Design of experiment for earth rotation and baseline parameter determination from very long baseline interferometry

The possibility of recovering earth rotation and network geometry (baseline) parameters are emphasized. The numerical simulated experiments performed are set up in an environment where station coordinates vary with respect to inertial space according to a simulated earth rotation model similar to the actual but unknown rotation of the earth. The basic technique of VLBI and its mathematical model are presented. The parametrization of earth rotation chosen is described and the resulting model is linearized. A simple analysis of the geometry of the observations leads to some useful hints on achieving maximum sensitivity of the observations with respect to the parameters considered. The basic philosophy for the simulation of data and their analysis through standard least squares adjustment techniques is presented. A number of characteristic network designs based on present and candidate station locations are chosen. The results of the simulations for each design are presented together with a summary of the conclusions

Probabilistic and deterministic aspects of linear estimation in geodesy

Recent advances in observational techniques related to geodetic work (VLBI, laser ranging) make it imperative that more consideration should be given to modeling problems. Uncertainties in the effect of atmospheric refraction, polar motion and precession-nutation parameters, cannot be dispensed with in the context of centimeter level geodesy. Even physical processes that have generally been previously altogether neglected (station motions) must now be taken into consideration. The problem of modeling functions of time or space, or at least their values at observation points (epochs) is explored. When the nature of the function to be modeled is unknown. The need to include a limited number of terms and to a priori decide upon a specific form may result in a representation which fails to sufficiently approximate the unknown function. An alternative approach of increasing application is the modeling of unknown functions as stochastic processes

Contribution of Apollo lunar photography to the establishment of selenodetic control

Among the various types of available data relevant to the establishment of geometric control on the moon, the only one covering significant portions of the lunar surface (20%) with sufficient information content, is lunar photography, taken at the proximity of the moon from lunar orbiters. The idea of free geodetic networks is introduced as a tool for the statistical comparison of the geometric aspects of the various data used. Methods were developed for the updating of the statistics of observations and the a priori parameter estimates to obtain statistically consistent solutions by means of the optimum relative weighting concept

ESA ice sheet CCI: derivation of the optimal method for surface elevation change detection of the Greenland ice sheet - round robin results

For more than two decades, radar altimetry missions have provided continuous elevation estimates of the Greenland ice sheet (GrIS). Here, we propose a method for using such data to estimate ice-sheet-wide surface elevation changes (SECs). The final data set will be based on observations acquired from the European Space Agency’s Environmental Satellite (ENVISAT), European Remote Sensing (ERS)-1 and -2, CryoSat-2, and, in the longer term, Sentinel-3 satellites. In order to find the best-performing method, an intercomparison exercise has been carried out in which the scientific community was asked to provide their best SEC estimates as well as feedback sheets describing the applied method. Due to the hitherto few radar-based SEC analyses as well as the higher accuracy of laser data, the participants were asked to use either ENVISAT radar or ICESat (Ice, Cloud, and land Elevation Satellite) laser altimetry over the Jakobshavn Isbræ drainage basin. The submissions were validated against airborne laser-scanner data, and intercomparisons were carried out to analyse the potential of the applied methods and to find whether the two altimeters were capable of resolving the same signal. The analyses found great potential of the applied repeat-track and cross-over techniques, and, for the first time over Greenland, that repeat-track analyses from radar altimetry agreed well with laser data. Since topography-related errors can be neglected in cross-over analyses, it is expected that the most accurate, ice-sheet-wide SEC estimates are obtained by combining the cross-over and repeat-track techniques. It is thus possible to exploit the high accuracy of the former and the large spatial data coverage of the latter. Based on CryoSat’s different operation modes, and the increased spatial and temporal data coverage, this shows good potential for a future inclusion of CryoSat-2 and Sentinel-3 data to continuously obtain accurate SEC estimates both in the interior and margin ice sheet

Non-stationary covariance function modelling in 2D least-squares collocation

Standard least-squares collocation (LSC) assumes 2D stationarity and 3D isotropy, and relies on a covariance function to account for spatial dependence in the ob-served data. However, the assumption that the spatial dependence is constant through-out the region of interest may sometimes be violated. Assuming a stationary covariance structure can result in over-smoothing of, e.g., the gravity field in mountains and under-smoothing in great plains. We introduce the kernel convolution method from spatial statistics for non-stationary covariance structures, and demonstrate its advantage fordealing with non-stationarity in geodetic data. We then compared stationary and non-stationary covariance functions in 2D LSC to the empirical example of gravity anomaly interpolation near the Darling Fault, Western Australia, where the field is anisotropic and non-stationary. The results with non-stationary covariance functions are better than standard LSC in terms of formal errors and cross-validation against data not used in the interpolation, demonstrating that the use of non-stationary covariance functions can improve upon standard (stationary) LSC

The treatment of time continuous GPS observations for the determination of regional deformation parameters

The calculation of invariant deformation parame-ters, entering in the constitutional equations of crustal dynamics, requires information on the ge-ometry of the crust in the study region, which is continuous in both the time and spatial domain. The use of continuously observing GPS stations pro-vides geodetic data which are practically time-continuous and must be only spatially interpolated. A strategy is developed for the treatment of dense series of horizontal coordinates from a regional GPS network, which are typically exhibiting a time-linear behavior. The role of the choice of reference system is examined for the removal of trend before the spatial interpolation as well as the determination of the motion of the region as whole with respect to the ITRF or of the relative motion of tectonically homogeneous sub regions. Rigorous formulas are presented for various horizontal deformation pa-rameters and their intrinsic time derivatives, without the usual infinitesimal approximations. Finally the problem of quality assessment for the derived pa-rameters is investigated completely ignoring the questionable formal statistical characteristic of the original geodetic data. A realistic numerical exam-ple demonstrates the suggested techniques, involv-ing spatial interpolation by the classical finite-element method. A software package in standard C language has been developed in order to implement the proposed algorithms