Ralph Kahle

The effectiveness of swath and Doppler spectrum reconstruction algorithms in cross-track and along-track multistatic synthetic aperture radar (SAR) formations heavily relies on the precise relative positioning of each spacecraft. Ideally, a static array configuration is desired, where the satellites are evenly distributed in an Earth-fixed frame. However, maintaining this ideal configuration is not feasible without constant active flight control to counter the satellites’ relative dynamics. Alternatively, one can design natural trajectories that result in the desired formation geometry within an acceptable margin for a significant fraction of the orbital period. In this paper, we present a relative motion description in an Earth-fixed geometry for distributed SAR concepts. We derive a general expression for the transformation matrix from the Hill-Clohessy-Wiltshire (HCW) frame to the SAR-appropriate zero-Doppler (ZD) frame, and propose a general optimization method to fit the best natural non-drifting formation solution for any desired formation configuration. By applying the developed technique to optimize along-track and cross-track relative positioning requirements, we obtain conforming baselines over extended orbit stretches. We present SAR imaging examples for along-track distributed formations and formations with small cross-track baselines, using distributed platforms spanning a 72° latitude range. The demonstrated configurations achieve orbit duty cycles exceeding 20%, with baseline errors kept below 5% relative to the ideal array element positions. These results indicate the feasibility of these concepts using natural orbit solutions.

This paper introduces a versatile approach for computing the risk of collision specifically tailored for scenarios featuring low relative encounter velocities, but with potential applicability across a wide range of situations. The technique employs Differential Algebra (DA) to express the non-linear dynamical flow of the initial distribution in the primary-secondary objects relative motion through high-order Taylor polynomials. The entire initial uncertainty set is subdivided into subsets through Automatic Domain Splitting (ADS) techniques to control the accuracy of the Taylor expansions. The methodology samples the initial conditions of the relative state and evaluates the polynomial expansions for each sample while retaining their temporal dependency. The classical numerical integration of the initial statistics over the set of conditions for which a collision occurs is thus reduced to an evaluation of mono-dimensional time polynomials. Specifically, samples reaching a relative distance below a critical value are identified along with the time at which this occurs. The approach is tested against a Monte Carlo (MC) simulation for various literature test cases, yielding accurate results and a consistent gain in computational time.

On Juni 21, 2010 the still unique TanDEM-X mission was launched and opened a new era in spaceborne radar remote sensing. The first formation flying radar system was built by extending the TerraSAR-X synthetic aperture radar (SAR) mission by a second, TerraSAR-X-like satellite TanDEM-X. The resulting large single-pass SAR interferometer features flexible baseline selection enabling the acquisition of highly accurate cross-track interferograms. The primary objective was the generation of a global Digital Elevation Model (DEM) with unprecedented accuracy (12 m horizontal resolution and 2 m relative height accuracy). While the main mission phase for DEM data acquisition has been finished in 2014, the processing of the global TanDEM-X DEM was concluded in September 2016. The final DEM is well within specifications and features an extremely low percentage of void areas. The scientific exploitation of TanDEM-X is not limited to the DEM and the unique capabilities enable numerous secondary mission objectives based on along-track interfero-metry as well as new bistatic and multistatic SAR techniques. Comparisons of the TanDEM-X DEM with SRTM [1] or of multi-temporal TanDEM-X data revealed dramatic changes and the high dynamic in the Earth's topography. It has been therefore decided to acquire data for a global change layer and the so-called change DEM will become available in 2021. Despite being well beyond their design lifetime, both satellites are still fully functional and have enough consumables for several additional years. Therefore, bistatic operations continue with a focus on changes in the cryosphere and biosphere.

The satellite of the TerraSAR-X mission, called TSX, was launched on 15 June 2007 and its identically constructed twin satellite TDX, which is required by the mission TanDEM-X, launched on 21 June 2010. Together they supply high-quality radar data in order to serve two mission goals: Scientific observation of Earth and the provisioning of remote sensing data for the commercial market (TerraSAR-X mission) and the generation of a global digital elevation model (DEM) of Earth’s surface (TanDEM-X mission). On the occasion of the 10th anniversary of the mission, the focus will be on the development of the TerraSAR-X system during this period, including the extension of the ground segment, the evolution of the product portfolio, dedicated mission campaigns, radar experiments, refinement of the satellite operations and orbit control, and the results of the performance monitoring. Despite numerous interventions in the overall system, we managed to incorporate new scientific and commercial requirements and to improve and enhance the overall system in order to fulfill the increasing demand for Earth observation data without noticeable interruptions to ongoing operations.

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.

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 analyze 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 10x10x34 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.