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In 2015, the International Association of Geodesy defined the International Height Reference System (IHRS) as the conventional gravity field-related global height system. The IHRS is a geopotential reference system co-rotating with the Earth. Coordinates of points or objects close to or on the Earth’s surface are given by geopotential numbers C ( P ) referring to an equipotential surface defined by the conventional value W 0  = 62,636,853.4 m 2  s −2 , and geocentric Cartesian coordinates X referring to the International Terrestrial Reference System (ITRS). Current efforts concentrate on an accurate, consistent, and well-defined realisation of the IHRS to provide an international standard for the precise determination of physical coordinates worldwide. Accordingly, this study focuses on the strategy for the realisation of the IHRS; i.e. the establishment of the International Height Reference Frame (IHRF). Four main aspects are considered: (1) methods for the determination of IHRF physical coordinates; (2) standards and conventions needed to ensure consistency between the definition and the realisation of the reference system; (3) criteria for the IHRF reference network design and station selection; and (4) operational infrastructure to guarantee a reliable and long-term sustainability of the IHRF. A highlight of this work is the evaluation of different approaches for the determination and accuracy assessment of IHRF coordinates based on the existing resources, namely (1) global gravity models of high resolution, (2) precise regional gravity field modelling, and (3) vertical datum unification of the local height systems into the IHRF. After a detailed discussion of the advantages, current limitations, and possibilities of improvement in the coordinate determination using these options, we define a strategy for the establishment of the IHRF including data requirements, a set of minimum standards/conventions for the determination of potential coordinates, a first IHRF reference network configuration, and a proposal to create a component of the International Gravity Field Service (IGFS) dedicated to the maintenance and servicing of the IHRS/IHRF.

The International Height Reference System (IHRS), adopted by International Association of Geodesy (IAG) in its Resolution No. 1 at the XXVI General Assembly of the International Union of Geodesy and Geophysics (IUGG) in Prague in 2015, contains two novelties. Firstly, the mean-tide concept is adopted for handling the permanent tide. While many national height systems continue to apply the mean-tide concept, this was the first time that the IAG officially introduced it for a potential field quantity. Secondly, the reference level of the height system is defined by the equipotential surface where the geopotential has a conventional value W 0  = 62,636,853.4 m 2  s –2 . This value was first determined empirically to provide a good approximation to the global mean sea level and then adopted as a reference value by convention. I analyse the tidal aspects of the reference level based on W 0 . By definition, W 0 is independent of the tidal concept that was adopted for the equipotential surface, but for different concepts, different functions are involved in the W of the equation W  =  W 0 . I find that, in the empirical determination of the adopted estimate W 0 , the permanent tide is treated inconsistently. However, the consistent estimate from the same data rounds off to the same value. I discuss the tidal conventions and formulas for the International Height Reference Frame (IHRF) and the realisation of the IHRS. I propose a simplified definition of IHRF geopotential numbers that would make it possible to transform between the IHRF and zero-tide geopotential numbers using a simple datum-difference surface. Such a transformation would not be adequate if rigorous mean-tide formulas were imposed. The IHRF should adopt a conventional (best) estimate of the permanent tide-generating potential, such as that which is contained in the International Earth Rotation and Reference Systems Service Conventions, and use it as a basis for other conventional formulas. The tide-free coordinates of the International Terrestrial Reference Frame and tide-free Global Geopotential Models are central in the modelling of geopotential for the purposes of the IHRF. I present a set of correction formulas that can be used to move to the zero-tide model before, during, or after the processing, and finally to the mean-tide IHRF. To reduce the confusion around the multitude of tidal concepts, I propose that modelling should primarily be done using the zero-tide concept, with the mean-tide potential as an add-on. The widespread use of the expression “systems of permanent tide” may also have contributed to the confusion, as such “systems” do not have the properties that are generally associated with other “systems” in geodesy. Hence, this paper mostly uses “concept” instead of “system” when referring to the permanent tide.

•Spatial navigation system involves the MTL, PPA, RSC, OPA, and PFC.•Navigation in vista and environmental spaces evoked the PPA, RSC, and OPA.•Navigation in environmental space evoked more brain areas than in vista space.•Both allocentric and egocentric frames evoked the bilateral PPA and right RSC.•Allocentric frame evoked three more areas, right culmen, left MFG, and LING than egocentric frame. Humans use different spatial reference frames (allocentric or egocentric) to navigate successfully toward their destination in different spatial scale spaces (environmental or vista). However, it remains unclear how the brain represents different spatial scales and different spatial reference frames. Thus, we conducted an activation likelihood estimation (ALE) meta-analysis of 47 fMRI articles involving human spatial navigation. We found that both the environmental and vista spaces activated the parahippocampal place area (PPA), retrosplenial complex (RSC), and occipital place area in the right hemisphere. The environmental space showed stronger activation than the vista space in the occipital and frontal regions. No brain region exhibited stronger activation for the vista than the environmental space. The allocentric and egocentric reference frames activated the bilateral PPA and right RSC. The allocentric frame showed more stronger activations than the egocentric frame in the right culmen, left middle frontal gyrus, and precuneus. No brain region displayed stronger activation for the egocentric than the allocentric navigation. Our findings suggest that navigation in different spatial scale spaces can evoke specific and common brain regions, and that the brain regions representing spatial reference frames are not absolutely separated.

Several works have demonstrated that visual experience plays a critical role in the development of allocentric spatial coding. Indeed, while children with a typical development start to code space by relying on allocentric landmarks from the first year of life, blind children remain anchored to an egocentric perspective until late adolescence. Nonetheless, little is known about when and how visually impaired children acquire the ability to switch from an egocentric to an allocentric frame of reference across childhood. This work aims to investigate whether visual experience is necessary to shift from bodily to external frames of reference. Children with low vision and sighted controls between 4 and 9 years of age were asked to solve a visual Switching-Perspective task requiring them to assume an egocentric or an allocentric perspective depending on the task condition. We hypothesize that, if visual experience is necessary for allocentric spatial coding, then low vision children would have been impaired to switch from egocentric to allocentric perspectives. Results support this hypothesis, confirming a developmental delay in the ability to update spatial coordinates in low vision children. It suggests a pivotal role of vision in shaping allocentric spatial coding across development.

Objectives Mindfulness training is believed to encourage self-transcendent states, but little research has examined this hypothesis. This study examined the effects of mindfulness training on two phenomenological features of self-transcendence: (1) perceived body boundary dissolution and (2) allocentric spatial frame of reference. Methods A sample of healthy, young adults ( n  = 45) were randomized to five sessions of mindfulness training or an active listening control condition. Results Results indicated that mindfulness training decreased perceived body boundaries ( F 4,172  = 6.010, p  < .001, η 2  = .12) and encouraged more allocentric frames of reference ( F 4,168  = 2.586, p  = .039, η 2  = .06). The expected inverse relationship was observed between perceived body boundaries and allocentric frames of reference (( β  = − .58, p  = .001)), and path analysis revealed that the effect of mindfulness training on allocentric frames of reference was mediated by decreased perceived body boundaries ( β  = .24, se  = .17, CI: 0.11 to 0.78). Conclusions Taken together, study results suggest that mindfulness training alters practitioners’ experience of self, relaxing the boundaries of the self and extending the spatial frame of reference further beyond the physical body. Future studies are needed to explore the psychophysiological changes that co-occur with phenomenological reports of self-transcendence and the behavioral consequences following self-transcendent experiences.

The scale of the last realization of the International Terrestrial Reference System, the frame ITRF2020, is derived from a combination of Very Long Baseline Interferometry (VLBI) and Satellite Laser Ranging observations. During the computations of ITRF2020, an unexpected VLBI scale drift after 2013.75 led to the exclusion of sessions beyond this epoch from the scale definition. An independent research of the origin of the suspected scale drift conducted by researchers of the Onsala Space Observatory (Chalmers University of Technology) suggested a mis-modeling of the station movement of the uniquely located VLBI antenna, NYALES20 (Svalbard, Norway), as the likely cause of these anomalies. The underlying assumption was motivated by station movement information available from the co-located Global Navigation Satellite Systems (GNSS) receiver, NYAL , aligning perfectly with the discontinuities visible in the session-wise station positions of NYALES20 . In our investigations, the additional discontinuity intervals are introduced in the determination of a VLBI-only terrestrial reference frame (TRF), and their impact on the session-wise scale is analyzed in comparison to the results of a reference solution. We evaluate the importance of four additional intervals suggested by the Onsala Space Observatory and the strategy of the ITRF2020-u2023, where only two of these intervals are implemented. New in our investigations is the analysis of the scale evolution based on a TRF determination from a combination at normal equation level with our software VieCompy. Through the latter, added value is warranted by applying a different concept of TRF combination, which differs from the combination of solutions at parameter level with full covariance transfer, as applied in the ITRF computations using the CATREF (Combination and Analysis of Terrestrial Reference Frame) software. In addition, our scale computations and considerations are entirely independent of the ITRF calculations and we extended the analyzed session-wise scale time series to 2024.0 to get a better insight into the long-term development. The comparison of the time series of session-wise estimated scale factors with the reference solution reveals a significant reduction in the VLBI drift by more than 50 % when accounting for a modified station movement model for NYALES20 . Therefore, we strongly advocate introducing an optimized station movement model for NYALES20 to account for climate-related processes to ensure the stability of the scale of global reference frames. Graphical Abstract

We report on recent refinements and the current status for the rotational state models and the reference frames of the planet Mercury. We summarize the performed measurements of Mercury rotation based on terrestrial radar observations as well as data from the Mariner 10 and the MESSENGER missions. Further, we describe the different available definitions of reference systems for Mercury and obtain the corresponding reference frame using data provided by instruments on board MESSENGER. In particular, we discuss the dynamical frame, the principal-axes frame, the ellipsoid frame, as well as the cartographic frame. We also describe the reference frame adopted by the MESSENGER science team for the release of their cartographic products, and we provide expressions for transformations from this frame to the other reference frames.

High penetration of wind power into the grid necessitates the coordinated action of wind energy conversion systems and the grid. A suitable generation control is required to fulfill the grid integration requirements, especially during faults. A system using a pair of voltage source converters with a squirrel cage induction generator coupled to a wind turbine is proposed to provide fault ride-through during grid faults. A threefold action is used for providing the effective fault ride-through via coordinated action of the machine side and the grid side converter. The entire wind energy conversion system is controlled such that the wind turbine remains connected even during the faults. To implement the threefold action: (i) A decoupled current controller is placed in the grid side converter, which separately controls the positive and negative sequence currents arising during faults. The grid side converter controller is capable of eliminating the double frequency oscillations at the dc-link voltage and, hence, real power, which arises during the unsymmetrical faults; (ii) Reactive power injection is additionally provided by the grid side converter for better grid support; and (iii) The vector control technique is used in machine side converter along with the droop control to adjust the generator speed and the torque resulting in actuation of the pitch control mechanism to limit power generation without shutdown of the turbine.

The Deutsches Geodätisches Forschungsinstitut der Technischen Universität München (DGFI-TUM) is one of the three Combination Centres of the International Earth Rotation and Reference Systems Service for the International Terrestrial Reference System (ITRS). In its upcoming realization of the ITRS, the DTRF2020, DGFI-TUM will again correct for non-tidal loading (NTL) effects at the normal equation level. Next to the dedicated NTL data set for the ITRS 2020 realization provided by the Global Geophysical Fluid Center (GGFC), we also considered the data provided by the Earth System Modelling group of the Deutsches GeoForschungsZentrum (ESMGFZ). Besides also comprising all NTL components (atmospheric, oceanic, hydrological) and being mass conserving, the ESMGFZ data has the advantage of daily availability and is already in use at DGFI-TUM. The decision for one or the other data set depends on their suitability for a secular terrestrial reference frame like the DTRF2020, which will be assessed in this work. Although we also compare the site displacements induced by NTL to the residuals of station positions of the Global Navigation Satellite Systems, we will not evaluate the quality of the underlying geophysical models per se. The two data sets differ w.r.t. the underlying hydrological models and the treatment of non-tidal oceanic loading, but the most relevant difference is given in terms of trends in the displacement time-series. After a close investigation of the latter, we finally decided to apply the GGFC contribution to the ITRS 2020 realization in the DTRF2020.

The integration of photovoltaic (PV) systems and renewable energy sources into modern utility grids presents substantial opportunities for sustainable energy, yet also introduces critical power quality challenges due to the proliferation of nonlinear and unbalanced loads. This paper proposes a dynamic multi-function reference frame control (DMRFC) strategy for a multifunctional bidirectional grid-interactive converter (µG-MPGIC), designed for PV-grid interconnection with enhanced power quality assistance. Built upon the Synchronous Reference Frame (SRF) theory, the DMRFC approach enables autonomous multifunctionality: (i) dynamic regulation of active power transfer based on load demands and available DC-side energy, (ii) bidirectional energy flow between AC and DC interfaces considering the battery's state of charge (SOC), (iii) harmonic current mitigation, reactive power compensation, and (iv) neutral current suppression under unbalanced load conditions. A small-signal transfer function model is developed for stability analysis using frequency-domain methods. Simulation studies conducted in MATLAB/SIMULINK demonstrate that the proposed DMRFC control achieves a total harmonic distortion (THD) reduction in grid currents to 1.25% , compared to 1.79% with conventional symmetrical component theory (SCT)-based control and 2.80% with Instantaneous Power Theory (IPT)-based control under identical conditions. Furthermore, the system achieves unity power factor operation under highly nonlinear loading, superior to the 0.96 and 0.93 power factors achieved with SCT and IPT, respectively. Under dynamic loading and fluctuating irradiation, the converter maintains a near-constant DC-link voltage, demonstrating robust grid synchronization and operational stability. The system also effectively supports bidirectional power flow, handling battery charging at −4.96 kW and discharging at +4.95 kW with seamless transitions, validated through grid current magnitude variations between 32 A and 42 A. The proposed DMRFC strategy offers a significant enhancement over conventional methods, delivering superior power quality improvement, intelligent energy management, and adaptive multifunctional operation in grid-connected PV systems.