Low-frequency calibration of accelerometers by rotation in the gravitational field at NIST

In this paper, we investigated the spreading of shear wave in an anisotropic non-homogeneous elastic medium under effect of dry sand, rotation, gravity, primary stress, and magnetic field. We have reached equation of variation of shear wave velocity c1 in an anisotropic incompressible medium according to sand, rotation, gravity, primary stress, and magnetic field, then we used graphs to illustrate to show the effect of direction of spreading of shear wave. The results indicate that the effect of dry sand, rotation, gravity, primary stress, and magnetic field on the spreading of shear wave in an anisotropic inhomogeneous elastic medium are very pronounced. The results have been obtained are discussed and presented visually, the results demonstrate that the effect of sand, gravity field, primary stress, magnetic field, anisotropy and rotation are noticeable.

The propagation of magneto-thermoelastic plane waves in an initially stressed, homogeneous orthotropic, conducting half-space under a magnetic field, rotation and gravity field have been investigated. The generalized theory of thermoelasticity is employed, by assuming the mechanical behavior as dynamic, to study the problem. The Lame’s potential is used to obtain the frequency equation that determines the velocity of Rayleigh waves that obtained as a real part and the attenuation coefficient as an imaginary part under the rotation, magnetic field, initial stress and gravity field. Numerical results have been given and illustrated graphically for each case considered. Dispersion curves of wave propagation are represented graphically in different theories of thermoelasticity. The results indicate that the effect of rotation, initial stress and gravity field are very pronounced. Comparison is made with the results predicted by the theory of thermoelasticity in the absence of rotation, initial stress and gravity field.

The uncertainties calculation procedure for the estimation of errors when the fringe counting method is used to get the sensitivity of standard accelerometers is developed. The fringe counting method is used in the frequency range from 50 to 800 Hz and into a dynamic range from 20 to 100 m s−2. Also, the reference condition is set up at 160 Hz and 50 m s−2, where the main objective is to get the lowest uncertainty between all the frequency and dynamic ranges mentioned above. This calculation procedure agrees with both the ‘‘Guide to the expression of uncertainty in measurement’’ and the ISO 5347-1 ‘‘Primary vibration calibration by laser interferometry.’’ Furthermore, type B uncertainties are received from specific technical information from the equipment used during the calibration procedure and the type A uncertainty is received from periodic measurements performed on the standard accelerometer which have been monitored. Data from primary calibrations have been used to validate the estimation of uncertainties. Moreover, this paper shows the differences on the levels of error sources involved in a standard accelerometer calibration.

Focus on sensors

As a key component in motion state sensing, the accuracy of accelerometers directly affects the performance and safety of their systems. However, their sensitivity can be influenced due to various factors during operation, necessitating both pre-deployment and periodic calibration. Traditional primary calibration methods rely on laser interferometers, yet their trueness and stability are compromised by environmental disturbances affecting the laser wavelength, making on-site traceability challenging. Addressing these issues, this study combines a Cr self-traceable grating with a homodyne Littrow grating interferometer and primary vibration calibration technique. Leveraging the high line density, stability, and traceability of the self-traceable grating, it achieves high accuracy and on-site traceable calibration. In experiments, the effectiveness of this calibration system was validated using commercial accelerometers, achieving a measurement uncertainty of 0.25%. This calibration technique not only enhances the accuracy and environmental adaptability of accelerometer calibration but also addresses the critical issue of on-site traceability, representing the future direction of in-field accelerometer calibration.

Abstract. Since the early days of satellite geodesy energy balance based methods for gravity field determination have been considered. If non-conservative forces are known the Hamiltonian along the orbit is a constant of the motion. Thus the gravity field can be determined if position and velocity of the satellite are known and accelerometer measurements are available to model the non-conservative part. CHAMP is the first satellite that provides the user with those three kinds of data nearly continuously. Numerical investigations using real CHAMP data are presented to show the feasibility of the method. Using a semi-analytical approach the gravity field can be determined efficiently by a 2D-Fourier method. Those fast computations also give way to application of the method not only to a full gravity field recovery but also, e.g. for quick-look and validation of SST observations for satellite missions like CHAMP, GRACE or GOCE. The method can also be used for estimation of accelerometer calibration parameters.Key words. gravity field, energy balance, Jacobi-integral, non-conservative forces, accelerometer calibration, CHAMP

To investigate the influence of K-Band microwave ranging (KBR) and Laser Ranging Interferometer (LRI) inter-satellite range-rates from the GRACE-FO mission on the recovery of gravity fields, we explores two distinct methods for accelerometer scale estimation, namely diagonal matrix parameterization and full matrix parameterization. Integrating both KBR and LRI data from GRACE-FO into gravity field recovery, we have derived six new time series of monthly gravity field solutions based on two different accelerometer calibration approaches, entitled KBRLRI_Com (incorporating both KBR and LRI data), KBR_Only (using pure KBR data), LRI_Only (solely utilizing LRI data) truncate to degree and order 60 over the period from January 2019 to June 2022. Analyses of KBRLRI_Com, KBR_Only, and LRI_Only reveal the following findings: (1) LRI demonstrates significant advantages over KBR in both diagonal and full scale matrix scenarios, across the time and frequency domains, which shows lower root mean square (RMS) values of the post-fit residuals in the time domain and substantially lower noise at higher frequencies; (2) the comparison between KBRLRI_Com, KBR_Only, and LRI_Only in terms of geoid degree error suggests that KBRLRI_Com agrees well with KBR_Only and LRI_Only at the low degrees (below degree 30), while effectively reducing the high-frequency noise, especially when the diagonal scale matrices are employed; the benefit of KBRLRI_Com solution is mainly attributed to the enhanced quantity of ranging observations. (3) by analyzing the signal and noise over the globe, ocean, Australian continent, and Amazon and Ganges river basins, we find that KBRLRI_Com is highly consistent with KBR_Only and LRI_Only in terms of spatial signals, while KBRLRI_Com exhibits less spatial noise; when employing diagonal and full matrices, the noise of gravity field solutions derived by incorporating LRI data is mitigated by 8.8% and 3.9% over the global ocean compared to KBR_Only, as well as 7.6% and 3.2% in the Australian continent; especially in the diagonal matrix case, the incorporation of LRI measurements for calculating monthly gravity fields results in a more pronounced decrease of spatial noise. (4) in the oceanic region, KBR_Only and LRI_Only have average RMS values of 11.3 cm and 11.6 cm in diagonal matrices, respectively, and 10.2cm and 11.6cm in the full matrix, indicating a generally comparable level of accuracy between the two models.

Contribution analysis of the addition of laser ranging interferometry on GRACE-FO gravity field estimation under different accelerometer calibration schemes

National Metrology Institutes (NMIs) worldwide make use of laser interferometry in compliance with the new International Standard ISO 16063-1 1 : 1999 to realize and disseminate the unit and the associated scale of the physical quantity of acceleration. By convention, the dissemination has up to now been carried out by primary vibration calibration of reference standard accelerometers as are used in accredited calibration laboratories to calibrate working standards by comparison. The calibration and measurement capabilities (CMCs) of the NMIs are published in the BIPM Key Comparison Database, Appendix C (cf. http://www.bipm.org, 2001). Recently, special commercial laser vibrometers have been developed which comply with the ISO standard and, consequently, may be applied as reference standards at any level of the traceability chain provided they are traced back to appropriate national standards and are provided with adequate uncertainty budgets. Though it may be expected that all calibration laboratories (NMIs included) establish uncertainty budgets in compliance with the ISO Guide to the Expression of Uncertainty in Measurement (GUM), the accuracy attained can be reliably assessed only by appropriate comparison measurements. A general account is given of the state of the art in vibration measurements and transducer calibration using laser interferometry, focusing on comparison results which have confirmed the lowest measurement uncertainty achieved so far. Results of vibration measurements and calibrations obtained by different interferometric methods will be presented. An analysis of international and regional comparison measurements (accelerometer calibrations) will be reported on.

In the framework of the EU-funded project Met4FoF Metrology for the Factory of the Future a method was developed to perform primary magnitude and phase calibration of accelerometers. The validation of the developed associated hard- and software, which is designed to complement conventional primary calibration systems, is demonstrated based on a comparison measurement between the project partners CEM and PTB. The results show that the statistical distribution of results is only a minor contribution to uncertainty. An evaluation of the comparison based on the conventional procedure and established CMCs proofed a good consistency between the two laboratories, although the utilized sensor was (only) industrial grade quality.

This paper aims to investigate the influence of rotation, initial stress and gravity field on the propagation of Rayleigh waves in a homogeneous orthotropic elastic medium. The government equations and Lame’s potentials are used to obtain the frequency equation which determines the velocity of Rayleigh waves, including rotation, initial stress and gravity field, in a homogeneous, orthotropic elastic medium has been investigated. The numerical results analyzing the frequency equation are discussed and presented graphically. It is important to note that the Rayleigh wave velocity in an orthotropic elastic medium increases a considerable amount in comparison to the Rayleigh wave velocity in an isotropic material. The results indicate that the effects of rotation, initial stress and gravity field on Rayleigh wave velocity are very pronounced.

TheBepiColombomission toMercury is an ESA/JAXAcornerstonemission, consisting of two spacecraft in orbit around Mercury addressing several scientific issues. One spacecraft is the Mercury Planetary Orbiter, with full instrumentation to perform radio science experiments. Very precise radio tracking from Earth, on-board accelerometer and optical measurements will provide large data sets. From these it will be possible to study the global gravity field of Mercury and its tidal variations, its rotation state and the orbit of its centre of mass. With the gravity field and rotation state, it is possible to constrain the internal structure of the planet. With the orbit of Mercury, it is possible to constrain relativistic theories of gravitation. In order to assess that all the scientific goals are achievable with the required level of accuracy, full cycle numerical simulations of the radio science experiment have been performed. Simulated tracking, accelerometer and optical camera data have been generated, and a long list of variables including the spacecraft initial conditions, the accelerometer calibrations and the gravity field coefficients have been determined by a least-squares fit. The simulation results are encouraging: the experiments are feasible at the required level of accuracy provided that some critical terms in the accelerometer error are moderated. We will show that BepiColombo will be able to provide at least an order of magnitude improvement in the knowledge of Love number k2, libration amplitudes and obliquity, along with a gravity field determination up to degree 25 with a signal-to-noise ratio of 10.

Primary vibration calibration according to ISO 16063 can be carried out in several ways using different methods. Because of the wide frequency range and the possibility to calibrate sensitivity magnitude and phase, method 3 of part 21 of the international standard is mostly used in practice. Several requirements for components, system integration and control ofthe system must be met to achieve the goals ofthe standard and obtain low uncertainties in measurement and calibration. Illustrated by the CS18P primary calibration system of SPEKTRA, the main requirements, special problems and well-investigated solutions will be discussed. It will be shown that the all-digital vibrometer of Polytec plays an important part but, in addition to that, system integration and optimization of all components must be implemented with great care by calibration specialists. Our paper comes to the conclusion that, for primary calibration, high quality components alone will not be enough. It is necessary to integrate these components in an optimized system that takes into consideration all requirements and influences and so allows to reduce the uncertainties ofthe calibration procedure to the lowest possible values.

The present paper is devoted to investigate the influence of the rotation, thermal field, initial stress, gravity field, electromagnetic and voids on the reflection of P wave under three models of generalized thermoelasticity: Classical and Dynamical coupled model (CD), Lord-Shulman model (LS), Green-Lindsay model (GL), The boundary conditions at stress-free thermally insulated surface are satisfied to obtain Algebraic system of four equations in the reflection coefficients of various reflected waves. It is shown that there exist four plane waves; P 1, P 2, P 3 and P 4. In addition, the reflection coefficients from insulated and isothermal stress-free surface for the incident P wave are obtained. Finally, numerical values of the complex modulus of the reflection coefficients are visualized graphically to display the effects of the rotation, initial stress, gravity field magnetic field, thermal relaxation times and voids parameters.

Primary accelerometer calibration with two-axis automatic positioning stage