radial direc-tion ensure a similar leveling for all baseline solutions.Note that the median cross-track values involving theAIUB solutions would change by up to 2 mm when usingthe gravity field model EIGEN-2 for PBD at AIUB, i.e.,a consistent force modeling is rather a prerequisite to keepbiases between different solutions small than significantlyimproving the STDs. It should be mentioned, however,that no attempt was made to optimize the constraints ofthe empirical orbit parameters when using the gravity fieldmodel EIGEN-2.

Fig. 3 shows the daily STDs of baseline comparisonbetween AIUB and GFZ solutions, either computed in24 h batches using the BSW or 12 h batches using EPOS(see Section 2.3). Missing bars are due to the lack of EPOSsolutions for the respective days. Available EPOS solutionscurrently still show some larger differences to solutions

1 6 11 16 21 26 31

−2

−1

0

1

2

Rad

ial (

mm

)

1 6 11 16 21 26 31

−2

−1

0

1

2

Alo

ng−t

rack

(mm

)

1 6 11 16 21 26 31

−2

−1

0

1

2

Out

-of-p

lane

(m

m)

January 2011

Fig. 2. Daily mean biases of inter-agency dual-frequency baselinecomparisons, maneuver periods excluded (in blue: GFZ-DLR, in green:GFZ-AIUB, in red: AIUB-DLR). (For interpretation of the references tocolor in this figure legend, the reader is referred to the web version of thisarticle.)

Table 4Median values (mm) of the daily mean biases of dual-frequency baselinecomparisons without (with) considering maneuver periods.

Comparison Radial Along-track Out-of-plane

GFZ – DLR �0.2 (�0.2) �0.4 (�0.4) �0.4 (�0.4)GFZ – AIUB �0.1 (�0.1) �1.2 (�1.2) �1.1 (�1.1)AIUB – DLR �0.1 (�0.1) 0.7 (0.7) 0.7 (0.7)

1 6 11 16 21 26 310

1

2

3

Rad

ial (

mm

)

1 6 11 16 21 26 310

1

2

3

Alo

ng−t

rack

(mm

)

1 6 11 16 21 26 310

1

2

3

Out

-of-p

lane

(mm

)

January 2011

ig. 3. Daily standard deviations of baseline comparisons between AIUBnd GFZ solutions, maneuver periods excluded (in blue: EPOS 0–12 h, inreen: BSW, in red: EPOS 12–24 h). (For interpretation of the references

color in this figure legend, the reader is referred to the web version ofis article.)

0 5 10 15 20−6

−5

−4

−3

−2

−1

0

1

2

3

4

Hours of day

Rad

ial (

mm

)

L1(C) & L2(P)L1(P) & L2(P)

Fig. 4. Radial baseline differences between AIUB solutions and thesolution from DLR for 8 January using different dual-frequency carrierphase observations together with tightly constrained relative dynamics(solid lines, nominal case) or more relaxed (kinematic-like) relativedynamics (dotted lines).

266 A. Jaggi et al. / Advances in Space Research 50 (2012) 260–271

used for the inter-agency comparison (compare Fig. 1) dueto problems with ambiguity fixing lasting for about onerevolution of the satellites, concurrently with maneuversin many cases.

4.1.1. L1(C) and L2(P) vs. L1(P) and L2(P) solutionsFig. 4 shows radial baseline differences of AIUB solu-

tions based on different ionosphere-free GPS observables(see Section 3.2) for one particular day with respect tothe DLR solution. The AIUB solutions were computedfor both ionosphere-free GPS observables by either tightlyconstraining (nominal case, see Section 2.1) the empiricalaccelerations between the two satellites, or by not applyingthe relative constraints to the constant empirical accelera-tions acting over the entire orbital arc. Fig. 4 shows thatthe different handling of the relative constraints has no vis-ible impact on the leveling of the radial baseline componentwhen using L1(C) and L2(P) data, but clearly shifts thesolution in the radial direction by about 4 mm when usingthe L1(P) and L2(P) observables.

Fagtoth

Not applying relative constraints to the constant empir-ical accelerations corresponds to a kinematic-like definitionof the baseline datum by the GPS measurements only, i.e.,not by the satellite dynamics as is the case for nominal

Table 5Median values (mm) of the daily standard deviations of baselinecomparisons between kinematic and reduced-dynamic dual-frequencysolutions without considering maneuver periods.

Comparison Radial Along-track Out-of-plane

AIUB 8.2 3.4 2.4DLR 9.2 3.6 2.8AIUB (ZD PCV) 11.2 4.5 3.0

A. Jaggi et al. / Advances in Space Research 50 (2012) 260–271 267

processing. The fact that no radial shift is observed whenusing L1(C) and L2(P) is explained by using a set ofantenna and phase center offsets which is fully consistentwith L1(C) and L2(P). Any calibration mismatch betweenthe two satellites would induce a corresponding baselineshift when not adopting the relative constraining, evenwhen using L1(C) and L2(P) data.

The radial shift of the kinematic-like L1(P) and L2(P)solution observed in Fig. 4 is caused by systematic, eleva-tion-dependent differences between L1(C) and L1(P) car-rier phase data collected by the onboard IGOR receiversas shown in Fig. 5 for TerraSAR-X (left) and TanDEM-X (right). Whereas these differences cause only a relativelysmall systematic shift of about 1 mm in the radial directionfor TerraSAR-X POD (when realizing the orbit datumkinematic-like by the GPS measurements only), the shiftis about �4 mm for TanDEM-X. Thanks to the resolutionof the double difference carrier phase ambiguities to theirinteger values for PBD, only about 4 out of the total5 mm shift are eventually seen in the baseline comparisonin Fig. 4.

4.1.2. Comparisons involving kinematic solutions

While reduced-dynamic PBD offers some protectionfrom systematic and random carrier phase errors, the kine-matic baseline processing is much more sensitive. Table 5shows the median values of the daily STDs obtained fromdifferences between AIUB and DLR 10 s kinematic base-line solutions with respect to the same reduced-dynamicbaseline solution computed at AIUB. The STDs are

Antenna Frame

+x (Az=90)

+y (Az=0)

-x (A

z=27

0)

-y (Az=180)

90 60 30 0

-3.5 -3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5

Carrier Phase Diff. (mm)

Fig. 5. Direct differences between the L1(P) and L1(C) carrier phase observTerraSAR-X (left) and TanDEM-X (right).

significantly larger than those obtained from reduced-dynamic baseline comparisons (compare Table 3) due tothe lacking dynamical constraints, and amount up to about9, 4, and 3 mm for the radial, along-track, and out-of-planedirection, respectively. A careful modeling of the carrierphase data is thus of much greater importance for kine-matic baseline determination. The solution “AIUB (ZDPCV)” of Table 5 illustrates, e.g., that ZD patterns (itera-tively derived as part of the ZD POD process, see Sec-tion 3.1) are not able to compensate systematic carrierphase errors to the same extent as differential PCVs (estab-lished from DD ambiguity-fixed GPS data, see Section 3.1).The median values in Table 3 for the reduced-dynamicbaseline comparisons in Section 4.1 would, however, onlyimprove by at maximum 0.1 mm when using differentialPCVs.

4.2. Single-frequency solutions

Fig. 6 compares the daily STDs between AIUB andDLR baseline solutions based on L1(C) and L2(P)

Antenna Frame

+x (Az=90)

+y (Az=0)

-x (A

z=27

0)

-y (Az=180)

90 60 30 0

-1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

Carrier Phase Diff. (mm)

ations (quarter-cycle removed) collected by the IGOR receivers onboard

1 6 11 16 21 26 310

1

2

3

Rad

ial (

mm

)

1 6 11 16 21 26 310

1

2

3

Alo

ng−t

rack

(mm

)

1 6 11 16 21 26 310

1

2

3

Out

-of-p

lane

(mm

)

January 2011

Fig. 6. Daily standard deviations of baseline comparisons AIUB-DLR,maneuver periods excluded (in blue: L1(C) and L2(P), in green: L1(P) andL2(P), in red: L1(C)-only). (For interpretation of the references to color inthis figure legend, the reader is referred to the web version of this article.)

Table 6Median values (mm) of the daily standard deviations of dual- and single-frequency baseline comparisons between AIUB and DLR (maneuverperiods excluded).

Comparison Radial Along-track Out-of-plane

L1(C) and L2(P) 0.5 0.9 1.0L1(P) and L2(P) 0.5 0.9 0.9L1(C) 0.3 0.4 0.8

Table 7Median values (mm) of the daily mean biases of dual- and single-frequency baseline comparisons between AIUB and DLR (maneuverperiods excluded).

Comparison Radial Along-track Out-of-plane

L1(C) and L2(P) �0.1 0.7 0.7L1(P) and L2(P) 0.0 1.3 0.5L1(C) 0.2 0.3 �0.1

1 6 11 16 21 26 310

1

2

3R

adia

l (m

m)

1 6 11 16 21 26 310

1

2

3

Alo

ng−t

rack

(mm

)

1 6 11 16 21 26 310

1

2

3

Out

-of-p

lane

(mm

)

January 2011

Fig. 7. Daily standard deviations of inter-agency single-frequency baselinecomparisons. Empty bars indicate the statistics for entire 24 h arcs,colored bars exclude maneuver periods (in blue: GFZ-DLR, in green:GFZ-AIUB, in red: AIUB-DLR). (For interpretation of the references tocolor in this figure legend, the reader is referred to the web version of thisarticle.)

268 A. Jaggi et al. / Advances in Space Research 50 (2012) 260–271

dual-frequency data, L1(P) and L2(P) dual-frequency data,and L1(C) single-frequency data, respectively.

Table 6 shows that the agreement between the AIUBand DLR reduced-dynamic baselines is similar for bothtypes of ionosphere-free linear combinations with represen-tative STDs of about 0.5, 1.0, and 1.0 mm for the radial,along-track, and out-of-plane components, respectively.Apart from the out-of-plane component, which exhibits aprominent once-per-rev variability as already mentionedin Section 4.1, the agreement can be significantly improvedto STDs of 0.3 and 0.4 mm for the radial and along-trackcomponents when using single-frequency data. Despiteneglecting differential ionospheric path delays for theAIUB solutions, reduced-dynamic single-frequency base-line solutions benefit from a more robust ambiguity fixing(for most days 100% of the ambiguities could be fixed totheir integer values) and the smaller carrier phase noise.Table 7 shows that biases between AIUB and DLR base-line solutions are below 0.5 mm in each axis when process-ing single-frequency data.

Fig. 7 shows the daily STDs of the inter-agency baselinecomparisons based on L1(C) GPS carrier phase observa-tions. Similar to the dual-frequency results shown inFig. 1, an almost constant consistency level between AIUBand DLR can be seen in Fig. 7 with STDs of about 0.3, 0.4,and 0.8 mm in the radial, along-track, and out-of-planecomponents, respectively (see Table 6). Apart from the

out-of-plane component, the comparison between GFZand the other agencies reveal a larger variability for theradial and along-track component with slightly largerSTDs of 0.4 and 0.7 mm. Fig. 7 (center) shows that forthe mid January period (apart from 14 January, see Sec-tion 4.1) the agreement between all three agencies is excel-lent and stable with a STD of about 0.4 mm.

Table 8Median values (mm) of the daily standard deviations of baselinecomparisons between kinematic and reduced-dynamic single-frequencysolutions (maneuver periods excluded).

Comparison Radial Along-track Out-of-plane

AIUB 5.5 2.6 1.6DLR 3.9 1.6 1.4

A. Jaggi et al. / Advances in Space Research 50 (2012) 260–271 269

4.2.1. Comparisons involving kinematic solutions

Table 8 shows the median values of the daily STDsobtained from differences between AIUB and DLRL1(C)-only 10 s kinematic baseline solutions with respectto the same L1(C)-only reduced-dynamic baseline solutionfrom AIUB. The STDs are notably smaller for the DLRsolution than for the AIUB solution. Since remaining dif-ferential ionospheric path delays are not modeled for theAIUB solution, as opposed to the modeling applied forthe DLR solution (cf. Table 1), AIUB kinematic solutionsare degraded despite the rather short baseline of a few hun-dred meters only. Whereas such a mismodeling can be tol-erated for reduced-dynamic baseline determination due tothe additional dynamical constraints, it may cause occa-sional outliers of up to 1 cm in the AIUB kinematic solu-tion, apparent in Fig. 8 for 1 January.

Fig. 8 shows the impact of the clock-offset correctionand extrapolation of the raw TanDEM-X and Terra-SAR-X measurements to integer GPS seconds (see Sec-tion 3.2) when using them for single-frequency kinematicbaseline determination. Due to the much better simultane-ity achieved with the corrected GPS measurements whenforming single- and double-differences, respectively, a clearreduction of along-track errors is visible in the kinematicbaseline estimates. The impact on the overall daily STDis, however, not dramatic as this value is dominated bythe errors caused by the remaining differential ionospheric

0 5 10 15 20−30

−20

−10

0

10

20

30

Alo

ng−t

rack

(mm

)

Hours of day

original obs.interpolated obs.

Fig. 8. Along-track differences between AIUB kinematic and reduced-dynamic baselines for 1 January using original or corrected single-frequency carrier phase observations.

path delays. The radial and out-of-plane components arenot affected at all by the asynchronicities in the measure-ment epochs of the two receivers. Only a very small impactresults for reduced-dynamic baseline determination whenusing corrected GPS measurements.

5. Conclusions

An inter-agency comparison of dual-frequency and sin-gle-frequency baseline solutions of the TanDEM-X missionwas performed using different software packages (BSW,GHOST, EPOS) and analysis strategies. Dual-frequencyreduced-dynamic baseline solutions similar to those gener-ated in the operational processing at GFZ and DLR werecompared for a 1-month test period in January 2011 withsolutions generated on a best effort basis at AIUB. Differ-ences between reduced-dynamic baseline solutions arefound to exhibit a representative standard deviation(STD) of 1 mm outside maneuver periods, while biasesare below 1 mm in each direction. A significant degrada-tion of the STD of up to a factor of two is observed duringmaneuver periods. The achieved baseline determinationperformance is close to the mission specification, but inde-pendent SAR calibration data takes will be required tofully meet the 1 mm 1D RMS target. Care has to be takento use a set of phase center offsets which is fully consistentwith the carrier phase measurements. Biases of a few milli-meters may otherwise be introduced for kinematic-like def-initions of the baseline datum due to systematic differencesfound between the carrier phase measurements L1(C) andL1(P) on the first frequency. Besides the operational solu-tions, single-frequency baseline solutions were tested aswell. They benefit from a more robust ambiguity fixingand show a slightly better agreement of below 1 mmSTD, but are potentially affected by errors caused by anincomplete compensation of differential ionospheric pathdelays. Such a mismodeling can be tolerated for reduced-dynamic baseline determination due to the additionaldynamical constraints, but it may cause occasional outliersof up to 1 cm in kinematic baseline solutions. Asynchronic-ities of several microseconds in the measurement epochs ofthe two receivers were found to impact the along-trackcomponent of kinematic baseline solutions, but are lesscritical for reduced-dynamic baseline solutions.

Acknowledgements

The TanDEM-X project is implemented in a Public-Pri-vate Partnership (PPP) between the German AerospaceCenter (DLR) and Astrium GmbH. DLR is responsiblefor the scientific exploitation of the TanDEM-X data aswell as for the planning and implementation of the mission,the spacecraft control and the generation of the digital ele-vation model. Astrium built the satellite and shares in thecost of its development and exploitation. As with Terra-SAR-X, the responsibility for the commercial marketing

270 A. Jaggi et al. / Advances in Space Research 50 (2012) 260–271

of TanDEM-X data lies in the hands of Infoterra GmbH, asubsidiary of Astrium.

References

Altamimi, Z., Collilieux, X., Legrand, J., et al. ITRF2005: a new release ofthe International Terrestrial Reference Frame based on time series ofstation positions and Earth Orientation Parameters. J. Geophys. Res.112 (B9), 401–409, http://dx.doi.org/10.1029/2007JB004949, 2007.

Bock, H., Dach, R., Jaggi, A., et al. High-rate GPS clock corrections fromCODE: support of 1 Hz applications. J. Geod. 83 (11), 1083–1094,http://dx.doi.org/10.1007/s00190-009-0326-1, 2009.

Bock, H., Jaggi, A., Meyer, U., et al. GPS-derived orbits for the GOCEsatellite. J. Geod. 85 (11), 807–818, http://dx.doi.org/10.1007/s00190-011-0484-9, 2011.

Dach, R., Hugentobler, U., Fridez, P., et al. (Eds.). Bernese GPS SoftwareVersion 5.0. Documentation. Astronomical Institute University ofBern, Bern, 2007.

Dach, R., Brockmann, E., Schaer, S., et al. GNSS processing at CODE:status report. J. Geod. 83 (3–4), 353–365, http://dx.doi.org/10.1007/s00190-008-0281-2, 2009.

Freeman, A., Evans, D., Van Zyl, J.J. SAR applications in the 21stcentury. AEU – Int. J. Electron. Commun. 50, 79–84, 1996.

Forste, C., Schmidt, R., Stubenvoll, R., et al. The GeoForschungsZen-trum Potsdam/Groupe de Recherche de Geodesie Spatiale satellite-only and combined gravity field models: EIGEN-GL04S1 andEIGEN-GL04C. J. Geod. 82 (6), 331–346, http://dx.doi.org/10.1007/s00190-007-0183-8, 2008a.

Forste, C., Flechtner, F., Schmidt, R., et al. EIGEN-GL05C – a newglobal combined high-resolution GRACE-based gravity field model ofthe GFZ-GRGS cooperation. Geophys. Res. Abstr. 10, EGU2008–A-03426, 2008b.

Gill, E. Smooth bi-polynomial interpolation of Jacchia 1971 atmosphericdensities for efficient satellite drag computation. DLR-GSOC IB 96-1,Deutsches Zentrum fur Luft und Raumfahrt, Oberpfaffenhofen,Germany, 1996.

Jaggi, A., Hugentobler, U., Beutler, G. Pseudo-stochastic orbit modelingtechniques for low-Earth orbiters. J. Geod. 80 (1), 47–60, http://dx.doi.org/10.1007/s00190-006-0029-9, 2006.

Jaggi, A., Hugentobler, U., Bock, H., et al. Precise orbit determination forGRACE using undifferenced or doubly differenced GPS data. Adv.Space Res. 39 (10), 1612–1619, http://dx.doi.org/10.1016/j.asr.2007.03.012, 2007.

Jaggi, A., Beutler, G., Prange, L., et al. Assessment of GPS-onlyobservables for gravity field recovery from GRACE, in: Sideris,M.G. (Ed.), Observing our Changing Earth. IAG Symposia, vol. 133,pp. 113–123, http://dx.doi.org/10.1007/978-3-540-85426-5_14, 2009a.

Jaggi, A., Dach, R., Montenbruck, O., et al. Phase center modeling forLEO GPS receiver antennas and its impact on precise orbit determi-nation. J. Geod. 83 (12), 1145–1162, http://dx.doi.org/10.1007/s00190-009-0333-2, 2009b.

Jaggi, A., Bock, H., Prange, L., et al. GPS-only gravity field recovery withGOCE, CHAMP, and GRACE. Adv. Space Res. 47 (6), 1020–1028,http://dx.doi.org/10.1016/j.asr.2010.11.008, 2011.

Kahle, R., Kazeminejad, B., Kirschner, M., et al. First in-orbit experienceof TerraSAR-X flight dynamics operations, in: 20th InternationalSymposium on Space Flight Dynamics, 24–28 September, Annapolis,USA, 2007.

Kahle, R., Schlepp, B., Kirschner, M. TerraSAR-X/TanDEM-X forma-tion control – first results from commissioning and routine operations.J. Aerospace Eng., Sci. Appl. 3 (2), 16–27, 22nd InternationalSymposium on Spaceflight Dynamics, 28 February–4 March, SaoJose dos Campos, Brazil, 2011.

Koop, R., Gruber, T., Rummel, R. The status of the GOCE high-levelprocessing facility, in: Proceedings of the 3rd GOCE User Workshop,Frascati, Italy. ESA SP-627, pp. 195–205, 2006.

Krieger, G., Moreira, A., Fiedler, H., et al. TanDEM-X: a satelliteformation for high-resolution SAR interferometry. IEEE Trans.Geosci. Remote Sens. 45 (11), 3317–3341, http://dx.doi.org/10.1109/TGRS.2007.900693, 2007.

Krieger, G., Hajnsek, I., Papathanassiou, K., et al. Interferometricsynthetic aperture radar (SAR) missions employing formation flying.Proc. IEEE 98 (5), 816–843, http://dx.doi.org/10.1109/JPROC.2009.2038948, 2010.

Kroes, R., Montenbruck, O., Bertiger, W., et al. Precise GRACE baselinedetermination using GPS. GPS Solut. 9, 21–31, http://dx.doi.org/10.1007/s10291-004-0123-5, 2005.

Kroes, R. Precise Relative Positioning of Formation Flying Spacecraftusing GPS. Ph.D. Thesis. TU Delft, 2006.

McCarthy, D.D. IERS Technical note no. 21. Central Bureau of IERS,Observatoire de Paris, France, 1996.

McCarthy, D.D., Petit, G. IERS Conventions 2003. IERS Technical noteno. 32. Bundesamt fur Kartographie und Geodasie, Frankfurt amMain, Germany, 2004.

Montenbruck, O., Garcia-Fernandez, M., Williams, J. Performancecomparison of semi-codeless GPS receivers for LEO satellites. GPSSolut. 10, 249–261, http://dx.doi.org/10.1007/s10291-006-0025-9,2006.

Montenbruck, O., Kahle, R., D’Amico, S., et al. Navigation and controlof the TanDEM-X formation. J. Astronaut. Sci. 56 (3), 341–357, 2008.

Montenbruck, O., Garcia-Fernandez, M., Yoon, Y., et al. Antenna phasecenter calibration for precise positioning of LEO satellites. GPS Solut.13 (1), 23–34, http://dx.doi.org/10.1007/s10291-008-0094-z, 2009.

Montenbruck, O., Wermuth, M., Kahle, R. GPS based relative navigationfor the TanDEM-X mission – first flight results, in: Proceedings of the23rd International Technical Meeting of The Satellite Division of theInstitute of Navigation (ION GNSS 2010), Portland, USA, pp. 2797–2807, 2010.

Montenbruck, O., D’Amico, S., Ardaens, J.-S., et al., 2011. Carrier phasedifferential GPS for LEO formation flying – the PRISMA andTanDEM-X flight experience, in: AAS Astrodynamics SpecialistConference, 31 July–4 August, Girdwood, USA. AAS 11-489, 2011.

Reigber, C., Schwintzer, P., Neumayer, K.H., et al. The CHAMP-onlyearth gravity field model EIGEN-2. Adv. Space Res. 31 (8), 1883–1888, http://dx.doi.org/10.1016/S0273-1177(03)00162-5, 2003.

Rothacher, M., Tapley, B.D., Reigber, C., et al. The Tracking, occultationand ranging (TOR) instrument onboard TerraSAR-X and on Tan-DEM-X, in: IEEE International Geoscience and Remote SensingSymposium (IGARSS), pp. 4983–4986, http://dx.doi.org/10.1109/IGARSS.2007.4423980, 2007.

Schmid, R., Steigenberger, P., Gendt, G., et al. Generation of a consistentabsolute phase center correction model for GPS receiver and satelliteantennas. J. Geod. 81 (12), 781–798, http://dx.doi.org/10.1007/s00190-007-0148-y, 2007.

Standish, E.M. The observational basis for JPL’s DE200 the planetaryephemerides of the astronomical almanac. Astron. Astrophys. 233,252–271, 1990.

Standish, E.M. JPL Planetary and Lunar Ephemerides, DE405/LE405.JPL IOM 312.F-98-048, 1998.

TanDEM-X Mission Requirements Document, TDX-PD-RS-0001, Issue1.1, Deutsches Zentrum fur Luft und Raumfahrt, Oberpfaffenhofen,Germany, 2007.

Tapley, B.D., Bettadpur, S., Watkins, M.M., et al. The gravity recoveryand climate experiment: mission overview and early results. Geophys.Res. Lett. 31, L09607, http://dx.doi.org/10.1029/2004GL019920,2004a.

Tapley, B.D., Bettadpur, S., Ries, J.C., et al. GRACE measurements ofmass variability in the Earth system. Science 305 (5683), 503–505,http://dx.doi.org/10.1126/science.1099192, 2004b.

Teunissen, P.J.G. The least squares ambiguity decorrelation adjustment:a method for fast GPS integer ambiguity rounding and bootstrap-ping. J. Geod. 70 (1–2), 65–82, http://dx.doi.org/10.1007/ BF00863419, 1995.

A. Jaggi et al. / Advances in Space Research 50 (2012) 260–271 271

UT/CSR Ocean Tide Models. University of Texas, Center for SpaceResearch, Austin, Texas. <ftp://ftp.csr.utexas.edu/pub/tide/oldfiles/spharm_schwid+>, 1995.

UT/CSR Ocean Tide Models. University of Texas, Center for SpaceResearch, Austin, Texas. <ftp://ftp.csr.utexas.edu/pub/tide/OTIDES.-TOPEX_3.0>, 1997.

UT/CSR ocean tide models, University of Texas, Center for SpaceResearch, Austin, Texas. <ftp://ftp.csr.utexas.edu/pub/grav/OTI-DES.TOPEX_3.0>, 2001.

Wermuth, M., Montenbruck, O., van Helleputte, T. GPS high precisionorbit determination software tools (GHOST), in: Proceedings of the

4th International Conference on Astrodynamics Tools and Tech-niques, Madrid, Spain.WPP-308, 2010.

Wermuth, M., Montenbruck, O., Wendleder, A. Relative navigation forthe TanDEM-X mission and evaluation with DEM calibration results,in: Proceedings of the 22nd International Symposium on SpaceflightDynamics, 28 February–4 March, Sao Jose dos Campos, Brazil, 2011.

Zhu, S., Reigber, C., Koenig, R. Integrated adjustment of CHAMP,GRACE, and GPS data. J. Geod. 78 (1–2), 103–108, http://dx.doi.org/10.1007/s00190-004-0379-0, 2004.