Ralph Kahle

Navigation and control of the TanDEM-X formation

Germany is presently preparing the first operational formation flying mission for Synthetic Aperture Radar (SAR) interferometry in low-Earth orbit. TanDEM-X comprises two nearly identical satellites (TSX and TDX) that are launched with a two-year time shift in 2007 and 2009, respectively. From 2009 onwards, the two satellites will fly in close proximity and collect SAR interferograms for digital elevation model (DEM) generation. The TanDEM-X mission profile is particularly challenging from a flight dynamics point of view and poses new needs for spacecraft navigation and control. These comprise the formation design, the ground-controlled and autonomous formation maintenance, as well as the highprecision reconstruction of the interferometric baseline. This paper discusses the geometry of the TanDEM-X formation along with a relative motion model that forms the basis of the formation control concept and the autonomous onboard navigation. Furthermore, the orbit control and precise orbit determination of the primary spacecraft TSX is illustrated using actual flight data from the first six months of operations.

Quality Assessment of Surface Current Fields From TerraSAR-X and TanDEM-X Along-Track Interferometry and Doppler Centroid Analysis

All existing examples of current measurements by spaceborne synthetic aperture radar (SAR) along-track (AT) interferometry (ATI) have suffered from short baselines and corresponding low sensitivities. Theoretically, the best data quality at X-band is expected at effective baselines on the order of 30 m, i.e., 30 times as long as the baselines of the divided-antenna modes of TerraSAR-X. In early 2012, we had a first opportunity to obtain data at near-optimum baselines from the TanDEM-X satellite formation. In this paper, we analyze two TanDEM-X interferograms acquired over the Pentland Firth (Scotland) with effective AT baselines of 25 and 40 m. For comparison, we consider a TerraSAR-X dual-receive-antenna (DRA)-mode interferogram with an effective baseline of 1.15 m, as well as velocity fields obtained by Doppler centroid analysis (DCA) of single-antenna data from the same three scenes. We show that currents derived from the TanDEM-X interferograms have a residual noise level of 0.1 m/s at an effective resolution of about 33 m × 33 m, while DRA-mode data must be averaged over 1000 m × 1000 m to reach the same level of accuracy. A comparison with reference currents from a 1-km resolution numerical tide computation system shows good agreement in all three cases. The DCA-based currents are found to be less accurate than the ATI-based ones but close to short-baseline ATI results in quality. We conclude that DCA is a considerable alternative to divided-antenna mode ATI, while our TanDEM-X results demonstrate the true potential of the ATI technique at near-optimum baselines.

The joint TerraSAR-X / TanDEM-X ground segment

This paper recalls the essential elements of the joint TerraSAR-X and TanDEM-X ground segment. It elaborates on some topics which are usually not in the primary focus from a pure SAR technical point of view, e.g. the flight formation. Both commissioning and early routine phase results from operating the joint TerraSAR-X and TanDEM-X ground segment are given.

Verification of the Total Zero Doppler Steering

In 2004, the total zero Doppler steering was proposed to minimize the Doppler centroid for SAR applications. It was firstly implemented in the German TerraSAR-X satellite. This satellite was launched May 2007. With the already analysed data, it is now possible to compare the predictions with the already taken data from the commissioning phase. It is shown that after an additional offset in the attitude control system of the satellite, the remaining Doppler centroid is well below 100 Hz as predicted.

Relative Navigation to Non-cooperative Targets in LEO: Achievable Accuracy from Radar Tracking Measurements

Any future space debris removal or on-orbit servicing mission faces the problem of the initial relative orbit determination of the servicing satellite to the non-cooperative target. In this work, we analyse the relative navigation accuracy that can be achieved in low Earth orbit, by using ground-based orbit determination from radar tracking measurements for the target, and classical GPS-based orbit determination for the servicing satellite. The analysis is based on the radar tracking measurements obtained from a 10 × 10 × 34 cm small object at an altitude of 635 km. The results show that the relative orbit can be determined with accuracy down to 2 m (RMS) in the semi-major axis, and down to 20 m (RMS) in both the radial and normal separations. From the results, we derive requirements on radar-tracking campaigns.

Flight Dynamics Operations of the TanDEM-X Formation

Since end of 2010 the German TerraSAR-X and TanDEM-X satellites are routinely operated as the first configurable single-pass Synthetic Aperture Radar interferometer in space. The two 1340 kg satellites fly in a 514 km sun-synchronous orbit. In order to collect sufficient measurements for the generation of a global digital elevation model and to demonstrate new interferometric SAR techniques and applications, more than three years of formation flying are foreseen with flexible baselines ranging from 150 m to few kilometers. As a prerequisite for the close formation flight an extensive flight dynamics system was established at DLR/GSOC, which comprises of GPS-based absolute and relative navigation and impulsive orbit and formation control. Daily formation maintenance maneuvers are performed by TanDEM-X to counterbalance natural and artificial disturbances. The paper elaborates on the routine flight dynamics operations and its interactions with mission planning and ground-station network. The navigation and formation control concepts and the achieved control accuracy are briefly outlined. Furthermore, the paper addresses non-routine operations experienced during formation acquisition, frequent formation reconfiguration, formation maintenance problems and space debris collision avoidance, which is even more challenging than for single-satellite operations. In particular two close approaches of debris are presented, which were experienced in March 2011 and April 2012. Finally, a formation break-up procedure is discussed which could be executed in case of severe onboard failures.

In-flight performance validation of the TanDEM-X autonomous formation flying system

The in-flight performance validation of the experimental autonomous formation keeping system embarked by the German TanDEM-X formation has been performed during a 12-day-long closed-loop campaign conducted in June 2012. Relative control performance better than 10 m was achieved, demonstrating that a significant gain of performance can be achieved when the control of the formation is done autonomously on-board instead of on-ground. Furthermore, the formation keeping system was shown to be operationally robust, easy to operate and fully predictable, i.e., fully suited for routine mission operations. This campaign concludes successfully a series of validation activities, opening new doors to future innovative scientific TanDEM-X experiments for which enhanced formation control is required.

Reversal of TanDEM-X’s Relative Motion from Counter-Clockwise to Clockwise

TerraSAR-X and TanDEM-X were launched in 2007 and 2010 in a polar low Earth orbit for the purpose of Earth Observation with Synthetic Aperture Radar. Both satellites fly in a sun-synchronous dusk-dawn orbit at a mean altitude of 514km. Main incentive of the combined mission is the generation of a digital elevation model with unprecedented accuracy on global scale of the Earth’s land surface. For retrieval of 3D data the payloads on both spacecraft are operated since end of 2010 in a combined, so-called bi-static mode, requiring close spatial proximity of TerraSAR-X and TanDEM-X for payload synchronization reasons. TerraSAR-X is maintained on a stringent reference orbit with an eleven day repeat cycle whereas TanDEM-X describes a close helix around TerraSAR-X. Typical inter-satellite distances range from 150 m to several hundreds of meters. The spacecraft are mainly separated horizontally at the equator crossings and mainly radially over polar region. The relative motion is accomplished by means of slightly differing inclination and eccentricity vectors. During the first three years TanDEM-X had been orbiting in counter clockwise motion (as seen in flight direction) around TerraSAR-X. In August 2013 the relative motion was inverted to a clockwise motion, which is referred to as swap. This campaign opened up the possibility for ground target scanning from the opposite point of view as compared to images acquired in the pre-swap phase. In general, 3D radar imagery requires a differing perspective of TerraSAR-X and TanDEM-X on the ground target. Since TanDEM-X is once orbiting around TerraSAR-X in the course of an Earth orbit, the difference in the perspective, the radar baseline, depends on the argument of latitude. Thus, two of four quarters of an orbit, the ones with most distinct baseline, are well suited for 3D imagery. Until August 2013 bi-static data taking was restricted to northern hemisphere targets in ascending orbit parts whereas southern hemisphere targets have been scanned in descending orbit fractions. Inverting the relative motion opens up the possibility to gain complementary datasets from northern hemisphere targets in now descending orbits and southern hemisphere targets in ascending orbits. Especially in mountainous regions this additional information is mandatory for the generation of the digital elevation model in order to compensate radar shadow and layover effects. This paper focuses on the practical implementation of the swap campaign. The maneuver sequence and the transition from original to final formation are presented in graphical form. The operations concepts with special emphasis on safety aspects that are of paramount importance at such close distance are detailed. Additionally, space craft configuration steps required for post-swap payload operations are described.

Verification of the TerraSAR-X system

The paper discusses the areas covered by the TerraSAR-X Calibration/Verification-Plan. By means of a commissioning phase planning tool the data take requests required for characterization, calibration and verification are sequentially arranged. The status of the individual data takes is tracked from request planning to the final image analysis. All data take requests and results are supervised and summarized in a so-called verification matrix. In the end the paper gives an overview about the commissioning phase schedule and the repeat cycle based planning.

Solar Sailing Kinetic Energy Impactor (KEI) Mission Design Tradeos for Impacting and Deflecting Asteroid 99942 Apophis

Near-Earth asteroid 99942 Apophis provides a typical example for the evolution of asteroid orbits that lead to Earth-impacts after a close Earth-encounter that results in a resonant return. Apophis will have a close Earth-encounter in 2029 with potential very close subsequent Earth-encounters (or even an impact) in 2036 or later, depending on whether it passes through one of several so-called gravitational keyholes during its 2029encounter. Several pre-2029-deflection scenarios to prevent Apophis from doing this have been investigated so far. Because the keyholes are less than 1 km in size, a pre-2029 kinetic impact is clearly the best option because it requires only a small change in Apophis’ orbit to nudge it out of a keyhole. A single solar sail Kinetic Energy Impactor (KEI) spacecraft that impacts Apophis from a retrograde trajectory with a very high relative velocity (7580 km/s) during one of its perihelion passages at about 0.75 AU would be a feasible option to do this. The spacecraft consists of a 160 m ◊ 160 m, 168 kg solar sail assembly and a 150 kg impactor. Although conventional spacecraft can also achieve the required minimum deflection of 1 km for this approx. 320 m-sized object from a prograde trajectory, our solar sail KEI concept also allows the deflection of larger objects. In this paper, we also show that, even after Apophis has flown through one of the gravitational keyholes in 2029, solar sail Kinetic Energy Impactor (KEI) spacecraft are still a feasible option to prevent Apophis from impacting the Earth, but many KEIs would be required for consecutive impacts to increase the total Earth-miss distance to a safe value. In this paper, we elaborate potential pre- and post-2029 KEI impact scenarios for a launch in 2020, and investigate tradeos between dierent mission parameters.