Differential geodetic stereo SAR with TerraSAR-X by exploiting small multi-directional radar reflectors

In this paper, we report on the direct positioning of small multi-directional radar reflectors, so-called octahedrons, with the synthetic aperture radar (SAR) satellite TerraSAR-X. Its highest resolution imaging mode termed staring spotlight enables the use of such octahedron reflectors with a dimension of only half a meter, but still providing backscatter equivalent to 1–2 cm observation error. Four octahedrons were deployed at Wettzell geodetic observatory, and observed by TerraSAR-X with 12 acquisitions in three different geometries. By applying our least squares stereo SAR algorithm already tested with common trihedral corner reflectors (CRs), and introducing a novel differential extension using one octahedron as reference point, the coordinates of the remaining octahedrons were directly retrieved in the International Terrestrial Reference Frame (ITRF). Contrary to our standard processing, the differential approach does not require external corrections for the atmospheric path delays and the geodynamic displacements, rendering it particularly useful for joint geodetic networks employing SAR and GNSS. In this paper, we present and discuss both methods based on results when applying them to the aforementioned Wettzell data set of the octahedrons. The comparison with the independently determined reference coordinates confirms the positioning accuracy with 2–5 cm for the standard approach, and 2–3 cm for the differential processing. Moreover, we present statistical uncertainty estimates of the observations and the positioning solutions, which are additionally provided by our parameter estimation algorithms. The results also include our 1.5 m CR available at Wettzell, and the outcomes clearly demonstrate the advantage of the multi-directional octahedrons over conventional CRs for global positioning applications with SAR.