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The positions of millisecond pulsars (MSPs) can be determined with sub-milliarcsecond (mas) accuracy using both Very Long Baseline Interferometry (VLBI) and timing, referenced to the International Celestial Reference Frame (ICRF) and planetary ephemerides frame, respectively, representing kinematic and dynamical reference frames. The two frames can be connected through observations of common celestial objects, MSPs observed with VLBI and timing. However, previous attempts to establish this connection were unreliable due to the limited number of MSPs observed by both techniques. Currently, 23 MSPs have been precisely measured using both multiple timing and VLBI networks. Among them, 17 MSPs are used to link the two reference frames, marking a significant three-fold increase in the number of common MSPs used for frame linking. Nevertheless, six MSPs located near the ecliptic plane are excluded from frame linkage due to positional differences exceeding 20 mas measured by VLBI and timing. This discrepancy is primarily attributed to errors introduced in fitting positions in timing methods. With astrometric parameters obtained via both VLBI and timing for these MSPs, the precision of linking DE436 and ICRF3 has surpassed 0.4 mas. Furthermore, thanks to the improved timing precision of MeerKAT, even with data from just 13 MSPs observed by both MeerKAT and VLBI, the precision of linking DE440 and ICRF3 can also exceed 0.4 mas. The reliability of this linkage depends on the precision of pulsar astrometric parameters, their spatial distribution, and discrepancies in pulsar positions obtained by the two techniques. Notably, proper motion differences identified by the two techniques are the most critical factors influencing the reference frame linking parameters. The core shift of the calibrators in VLBI pulsar observations is one of the factors causing proper motion discrepancies, and multi-wavelength observations are expected to solve it. With the improvement in timing accuracy and the application of new observation modes like multi-view and multi-band observations in VLBI, the linkage accuracy of the dynamical and kinematic reference frames is expected to reach 0.3 mas.

The q-method for pose estimation utilizes on-board measurement vectors of reference objects to calculate air vehicle position and orientation with respect to an Inertial frame. This new method solves for the quaternion eigenvalue solution of the optimal pose to minimize the error in the derived system of equations. The generalized q-method extends Davenport’s q-method for satellite attitude estimation by incorporating inertial position into the relative model and eliminating assumptions throughout the derivation that require spacecraft applications. Thus, the pose estimation model is developed and implemented for UAV applications using an onboard camera to obtain measurements in a controlled environment. Combined with numerical methods, algorithm outputs for position and orientation are validated against truth data to prove accurate estimation despite sensor error.

According to the single-mode approximation applied to two different mo des, each associated with different uniformly accelerating reference frames, we present analytical expression of the Minkowski states for both the ground and first excited states. Applying such an approximation, we study the entanglement property of Bell and Greenberger–Horne–Zeilinger (GHZ) states formed by such states. The corresponding entanglement properties are described by studying negativity and von Neumann entropy. The degree of entanglement will be degraded when the acceleration parameters increase. We find that the greater the number of particles in the entangled system, the more stable the system that is studied by the von Neumann entropy. The present results will be reduced to those in the case of the uniformly accelerating reference frame.

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

The Unruh effect can be considered a source of particle production. The idea has been widely employed in order to explain multiparticle production in hadronic and heavy-ion collisions at ultrarelativistic energies. The attractive feature of the application of the Unruh effect as a possible mechanism of the multiparticle production is the thermalized spectra of newly produced particles. In the present paper, the total entropy generated by the Unruh effect is calculated within the framework of information theory. In contrast to previous studies, here the calculations are conducted for the finite time of existence of the non-inertial reference frame. In this case, only a finite number of particles are produced. The dependence on the mass of the emitted particles is taken into account. Analytic expression for the entropy of radiated boson and fermion spectra is derived. We study also its asymptotics corresponding to low- and high-acceleration limiting cases. The obtained results can be further generalized to other intrinsic degrees of freedom of the emitted particles, such as spin and electric charge.

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.

Our starting point is the covariant coordinate transformation equation of a relativistic positioning system in Minkowski space–time that maps the receiver’s emission coordinates (proper times broadcast by the emitters) to its coordinates in some inertial reference frame. Bancroft’s analytical (closed-form) solution to the basic pseudorange navigation equations with four emitters is recovered, and the subjacent elements are geometrically interpreted. The case of four static beacons is analysed as a clarifying situation.

The International Association of Geodesy (IAG) aims to establish the International Height Reference System (IHRS) as one of its primary scientific objectives. Central to the realization of the IHRS is global vertical datum unification, which requires the connection of existing local vertical height reference systems (VHS) robustly and consistently. However, conventional methods are not suitable for estimating the offsets between two distant local height systems. In this paper, we propose a framework for connecting two local VHSs using ultraprecise clock frequency signal links between satellites and ground stations, referred to as the satellite frequency signal transmission (SFST) approach. The SFST approach allows for the direct determination of the geopotential and height differences between two ground datum stations without any location restrictions between the two VHSs. The simulation results show that the VHSs of China and the US can be unified with an accuracy of several centimeters, provided that the stability of atomic clocks used on-board the satellite and at on-ground datum locations reaches 4.8×10−17τ−1/2 for an averaging time τ (in seconds). We conclude that the SFST approach shows promise for achieving centimeter-level accuracy in unifying the global vertical height datum and represents a new paradigm for the realization of the IHRS.

We study the impact on the cosmic microwave background (CMB) landscape of peculiar rotational general relativistic effects. These effects, on galactic scales, do not possess a Newtonian analogue, and therefore could a priori impact CMB analysis. We find that the velocity inferred from the CMB dipole, under the kinematic interpretation, coincides with that measured by a stationary observer within the Milky Way and not with the one measured by the zero angular momentum observer. We show that the galaxy peculiar frame-dragging effects do not impact the standard CMB analysis, as these modify the multipole coefficients only at higher orders with respect to the dominant terms. Moreover, we prove that no general relativistic framework at the galactic scale patched within the standard cosmological model can account for the current tension on the CMB quadrupole amplitude.

In axistationary, asymptotically flat spacetimes, zero angular momentum observers (ZAMOs) define an absolute standard of non-rotation locally, as can be verified by the absence of any Sagnac effect for these observers. Nevertheless, we argue that on a global scale the only physically meaningful concept is that of relative rotation. The argument is substantiated by solving Einstein’s equations for an approximate thin shell model, where we maintain a degree of freedom, by relaxing the natural assumption of vanishing rotation at asymptotic infinity, at the outset of the analysis. The solution reveals that Einstein’s equations only determine differences in the rotation rate of ZAMOs, thereby establishing the concept of relative rotation globally. The interpretation of rotation as relative in a global context is inherently linked to the freedom to transform between coordinate systems rotating relative to each other, implying that an arbitrary ZAMO located at any radius may claim to be the one that is non-rotating on a global scale, and that the notion of an asymptotic Lorentz frame relative to which one may measure absolute rotation is devoid of any meaning. The concept of rotation in Kerr spacetime is then briefly discussed in the context of this interpretation.