Design considerations for future geodesy missions and for space laser interferometry

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Scale Factor Determination for the GRACE-Follow On Laser Ranging Interferometer including Thermal Coupling

The GRACE Follow-On satellites carry the very first inter-spacecraft Laser Ranging Interferometer (LRI). After more than four years in orbit, the LRI outperforms the sensitivity of the conventional Microwave Instrument (MWI). However, in the current data processing scheme, the LRI product still needs the MWI data to determine the unknown absolute laser frequency, representing the ruler for converting the raw phase measurements into a physical displacement in meters. In this paper, we derive formulas for precisely performing that conversion from the phase measurement into a range, accounting for a varying carrier frequency. Furthermore, the dominant errors due to knowledge uncertainty of the carrier frequency as well as uncorrected time biases are derived. In the second part, we address the dependency of the LRI on the MWI in the currently employed cross-calibration scheme and present three different models for the LRI laser frequency, two of which are largely independent of the MWI. Furthermore, we analyze the contribution of thermal variations on the scale factor estimates and the LRI-MWI residuals. A linear model called Thermal Coupling (TC) is derived that significantly reduces the differences between LRI and MWI to a level where the MWI observations limit the comparison.Comment: 26 pages, 15 figure

Revisiting the Light Time Correction in Gravimetric Missions Like GRACE and GRACE Follow-On

The gravity field maps of the satellite gravimetry missions GRACE (Gravity Recovery and Climate Experiment) 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 non-zero 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.Comment: This is a preprint of an open-access article published in Journal of Geodesy. The final authenticated version is available online at: https://doi.org/10.1007/s00190-021-01498-

Disturbances from Single Event Upsets in the GRACE Follow-On Laser Ranging Interferometer

The Gravity Recovery And Climate Experiment - Follow On (GRACE-FO) satellite mission (2018-now) hosts the novel Laser Ranging Interferometer (LRI), a technology demonstrator for proving the feasibility of laser interferometry for inter-satellite ranging measurements. The GRACE-FO mission extends the valuable climate data record of changing mass distribution in the system Earth, which was started by the original GRACE mission (2002-2017). The mass distribution can be deduced from observing changes in the distance of two low-earth orbiters employing interferometry of electromagnetic waves in the K-Band for the conventional K-Band Ranging (KBR) and in near-infrared for the novel LRI. This paper identifies possible radiation-induced Single Event Upset (SEU) events in the LRI phase measurement. We simulate the phase data processing within the Laser Ranging Processor (LRP) and use a template-based fitting approach to determine the parameters of the SEU and subtract the events from the ranging data. Over four years of LRI data, 29 of such events were identified and characterized

Evaluation of optical accelerometry for next generation gravimetry missions

Twenty years of gravity observations from the satellite missions GRACE, GOCE, GRACE-FO have provided unique data about mass redistribution processes in the Earth system, such as melting of Greenland's ice shields, sea level changes, underground water depletion, droughts, floods, etc. Ongoing climate change underlines the urgent need to continue this kind of observations utilizing Next Generation Gravimetry Missions (NGGM) with enhanced instruments. Here, we focus on accelerometers (ACC). Drifts of the electrostatic accelerometers (EA) are one of the limiting factors in the current space gravimetry missions dominating the error contribution at low frequencies (<1e-3 Hz). The focus of this study is on the modelling of enhanced EAs with laser-interferometric readout, so called "optical accelerometers" and evaluating their performance at Low Earth Orbits (LEO). Contrary to GRACE(-FO) or GOCE capacitive accelerometers, optical ones sense the motion of the test mass (TM) in one or more axes by applying laser interferometry. Combination of sensing in multiple directions and of several test masses would lead to enhanced gradiometry which would improve the determination of the static gravity field to a higher spatial resolution and may even enable to observe time-variable gravity changes. Our research is based on very promising results of the mission LISA-Pathfinder which has demonstrated the benefit of using a drag-free system in combination with optical accelerometry and UV TM discharge which allowed sensing of non-gravitational accelerations several orders of magnitude more accurate than it is realized in current gravity missions like GRACE-FO. This research project is carried out in close collaboration with the IGP and the DLR-SI, to provide - on the long run - a roadmap for improved angular and linear accelerometry for NGGM. In this presentation, we now introduce a framework for modeling enhanced EA with laser-interferometric readout mainly developed by IGP including major noise sources, like actuation noise, capacitive sensing, stiffness and thermal bias. Also, parametrization of the developed ACC model will be discussed including different TM weights and TM-electrode housing gaps. Finally, improved results of the recovered gravity field will be shown based on various mission scenarios applying optical accelerometry and gradiometry

Accelerated physical emulation of Bayesian inference in spiking neural networks

The massively parallel nature of biological information processing plays an important role for its superiority to human-engineered computing devices. In particular, it may hold the key to overcoming the von Neumann bottleneck that limits contemporary computer architectures. Physical-model neuromorphic devices seek to replicate not only this inherent parallelism, but also aspects of its microscopic dynamics in analog circuits emulating neurons and synapses. However, these machines require network models that are not only adept at solving particular tasks, but that can also cope with the inherent imperfections of analog substrates. We present a spiking network model that performs Bayesian inference through sampling on the BrainScaleS neuromorphic platform, where we use it for generative and discriminative computations on visual data. By illustrating its functionality on this platform, we implicitly demonstrate its robustness to various substrate-specific distortive effects, as well as its accelerated capability for computation. These results showcase the advantages of brain-inspired physical computation and provide important building blocks for large-scale neuromorphic applications.Comment: This preprint has been published 2019 November 14. Please cite as: Kungl A. F. et al. (2019) Accelerated Physical Emulation of Bayesian Inference in Spiking Neural Networks. Front. Neurosci. 13:1201. doi: 10.3389/fnins.2019.0120

Comparing GRACE-FO KBR and LRI Ranging Data with Focus on Carrier Frequency Variations

The GRACE Follow-On satellite mission measures distance variations between its two satellites in order to derive monthly gravity field maps, indicating mass variability on Earth on a scale of a few 100 km originating from hydrology, seismology, climatology and other sources. This mission hosts two ranging instruments, a conventional microwave system based on K(a)-band ranging (KBR) and a novel laser ranging instrument (LRI), both relying on interferometric phase readout. In this paper, we show how the phase measurements can be converted into range data using a time-dependent carrier frequency (or wavelength) that takes into account potential intraday variability in the microwave or laser frequency. Moreover, we analyze the KBR-LRI residuals and discuss which error and noise contributors limit the residuals at high and low Fourier frequencies. It turns out that the agreement between KBR and LRI biased range observations can be slightly improved by considering intraday carrier frequency variations in the processing. Although the effect is probably small enough to have little relevance for gravity field determination at the current precision level, this analysis is of relevance for detailed instrument characterization and potentially for future more precise missions

Satellite Gravity Field Recovery Using Variance-Covariance Information From Ocean Tide Models

Monthly gravity field recovery using data from the GRACE and GRACE Follow-On missions includes errors limiting the spatial and temporal resolution of the estimated gravity fields. The major error contributions, besides the noise of the accelerometer instruments, arise from temporal aliasing errors due to imperfections in the non-tidal atmospheric and oceanic de-aliasing models and ocean tide models. We derive uncertainty information for the eight major tidal constituents from five different ocean tide models and introduce it into the gravity field recovery process in terms of a constrained normal equation system while expanding the parameter space by additional tidal parameters to be adjusted. We prove the effectiveness of the ocean tide variance-covariance information through realistic simulations and we assess its potential based on microwave and laser interferometer observations from the GRACE Follow-On mission. We show that errors are reduced by more than 20% ocean wRMS for a Gaussian filter radius of 300 km if uncertainty information for ocean tides is considered and stochastic modeling of instrument errors is applied, compared to the latest GFZ release 6.1. Our results also show the limited visibility of the effectiveness of the ocean tide variance-covariance information due to the dominating error contribution of non-tidal atmospheric and oceanic mass variations. Additionally, we investigate the option of estimating ocean tide parameters over a 1-year period while including ocean tide uncertainty information in order to improve ocean tide background modeling

Satellite Gravity Field Recovery Using Variance-Covariance Information From Ocean Tide Models

Monthly gravity field recovery using data from the GRACE and GRACE Follow-On missions includes errors limiting the spatial and temporal resolution of the estimated gravity fields. The major error contributions, besides the noise of the accelerometer instruments, arise from temporal aliasing errors due to imperfections in the non-tidal atmospheric and oceanic de-aliasing models and ocean tide models. We derive uncertainty information for the eight major tidal constituents from five different ocean tide models and introduce it into the gravity field recovery process in terms of a constrained normal equation system while expanding the parameter space by additional tidal parameters to be adjusted. We prove the effectiveness of the ocean tide variance-covariance information through realistic simulations and we assess its potential based on microwave and laser interferometer observations from the GRACE Follow-On mission. We show that errors are reduced by more than 20% ocean wRMS for a Gaussian filter radius of 300 km if uncertainty information for ocean tides is considered and stochastic modeling of instrument errors is applied, compared to the latest GFZ release 6.1. Our results also show the limited visibility of the effectiveness of the ocean tide variance-covariance information due to the dominating error contribution of non-tidal atmospheric and oceanic mass variations. Additionally, we investigate the option of estimating ocean tide parameters over a 1-year period while including ocean tide uncertainty information in order to improve ocean tide background modeling