Andreas Kohlhase 1 , Remco Kroes 2 , Simone D‘Amico 1 , Michael Eineder 3

1. Evaluating interferometric baseline performances in a close SAR formation flight by using relative GRACE GPS navigation solutions Andreas Kohlhase1, Remco Kroes2, Simone D‘Amico1, Michael Eineder3 1German Space Operations Center, DLR Oberpfaffenhofen, Germany 2Department of Earth Observation and Space Systems, TU Delft, Netherlands 3Remote Sensing Technology Institute, DLR Oberpfaffenhofen, Germany e-mail: andreas.kohlhase@dlr.de FRINGE 2005 Workshop, ESA ESRIN 28 Nov – 3 Dec 2005, Frascati, Italy

2. Background and motivation • Usefulness of dual-frequency GPS receivers for highly accurate post-facto relative positioning of formation flying satellites has been demonstrated in recent studies • For future formation flying satellite missions, high-precise distance/baseline determination will be essential to satisfy scientific mission requirements (especially of multistatic SAR missions) • Detailed analysis of the specific performance under rapidly changing (multistatic) baseline conditions is still required → achievable accuracy changes for different baseline determination strategies • Use of real GPS navigation solutions from the Gravity Recovery And Climate Experiment mission (GRACE) • to estimate baseline errors for different interferometric scenarios • availability of the KBR link as a unique operation for validating DGPS solutions • realistic accuracy estimates can be derived (no S/W and H/W-in-the-loop sim.) • the first mission with twin satellites flying in formation FRINGE 2005 Workshop, ESA ESRIN 28 Nov – 3 Dec 2005, Frascati, Italy

3. Requirements and basic assumptions • Definition of three InSAR scenarios with 2 satellites flying in formation • bistatic acquisition mode: S/C A (t0), S/C B (t0) • Monostatic acquisition mode with an along-track offset: S/C A (t0+Δt), S/C B (t0) • Repeat-pass scenario as an add-on case: S/C A (t1), S/C A (t2) • Derivation of (relative) height errors to evaluate the baseline performance of the 2 single-pass scenarios w.r.t. the DTED-3 requirement: |1σ| < 1 m in case of no tie point availability • Interferometric phase errors can be modeled to separate the baseline from the purely phase noise induced height bias • Prediction of relative motion to have an a priori information of the baseline vector → Choosing initial orbital elements of both satellites in such a way that the characteristic Helix rotation is obtained FRINGE 2005 Workshop, ESA ESRIN 28 Nov – 3 Dec 2005, Frascati, Italy

4. Performances of baseline determination strategies (I) • Dual frequency GPS receivers are required for high accurate relative positioning - to correct for 1st order ionospheric delays - to resolve integer Double Difference (DD) carrier phase ambiguities (|B| > 1 km) • Measured distance ρKBRwith a noise level (εKBR) of 10 µm is used to validate the relative positioning vector Δr along the track • A 24h-KBR fit for 2003 DOY 215 reveals a standard deviation of σT = ± 1.03 mm Comparison of the relative orbit solutions for GRACE A & B using an 11-day data arc (level 1B, 2003 DOY 210 – 220) FRINGE 2005 Workshop, ESA ESRIN 28 Nov – 3 Dec 2005, Frascati, Italy

5. Performances of baseline determination strategies (II) Comparison of absolute JPL and DLR POD solutions for GRACE A & B using an 11-day GPS data arc (2003 DOY 210 – 220) Repeat-pass case: Bistatic case: Monostatic case with an along-track offset: FRINGE 2005 Workshop, ESA ESRIN 28 Nov – 3 Dec 2005, Frascati, Italy

6. Performance analysis • A prioriperformance estimation using the worst case |σB| = 1,7 mm, a mean H = 520 km and assuming a flat terrain (i = θp) • Height accuracy as function of dynamic baseline size (B, α) and radar look angle θp • Height accuracy is very sensitive in flight direction due to the dynamic baseline - accuracy requirement is not fulfilled for all baseline constellations - importance for mission planning FRINGE 2005 Workshop, ESA ESRIN 28 Nov – 3 Dec 2005, Frascati, Italy

7. Orbit 2 reference InterferogramSimulation Φ1(rg, az) Orbit 1 Difference & Color Coding DEM InterferogramSimulation Φ2(rg, az) DifferencedInterferogramΔΦ(rg, az) Orbit 2 with Errors Simulation results • Simulating the residual Orbital Phase Screen (OPS) by differencing 2 simulated X-band interferograms (λ = 3.1 cm) calculated from 3 orbit estimates Simulation of the interferometric phase Φ in case of a monostatic single-pass acquisition FRINGE 2005 Workshop, ESA ESRIN 28 Nov – 3 Dec 2005, Frascati, Italy

8. Δh=1035*0.05/2pi=8.2 m 30 km 152 km ~ 20 s Az NR FR Rg Simulation results (II) • Real GRACE DGPS noise (σ≈ ± 1.4 mm) • B = 10 m, Beff = 5.64 m, H = 514 km • ha = 1035 m at mid-swath i = 36.2° x 10 FRINGE 2005 Workshop, ESA ESRIN 28 Nov – 3 Dec 2005, Frascati, Italy

9. Az Rg Simulation results (III) • Real GRACE absolute GPS noise (σ≈ ± 4.3 cm) • B = 10 m, Beff = 5.64 m, H = 514 km • ha = 1035 m at mid-swath i = 36.2° x 10 NR FR FRINGE 2005 Workshop, ESA ESRIN 28 Nov – 3 Dec 2005, Frascati, Italy

10. Az Rg Simulation results (IV) • Simulated (Gaussian) noise (σ≈ ± 1 mm) • B = 10 m, Beff = 5.64 m, H = 514 km • ha = 1035 m at mid-swath i = 36.2° Δh=1035*1.0/2pi=164 m x 10 NR FR FRINGE 2005 Workshop, ESA ESRIN 28 Nov – 3 Dec 2005, Frascati, Italy

11. Acknowledgment Investigation has mainly been carried out in the framework of research fellowship awarded by the German Research Establishment (DFG) Main conclusions and acknowledgment • Baseline performance in a single-pass SAR formation flight fulfills the DTED-3 height accuracy requirement for most of the baseline constellations if dual-frequency GPSreceivers are used for relative navigation onboard the SAR satellites • Classical repeat-pass interferometry (for long-term D-InSAR) still requires new orbital/baseline tuning approaches → improvement of absolute accuracy • Scaling the generated DEMs against existing ones (SRTM) or against tie points may also help to perform baseline optimization und thus to conduct terrain height corrections • A further analysis could clarify the propagation of the total 3-D baseline vector to the height and horizontal circular bias FRINGE 2005 Workshop, ESA ESRIN 28 Nov – 3 Dec 2005, Frascati, Italy