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

Development of the TanDEM-X Calibration Concept: Analysis of Systematic Errors

The TanDEM-X mission, result of the partnership between the German Aerospace Center (DLR) and Astrium GmbH, opens a new era in spaceborne radar remote sensing. The first bistatic satellite synthetic aperture radar mission is formed by flying the TanDEM-X and TerraSAR-X in a closely controlled helix formation. The primary mission goal is the derivation of a high-precision global digital elevation model (DEM) according to High-Resolution Terrain Information (HRTI) level 3 accuracy. The finite precision of the baseline knowledge and uncompensated radar instrument drifts introduce errors that may compromise the height accuracy requirements. By means of a DEM calibration, which uses absolute height references, and the information provided by adjacent interferogram overlaps, these height errors can be minimized. This paper summarizes the exhaustive studies of the nature of the residual-error sources that have been carried out during the development of the DEM calibration concept. Models for these errors are set up and simulations of the resulting DEM height error for different scenarios provide the basis for the development of a successful DEM calibration strategy for the TanDEM-X mission

Phase center modeling for LEO GPS receiver antennas and its impact on precise orbit determination

Most satellites in a low-Earth orbit (LEO) with demanding requirements on precise orbit determination (POD) are equipped with on-board receivers to collect the observations from Global Navigation Satellite systems (GNSS), such as the Global Positioning System (GPS). Limiting factors for LEO POD are nowadays mainly encountered with the modeling of the carrier phase observations, where a precise knowledge of the phase center location of the GNSS antennas is a prerequisite for high-precision orbit analyses. Since 5 November 2006 (GPS week 1400), absolute instead of relative values for the phase center location of GNSS receiver and transmitter antennas are adopted in the processing standards of the International GNSS Service (IGS). The absolute phase center modeling is based on robot calibrations for a number of terrestrial receiver antennas, whereas compatible antenna models were subsequently derived for the remaining terrestrial receiver antennas by conversion (from relative corrections), and for the GNSS transmitter antennas by estimation. However, consistent receiver antenna models for space missions such as GRACE and TerraSAR-X, which are equipped with non-geodetic receiver antennas, are only available since a short time from robot calibrations. We use GPS data of the aforementioned LEOs of the year 2007 together with the absolute antenna modeling to assess the presently achieved accuracy from state-of-the-art reduced-dynamic LEO POD strategies for absolute and relative navigation. Near-field multipath and cross-talk with active GPS occultation antennas turn out to be important and significant sources for systematic carrier phase measurement errors that are encountered in the actual spacecraft environments. We assess different methodologies for the in-flight determination of empirical phase pattern corrections for LEO receiver antennas and discuss their impact on POD. By means of independent K-band measurements, we show that zero-difference GRACE orbits can be significantly improved from about 10 to 6mm K-band standard deviation when taking empirical phase corrections into account, and assess the impact of the corrections on precise baseline estimates and further applications such as gravity field recovery from kinematic LEO position

Satellite Formation-Flying and Rendezvous

GNSS has come to play an increasingly important role in satellite formation-flying and rendezvous applications. In the last decades, the use of GNSS measurements has provided the primary technique for determining the relative position of cooperative co-orbiting satellites in low Earth orbit

GPS-Based Precision Baseline Reconstruction for the TanDEM-X SAR-Formation

The TanDEM-X formation employs two separate spacecraft to collect interferometric Synthetic Aperture Radar (SAR) measurements over baselines of about 1 km. These will allow the generation ofa global Digital Elevation Model (DEM) with an relative vertical accuracy of 2-4 m and a 10 m ground resolution. As part of the ground processing, the separation of the SAR antennas at the time of each data take must be reconstructed with a 1 mm accuracy using measurements from two geodetic grade GPS receivers. The paper discusses the TanDEM-X mission as well as the methods employed for determining the interferometric baseline with utmost precision. Measurements collected during the close fly-by of the two GRACE satellites serve as a reference case to illustrate the processing concept, expected accuracy and quality control strategies

IMPROVING AND EXPANDING PRECISION ORBIT DERIVED ATMOSPHERIC DENSITIES

Atmospheric drag is the most uncertain non-conservative force acting on a low Earth orbiting satellite. The existing atmospheric density models are not accurate enough to model the variations in density, which significantly affect the drag on satellites since drag is directly proportional to atmospheric density. In this research, precision orbit ephemerides (POE) are used as measurements in an optimal orbit determination scheme to estimate corrections to baseline atmospheric density models. These corrections improve the drag estimates, which in turn improve orbit determination and prediction and also provide a better understanding of the upper atmosphere. The POE are used as measurements in a sequential measurement and filtering scheme using the Orbit Determination Tool Kit (ODTK) software, which provides the orbit determination. Five atmospheric density models are available in ODTK, which are used as baseline atmospheric density models to which corrections are made in the orbit determination. These density models are Jacchia 1971, Jacchia-Roberts, CIRA 1972, MSISE 1990, and NRLMSISE 2000. The user has the option to specify the ballistic coefficient (BC) correlated half-life and density correlated half-life. These half-lives are usually given values of 1.8, 18, or 180 minutes. If all five baseline density models are used along with three different combinations of ballistic coefficient and density correlated half-lives, then this would result in forty-five different cases. All the forty-five cases are examined in some studies and only a selected few are examined in others, the details of which are given in the appropriate sections. The POE derived densities are validated by comparing them with accelerometer derived densities for satellites which have accelerometers onboard, such as the Challenging Minisatellite Payload (CHAMP) and the Gravity Recovery and Climate Experiment (GRACE). The trend in the variation is compared quantitatively by calculating the cross correlation between the POE and accelerometer derived densities, and the magnitude is compared by calculating the root mean square between the two. The accelerometer derived densities for both CHAMP and GRACE are available from Sean Bruinsma of CNES and also from Eric Sutton of the United States Air Force Research Laboratory, and are used in this research. The effect of different functions of geomagnetic planetary amplitude (ap) as an input in orbit determination to estimate atmospheric density was investigated. The three different functions of input are 3-hourly ap step functions, linear interpolated ap functions, and ap osculating spline functions. These three different types of functions were used as inputs for all the forty-five different combinations obtained by using the five different baseline atmospheric density models and three different combinations of ballistic coefficient and density correlated half-lives as stated earlier, and POE derived density was estimated for both CHAMP and GRACE. The POE derived densities were compared with the accelerometer derived densities by calculating the CC and RMS. To create continuous data sets of POE derived densities that span a period of one week, the linear weighted blending technique was used to blend the 14 hour POE derived densities in their overlap periods. CIRA 1972 was used as the baseline atmospheric density model and a BC correlated half-life of 1.8 minutes and density correlated half-life of 180 minutes were used as inputs in ODTK to generate these POE derived density estimates. These one week continuous POE derived densities showed better correlation with accelerometer derived densities than HASDM densities for both CHAMP and GRACE. The average cross-sectional area of the satellite that is normal to the velocity vector, the area facing the Sun, and the area facing the Earth, were determined so that these areas could be used to estimate the atmospheric drag, the force due to solar radiation pressure, and the force due to Earth radiation pressure (infrared and Earth albedo). This was done for both TerraSAR-X and ICESat. For TerraSAR-X, the area normal to the velocity vector was assumed be a constant and equal to the frontal area, and the area facing the Earth was also assumed to be constant. However, the area facing the Sun varied with time. The average area facing the Sun for a period of 14 hours and also the annual average area were calculated and used to calculate the POE derived densities. The POE derived densities calculated using these two different average areas facing the Sun were found to be very similar. Since TerraSAR-X does not have an accelerometer onboard, the POE derived densities could not be compared with accelerometer derived densities, but instead were compared with Jacchia-71 densities since this was also one of the outputs from ODTK. The POE derived densities were also compared with NRLMSISE 2000 densities. The attitude of ICESat as a function of beta angle was given in the literature and so was the average area of each side of the satellite when it was modeled as a rectangular box with two solar panels. This information was used to estimate the 30-hour average area normal to the velocity vector, area facing the Earth, and area facing the Sun, for ICESat. The POE derived densities using these areas were estimated by ODTK and compared with the Jacchai-71 density model

Precise orbit determination of LEO satellites : a systematic review

The need for precise orbit determination (POD) has grown significantly due to the increased amount of space-based activities taking place at an accelerating pace. Accurate POD positively contributes to achieving the requirements of Low-Earth Orbit (LEO) satellite missions, including improved tracking, reliability and continuity. This research aims to systematically analyze the LEO–POD in four aspects: (i) data sources used; (ii) POD technique implemented; (iii) validation method applied; (iv) accuracy level obtained. We also present the most used GNSS systems, satellite missions, processing procedures and ephemeris. The review includes studies on LEO–POD algorithms/methods and software published in the last two decades (2000–2021). To this end, 137 primary studies relevant to achieving the objective of this research were identified. After the investigation of these primary studies, it was found that several types of POD techniques have been employed in the POD of LEO satellites, with a clear trend observed for techniques using reduced-dynamic model, least-squares solvers, dual-frequency signals with undifferenced phase and code observations in post-processing mode. This review provides an understanding of the various POD techniques, dataset utilized, validation techniques, and accuracy level of LEO satellites, which have interest to developers of small satellites, new researchers and practitioners.© The Author(s) 2023. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.fi=vertaisarvioitu|en=peerReviewed

An Interferometric SAR Satellite Mission

The paper provides a critical review of the achievements in SAR interferometry from the ERS mission as well as from the Shuttle Radar Topography Mission SRTM. It describes the development from the original idea of the Interferometric Cartwheel to the concept of a formation flight of identical and active SAR satellites. From the experience gained from ERS and SRTM interferometric data processing as well as from the analysis of the Cartwheel concept a list of mission requirements has been set up. The most demanding one is the autonomous configuration flight of a tight x-band constellation, where the satellites fly as close as up to 30 m with a dead-band of +/- 10 m. The guidance, navigation and control considerations come to the conclusion that such a mission is feasible

In-depth verification of Sentinel-1 and TerraSAR-X geolocation accuracy using the Australian Corner Reflector Array

This article shows how the array of corner reflectors (CRs) in Queensland, Australia, together with highly accurate geodetic synthetic aperture radar (SAR) techniques—also called imaging geodesy—can be used to measure the absolute and relative geometric fidelity of SAR missions. We describe, in detail, the end-to-end methodology and apply it to TerraSAR-X Stripmap (SM) and ScanSAR (SC) data and to Sentinel-1interferometric wide swath (IW) data. Geometric distortions within images that are caused by commonly used SAR processor approximations are explained, and we show how to correct them during postprocessing. Our results, supported by the analysis of 140 images across the different SAR modes and using the 40 reflectors of the array, confirm our methodology and achieve the limits predicted by theory for both Sentinel-1 and TerraSAR-X. After our corrections, the Sentinel-1 residual errors are 6 cm in range and 26 cm in azimuth, including all error sources. The findings are confirmed by the mutual independent processing carried out at University of Zurich (UZH) and German Aerospace Center (DLR). This represents an improve�ment of the geolocation accuracy by approximately a factor of four in range and a factor of two in azimuth compared with the standard Sentinel-1 products. The TerraSAR-X results are even better. The achieved geolocation accuracy now approaches that of the global navigation satellite system (GNSS)-based survey of the CRs positions, which highlights the potential of the end-to-end SAR methodology for imaging geodesy