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The Astronomical Institute of the University of Bern (AIUB) has been performing GPS-based Precise Orbit Determination (POD) for a large variety of Low Earth Orbit (LEO) satellites since two decades. Traditionally, LEO orbits have been generated by a reduced-dynamic POD strategy using the Bernese GNSS Software, replacing an explicit modeling of non-gravitational forces by dedicated empirical orbit parametrizations. This LEO POD strategy can be advanced by two main developments: on the one hand, use is made of the GNSS Observation-Specific Bias (OSB) and clock products provided by the Center for Orbit Determination in Europe (CODE), allowing for the resolution of single-receiver GNSS carrier-phase ambiguities. On the other hand, the main focus of this article, a refined satellite non-gravitational force modeling strategy is constructed to reduce the amount of empirical parameters used to compensate for force modeling deficiencies. LEO POD is first performed for Sentinel-3, a satellite formation currently consists of two identical satellites −3A and −3B, which experience a similar in-flight environment and allow for direct POD performance comparisons. A third satellite Swarm-C, which flies at a lower altitude and has a more sophisticated surface geometry, is selected to validate the robustness of the new POD strategy. As a result, both the internal consistency checks and external orbit validations suggest superior orbit quality obtained for the three satellites for a time span of 1.5 years (7 June, 2018 to 31 December, 2019). The ambiguity resolution adds strong constraints to the orbits and the satellite non-gravitational force modeling leads to more tightly constrained (towards zero) pseudo-stochastic empirical parameters. The final orbit solutions agree with external orbit solutions and independent satellite laser ranging measurements at levels of sub-cm, indicating approximately 20 % improvement w.r.t. the nominal reduced-dynamic orbit solutions. This suggests potential benefits to the space geodesy community that always pursues best-possible satellite orbits.

Precision Orbit Determination (POD) is a prerequisite for the success of many Low Earth Orbiting (LEO) satellite missions. With high-quality, dual-frequency Global Positioning System (GPS) receivers, typically precisions of the order of a few cm are possible for single-satellite POD, and of a few mm for relative POD of formation flying spacecraft with baselines up to hundreds of km. To achieve the best precision, the use of Phase Center Variation (PCV) maps is indispensable. For LEO GPS receivers, often a-priori PCV maps are obtained by a pre-launch ground campaign, which is not able to represent the real space-borne environment of satellites. Therefore, in-flight calibration of the GPS antenna is more widely conducted. This paper shows that a further improvement is possible by including the so-called Code Residual Variation (CRV) maps in absolute/undifferenced and relative/Double-differenced (DD) POD schemes. Orbit solutions are produced for the GRACE satellite formation for a four months test period (August-November, 2014), demonstrating enhanced orbit precision after first using the in-flight PCV maps and a further improvement after including the CRV maps. The application of antenna maps leads to a better consistency with independent Satellite Laser Ranging (SLR) and K-band Ranging (KBR) low-low Satellite-to-Satellite Tracking (ll-SST) observations. The inclusion of the CRV maps results also in a much better consistency between reduced-dynamic and kinematic orbit solutions for especially the cross-track direction. The improvements are largest for GRACE-B, where a cross-talk between the GPS main antenna and the occultation antenna yields higher systematic observation residuals. For high-precision relative POD which necessitates DD carrier-phase ambiguity fixing, in principle frequency-dependent PCV maps would be required. To this aim, use is made of an Extended Kalman Filter (EKF) that is capable of optimizing relative spacecraft dynamics and iteratively fixing the DD carrier-phase ambiguities. It is found that PCV maps significantly improve the baseline solution. CRV maps slightly enhance the baseline precision, more significantly they lead to a much better initialization of the ambiguity fixing. The GRACE single-satellite orbit solutions compare to within a few cm 3-dimensionally with state-of-the-art external orbit solutions and SLR observations, whereas for the baseline a consistency of better than 0.7 mm with KBR observations is achieved.

A further-miniaturized specimen punch (SP) test has been developed to extract fracture strain and strength information from TEM disc specimens as small as 3 mm diameter and 0.25 mm in thickness. The test is based on driving a steel ball punch through a clamped specimen. A perfect-rigid plastic analysis has been made to extract fracture strain and the deformation process of the further-miniaturized specimen test is divided into three regions, as in the 10 mm × 10 mm × 0.5 mm specimen. The size effect of biaxial equivalent fracture strain of various kinds of materials has been demonstrated. The results of fracture strain obtained from 3 mm diameter specimens can be related almost linearly to the fracture toughness, J IC , for elastic-plastic behavior. A number of correlations also have been obtained between features of the load-displacement curve of the SP test and the mechanical properties, such as yield stress and ultimate stress.