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 TerraSAR-X Stripmap (SM) and ScanSAR (SC) data and to Sentinel-1 interferometric 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 improvement 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.

Low-pass filters are commonly used for the processing of airborne gravity observations. In this paper, for the first time, we include the resulting correlations consistently in the functional and stochastic model of residual least-squares collocation. We demonstrate the necessity of removing high-frequency noise from airborne gravity observations, and derive corresponding parameters for a Gaussian low-pass filter. Thereby, we intend an optimal combination of terrestrial and airborne gravity observations in the mountainous area of Colorado. We validate the combination in the frame of our participation in ‘the 1 cm geoid experiment’. This regional geoid modeling inter-comparison exercise allows the calculation of a reference solution, which is defined as the mean value of 13 independent height anomaly results in this area. Our result performs among the best and with 7.5 mm shows the lowest standard deviation to the reference. From internal validation we furthermore conclude that the input from airborne and terrestrial gravity observations is consistent in large parts of the target area, but not necessarily in the highly mountainous areas. Therefore, the relative weighting between these two data sets turns out to be a main driver for the final result, and is an important factor in explaining the remaining differences between various height anomaly results in this experiment.

The signal content and error level of recent GOCE-based high resolution gravity field models is assessed by means of signal degree variances and comparisons to independent GNSS-levelling geoid heights. The signal of the spherical harmonic series of these models is compared to the pre-GOCE EGM2008 model in order to identify the impact of GOCE data, of improved surface and altimetric gravity data and of modelling approaches. Results of the signal analysis show that in a global average roughly 80% of the differences are due to the inclusion of GOCE satellite information, while the remaining 20% are contributed by improved surface data. Comparisons of the global models to GNSS-levelling derived geoid heights demonstrate that a 1 cm geoid from the global model is feasible, if there is a high quality terrestrial gravity data set available. For areas with less good coverage an accuracy of several centimetres to a decimetre is feasible taking into account that GOCE provides now the geoid with a centimetre accuracy at spatial scales of 80 to 100 km. Comparisons with GNSS-levelling geoid heights also are a good tool to investigate possible systematic errors in the global models, in the spirit levelling and in the GNSS height observations. By means of geoid height differences and geoid slope differences one can draw conclusions for each regional data set separately. These conclusions need to be considered for a refined analysis e.g. to eliminate suspicious GNSS-levelling data, to improve the global modelling by using full variance-covariance matrices and by consistently weighting the various data sources used for high resolution gravity field models. The paper describes the applied procedures, shows results for these geoid height and geoid slope differences for some regional data sets and draws conclusions about possible error sources and future work to be done in this context.

Various types of heterogeneous observations can be combined within a parameter estimation process using spherical radial basis functions (SRBFs) for regional gravity field refinement. In this process, regularization is in most cases inevitable, and choosing an appropriate value for the regularization parameter is a crucial issue. This study discusses the drawbacks of two frequently used methods for choosing the regularization parameter, which are the L-curve method and the variance component estimation (VCE). To overcome their drawbacks, two approaches for the regularization parameter determination are proposed, which combine the L-curve method and VCE. The first approach, denoted as “VCE-Lc”, starts with the calculation of the relative weights between the observation techniques by means of VCE. Based on these weights, the L-curve method is applied to determine the regularization parameter. In the second approach, called “Lc-VCE”, the L-curve method determines first the regularization parameter, and it is set to be fixed during the calculation of the relative weights between the observation techniques from VCE. To evaluate and compare the performance of the two proposed methods with the L-curve method and VCE, all these four methods are applied in six study cases using four types of simulated observations in Europe, and their modeling results are compared with the validation data. The RMS errors (w.r.t the validation data) obtained by VCE-Lc and Lc-VCE are smaller than those obtained from the L-curve method and VCE in all the six cases. VCE-Lc performs the best among these four tested methods, no matter if using SRBFs with smoothing or non-smoothing features. These results prove the benefits of the two proposed methods for regularization parameter determination when different data sets are to be combined.