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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.

In a recent paper we discussed when it is possible to define reference frames nonrotating with respect to distant inertial reference objects (extension of the IAU reference systems to exact general relativity), and how to construct them. We briefly review the construction, illustrating it with further examples, and caution against the recent misuse of zero angular momentum observers (ZAMOs).

The problem of static seal leakage in a non-inertial reference system is different from that in a traditional inertial coordinate system in several ways. Although the seals and grooves remain relatively stationary, the overall motion of the equipment leads to an increase in the variance of the load fluctuations on the contact surfaces, and thus, leakage is more likely to occur at the sealing interfaces in a non-inertial reference system. This paper reviews and analyses the current related work from four aspects, namely, long-term modulus analysis of materials, analysis of loading spectral values, analysis of surface morphology characteristics, and the basis for leakage judgement. Based on these analyses, a new framework for leakage judgment specific to non-inertial systems is proposed. This framework addresses the increased variance in load distribution caused by non-inertial conditions, offering a targeted solution to the problem of seal leakage. Ultimately, the findings in this paper serve to enhance our understanding of the sealing behavior in dynamic systems, contributing to improved sealing performance and reliability in various applications.

Background Although digital mobility outcomes (DMOs) can be readily calculated from real-world data collected with wearable devices and ad-hoc algorithms, technical validation is still required. The aim of this paper is to comparatively assess and validate DMOs estimated using real-world gait data from six different cohorts, focusing on gait sequence detection, foot initial contact detection (ICD), cadence (CAD) and stride length (SL) estimates. Methods Twenty healthy older adults, 20 people with Parkinson’s disease, 20 with multiple sclerosis, 19 with proximal femoral fracture, 17 with chronic obstructive pulmonary disease and 12 with congestive heart failure were monitored for 2.5 h in the real-world, using a single wearable device worn on the lower back. A reference system combining inertial modules with distance sensors and pressure insoles was used for comparison of DMOs from the single wearable device. We assessed and validated three algorithms for gait sequence detection, four for ICD, three for CAD and four for SL by concurrently comparing their performances (e.g., accuracy, specificity, sensitivity, absolute and relative errors). Additionally, the effects of walking bout (WB) speed and duration on algorithm performance were investigated. Results We identified two cohort-specific top performing algorithms for gait sequence detection and CAD, and a single best for ICD and SL. Best gait sequence detection algorithms showed good performances (sensitivity > 0.73, positive predictive values > 0.75, specificity > 0.95, accuracy > 0.94). ICD and CAD algorithms presented excellent results, with sensitivity > 0.79, positive predictive values > 0.89 and relative errors < 11% for ICD and < 8.5% for CAD. The best identified SL algorithm showed lower performances than other DMOs (absolute error < 0.21 m). Lower performances across all DMOs were found for the cohort with most severe gait impairments (proximal femoral fracture). Algorithms’ performances were lower for short walking bouts; slower gait speeds (< 0.5 m/s) resulted in reduced performance of the CAD and SL algorithms. Conclusions Overall, the identified algorithms enabled a robust estimation of key DMOs. Our findings showed that the choice of algorithm for estimation of gait sequence detection and CAD should be cohort-specific (e.g., slow walkers and with gait impairments). Short walking bout length and slow walking speed worsened algorithms’ performances. Trial registration ISRCTN – 12246987.

We present a unified post-Newtonian framework for relativistic timing and coordinate transformations across the Barycentric, Geocentric, and Lunicentric Celestial Reference Systems (LCRS) and six timescales: Barycentric Coordinate Time (TCB), Geocentric Coordinate Time (TCG), Terrestrial Time (TT), Barycentric Dynamical Time (TDB), Lunicentric Coordinate Time (TCL)​​​, and Lunar Time (TL). Following IAU Resolution II (2024), we implement an LCRS metric with time coordinate TCL, linked to TCB via the IAU B1.5 prescription with lunar quantities. We truncate all series to retain contributions above a fractional threshold of 5 × 10−18 and timing terms exceeding 0.1 ps, expanding the lunar gravity to degree ℓ = 9 with Love number variations and including external tidal and inertial multipoles through the octupole. We derive closed-form mappings among TCB, TCG, TT, TDB, TCL, and TL, giving proper-to-coordinate time conversions and one-/two-way time-transfer corrections at subpicosecond accuracy. Secular rates and periodic perturbations from kinematic dilation, lunar monopole and multipoles, Earth tides, and gravitomagnetism are evaluated for clocks on the lunar surface in Very Low and Low Lunar Orbits, in elliptical lunar frozen orbits, at the Earth–Moon L1 point, and in Near-rectilinear Halo Orbits (NRHOs). Harmonics through ℓ = 9 and tides through ℓ = 8 suffice to meet 5 × 10−18 stability in deep cislunar regimes (e.g., NRHO, L1), supporting subpicosend synchronization and centimeter-level navigation, whereas near-surface and Very Low Lunar Orbits require much higher degree (typically ℓmax≳300 ). The framework implements the IAU LCRS/TCL prescription and supplies accuracy budgets for high-precision time/frequency transfer, relativistic geodesy, quantum links, and fundamental tests beyond low Earth orbit.

Inertial Reference System (IRS) is one of the important onboard systems; it can provide the attitude, heading, angle rate and accelerations, etc. to the display system, flight control system and other systems on the aircraft; and it can be the navigation source of the flight management system to provide the position data. The consequences of IRS parameters failure effects are difficult to determine. This paper applies the cascading effect analysis method to carry out IRS parameters failure safety assessment. A method is given to identify the initiating state of the IRS parameters. An initiating state of IRS parameters is taken as an example to analyze safety effects and obtain the aircraft-level safety classification. The safety classification is compared with source analysis to determine whether the aircraft safety requirement is met.

The orientation dynamics of inertialess prolate and oblate spheroidal particles in a directly simulated spanwise-rotating turbulent channel flow has been investigated by means of an Eulerian–Lagrangian point-particle approach. The channel rotation and the particle shape were parameterized using a rotation number Ro and the aspect ratio λ, respectively. Eleven particle shapes 0.05 ≤ λ ≤ 20 and four rotation rates 0 ≤ Ro ≤ 10 have been examined. The spheroidal particles retained their almost isotropic orientation in the core region of the channel, despite the significant mean shear rate set up by the Coriolis force. Irrespective of channel rotation rate Ro, rod-like spheroids tend to align in the streamwise direction, while disk-like particles are oriented in the wall-normal direction. These trends were accentuated with increasing departure from sphericity λ = 1. The changeover from the isotropic orientation mode in the centre to the highly anisotropic near-wall orientation mode commenced further away from the suction-side wall with increasing Ro, whereas the particle orientations on the pressure side of the rotating channel remained essentially unaffected by Ro. We observed that the alignments of the fluid rotation vector with the Lagrangian stretching direction were similarly unaffected by the imposed system rotation, except that the de-alignment set in deeper into the core at high Ro. This contrasts with the well-known substantial impact of system rotation on the velocity and vorticity fields. Similarly, slender rods and flatter disks were aligned with the Lagrangian stretching and compression directions, respectively, for all Ro considered, except in the vicinity of the walls. The typical near-wall de-alignment extended considerably further away from the suction-side wall at high Ro. We conjecture that this phenomenon reflects a change in the relative importance of mean shear and small-scale turbulence caused by the Coriolis force. Preferential particle alignment with Lagrangian stretching and compression directions are known from isotropic and anisotropic turbulence in inertial reference systems. The present results demonstrate the validity of this principle also in a non-inertial system.

Continuous-variable quantum key distribution has gradually shifted from optical fiber communication to space communication. In free-space quantum communication, the influence of gravity cannot be ignored. In light of the influence of gravity, this study assesses the efficacy of the thermal-state continuous-variable quantum key distribution (QKD) protocol in a non-inertial reference frame. This differs from the conventional scenario in an inertial reference frame, where pure vacuum Gaussian states are employed without consideration of the influence of gravity. This study examines the potential and challenges of quantum key distribution in the presence of gravitational effects. The feasibility of generating the key under the influence of gravity through the lens of quantum state transfer in a non-inertial reference system is also analyzed. It presents a comprehensive mathematical derivation and simulation of the secret key rate for maintaining a positive rate under specific conditions. Furthermore, it presents a detailed implementation plan for thermal-state quantum key distribution in a non-inertial reference frame, particularly in the context of gravity. It offers valuable insights into the performance of quantum communication in unconventional settings.

The increasing importance of terrestrial gravimetry in monitoring global change processes, in providing a reference for satellite measurements and in applications in metrology necessitates a stable reference system reflecting the measurement accuracy achievable by modern gravimeters. Therefore, over the last decade, the International Association of Geodesy (IAG) has developed a system to achieve accurate, homogeneous, long-term global recording of Earth’s gravity, while taking advantage of the potential of today’s absolute gravity measurements. The current status of the International Gravity Reference System and Frame is presented as worked out by the IAG Joint Working Group 2.1.1 “Establishment of a global absolute gravity reference system” during the period 2015–2019. Here, the system is defined by the instantaneous acceleration of free-fall, expressed in the International System of Units (SI) and a set of conventional corrections for the time-independent components of gravity effects. The frame as the systems realization includes a set of conventional temporal gravity corrections which represent a uniform set of minimum requirements. Measurements with absolute gravimeters, the traceability of which is ensured by comparisons and monitoring at reference stations, provide the basis of the frame. A global set of such stations providing absolute gravity values at the microgal level is the backbone of the frame. Core stations with at least one available space geodetic technique will provide a link to the terrestrial reference frame. Expanded facilities enabling instrumental verification as well as repeated regional and additional comparisons will complement key comparisons at the level of the International Committee for Weights and Measures (CIPM) and ensure a common reference and the traceability to the SI. To make the gravity reference system accessible to any user and to replace the previous IGSN71 network, an infrastructure based on absolute gravity observations needs to be built up. This requires the support of national agencies, which are encouraged to establish compatible first order gravity networks and to provide information about existing absolute gravity observations.