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  • Atomic gradiometry  (1)
  • Forward gravity modeling  (1)
  • Frequency stability  (1)
  • GRACE follow-on  (1)
  • 1
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    Performance of miniaturized atomic clocks in static laboratory and dynamic flight environments (2020)
    Springer Berlin Heidelberg
    Details
    Publication Date: 2023-06-16
    Description: Miniaturized atomic clocks with high frequency stability as local oscillators in global navigation satellite system (GNSS) receivers promise to improve real-time kinematic applications. For a number of years, such oscillators are being investigated regarding their overall technical applicability, i.e., transportability, and performance in dynamic environments. The short-term frequency stability of these clocks is usually specified by the manufacturer, being valid for stationary applications. Since the performance of most oscillators is likely degraded in dynamic conditions, various oscillators are tested to find the limits of receiver clock modeling in dynamic cases and consequently derive adequate stochastic models to be used in navigation. We present the performance of three different oscillators (Microsemi MAC SA.35m, Spectratime LCR-900 and Stanford Research Systems SC10) for static and dynamic applications. For the static case, all three oscillators are characterized in terms of their frequency stability at Physikalisch-Technische Bundesanstalt, Germany's national metrology institute. The resulting Allan deviations agree well with the manufacturer's data. Furthermore, a flight experiment was conducted in order to evaluate the performance of the oscillators under dynamic conditions. Here, each oscillator is replacing the internal oscillator of a geodetic-grade GNSS receiver and the stability of the receiver clock biases is determined. The time and frequency offsets of the oscillators are characterized with regard to the flight dynamics recorded by a navigation-grade inertial measurement unit. The results of the experiment show that the frequency stability of each oscillator is degraded by about at least one order of magnitude compared to the static case. Also, the two quartz oscillators show a significant g-sensitivity resulting in frequency shifts of − 1.2 × 10−9 and + 1.5 × 10−9, respectively, while the rubidium clocks are less sensitive, thus enabling receiver clock modeling and strengthening of the navigation performance even in high dynamics.
    Description: Bundesministerium für Wirtschaft und Energie http://dx.doi.org/10.13039/501100006360
    Description: Gottfried Wilhelm Leibniz Universität Hannover (1038)
    Keywords: ddc:526 ; Allan variance ; Miniaturized atomic clocks ; Frequency stability ; Flight navigation ; GNSS
    Language: English
    Type: doc-type:article
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    CITATION GEO-LEO
  • 2
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    Using quantum optical sensors for determining the Earth’s gravity field from space (2020)
    Springer Berlin Heidelberg
    Details
    Publication Date: 2023-07-03
    Description: Quantum optical technology provides an opportunity to develop new kinds of gravity sensors and to enable novel measurement concepts for gravimetry. Two candidates are considered in this study: the cold atom interferometry (CAI) gradiometer and optical clocks. Both sensors show a high sensitivity and long-term stability. They are assumed on board of a low-orbit satellite like gravity field and steady-state ocean circulation explorer (GOCE) and gravity recovery and climate experiment (GRACE) to determine the Earth’s gravity field. Their individual contributions were assessed through closed-loop simulations which rigorously mapped the sensors’ sensitivities to the gravity field coefficients. Clocks, which can directly obtain the gravity potential (differences) through frequency comparison, show a high sensitivity to the very long-wavelength gravity field. In the GRACE orbit, clocks with an uncertainty level of 1.0 × 10−18 are capable to retrieve temporal gravity signals below degree 12, while 1.0 × 10−17 clocks are useful for detecting the signals of degree 2 only. However, it poses challenges for clocks to achieve such uncertainties in a short time. In space, the CAI gradiometer is expected to have its ultimate sensitivity and a remarkable stability over a long time (measurements are precise down to very low frequencies). The three diagonal gravity gradients can properly be measured by CAI gradiometry with a same noise level of 5.0 mE/√Hz. They can potentially lead to a 2–5 times better solution of the static gravity field than that of GOCE above degree and order 50, where the GOCE solution is mainly dominated by the gradient measurements. In the lower degree part, benefits from CAI gradiometry are still visible, but there, solutions from GRACE-like missions are superior.
    Description: Deutsche Forschungsgemeinschaft
    Description: http://icgem.gfz-potsdam.de/tom_longtime
    Description: https://earth.esa.int/web/guest/-/goce-data-access-7219
    Description: ftp://podaac.jpl.nasa.gov/allData/grace/L1B/JPL/
    Keywords: ddc:526 ; Quantum optical sensors ; Optical clocks ; Relativistic geodesy ; Atomic gradiometry ; Gravity field
    Language: English
    Type: doc-type:article
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  • 3
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    Gravity Field Modeling Using Tesseroids with Variable Density in the Vertical Direction (2020)
    Springer Netherlands
    Details
    Publication Date: 2023-06-09
    Description: We present an accurate method for the calculation of gravitational potential (GP), vector (GV), and gradient tensor (GGT) of a tesseroid, considering a density model in the form of a polynomial up to cubic order along the vertical direction. The method solves volume integral equations for the gravitational effects due to a tesseroid by the Gauss–Legendre quadrature rule. A two-dimensional adaptive subdivision technique, which automatically divides the tesseroids near the computation point into smaller elements, is applied to improve the computational accuracy. For those tesseroids having small vertical dimensions, an extension technique is additionally utilized to ensure acceptable accuracy, in particular for the evaluation of GV and GGT. Numerical experiments based on spherical shell models, for which analytical solutions exist, are implemented to test the accuracy of the method. The results demonstrate that the new method is capable of computing the gravitational effects of the tesseroids with various horizontal and vertical dimensions as well as density models, while the evaluation point can be on the surface of, near the surface of, outside the tesseroid, or even inside it (only suited for GP and GV). Thus, the method is attractive for many geodetic and geophysical applications on regional and global scales, including the computation of atmospheric effects for terrestrial and satellite usage. Finally, we apply this method for computing the topographic effects in the Himalaya region based on a given digital terrain model and the global atmospheric effects on the Earth’s surface by using three polynomial density models which are derived from the US Standard Atmosphere 1976.
    Keywords: ddc:550.2 ; Forward gravity modeling ; Gauss–Legendre quadrature ; Tesseroids ; Polynomial density model ; Topographic and atmospheric effects
    Language: English
    Type: doc-type:article
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    CITATION GEO-LEO
  • 4
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    Revisiting the light time correction in gravimetric missions like GRACE and GRACE follow-on (2021)
    Springer Berlin Heidelberg
    Details
    Publication Date: 2023-06-22
    Description: The gravity field maps of the satellite gravimetry missions Gravity Recovery and Climate Experiment (GRACE ) and GRACE Follow-On are derived by means of precise orbit determination. The key observation is the biased inter-satellite range, which is measured primarily by a K-Band Ranging system (KBR) in GRACE and GRACE Follow-On. The GRACE Follow-On satellites are additionally equipped with a Laser Ranging Interferometer (LRI), which provides measurements with lower noise compared to the KBR. The biased range of KBR and LRI needs to be converted for gravity field recovery into an instantaneous range, i.e. the biased Euclidean distance between the satellites’ center-of-mass at the same time. One contributor to the difference between measured and instantaneous range arises due to the nonzero travel time of electro-magnetic waves between the spacecraft. We revisit the calculation of the light time correction (LTC) from first principles considering general relativistic effects and state-of-the-art models of Earth’s potential field. The novel analytical expressions for the LTC of KBR and LRI can circumvent numerical limitations of the classical approach. The dependency of the LTC on geopotential models and on the parameterization is studied, and afterwards the results are compared against the LTC provided in the official datasets of GRACE and GRACE Follow-On. It is shown that the new approach has a significantly lower noise, well below the instrument noise of current instruments, especially relevant for the LRI, and even if used with kinematic orbit products. This allows calculating the LTC accurate enough even for the next generation of gravimetric missions.
    Description: Max-Planck-Gesellschaft http://dx.doi.org/10.13039/501100004189
    Description: National Natural Science Foundation of China http://dx.doi.org/10.13039/501100001809
    Keywords: ddc:526 ; GRACE follow-on ; Light time correction ; General relativity ; Laser interferomery ; K-band ranging
    Language: English
    Type: doc-type:article
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