Estimating low resolution gravity fields at short time intervals to reduce temporal aliasing errors

The Gravity Recovery and Climate Experiment (GRACE) satellite mission has been estimating temporal changes in the Earth’s gravitational field since its launch in 2002. While it is not yet fully resolved what the limiting source of error is for GRACE, studies on future missions have shown that temporal aliasing errors due to undersampling signals of interest (such as hydrological variations) and errors in atmospheric, ocean, and tide models will be a limiting source of error for missions taking advantage of improved technologies (flying drag-free with a laser interferometer). This paper explores the option of reducing the effects of temporal aliasing errors by directly estimating low degree and order gravity fields at short time intervals, ultimately resulting in data products with improved spatial resolution. Three potential architectures are considered: a single pair of polar orbiting satellites, two pairs of polar orbiting satellites, and a polar orbiting pair of satellites coupled with a lower inclined pair of satellites. Results show that improvements in spatial resolution are obtained when one estimates a low resolution gravity field every two days for the case of a single pair of satellites, and every day for the case of two polar pairs of satellites. However, the spatial resolution for these cases is still lower than that provided by simply destriping and smoothing the solutions via standard GRACE post-processing techniques. Alternately, estimating daily gravity fields for the case of a polar pair of satellites coupled with a lower inclined pair results in solutions with superior spatial resolution than that offered by simply destriping and smoothing the solutions.     

Finding the suitable drag-free acceleration noise level for future low-low satellite-to-satellite tracking geodesy missions

This paper evaluates the impact of residual acceleration noise on the estimation of the Earth’s time-varying gravity field for future low-low satellite-to-satellite tracking missions. The goal is to determine the maximum level of residual acceleration noise that does not adversely affect the estimation error. The Gravity Recovery And Climate Experiment (GRACE) has provided monthly average gravity field solutions in spherical harmonic coefficients for more than a decade. It provides information about land and ocean mass variations with a spatial resolution of ～350?km and with an accuracy within 2?cm throughout the entire Earth. GRACE Follow-on was launched in May 2018 to advance the work of GRACE and to test a new laser ranging interferometer, which measures the range between the two satellites with higher precision than the K-Band ranging system used in GRACE. Moreover, there have been simulation studies that show, an additional pair of satellites in an inclined orbit increases the sampling frequency and reduces temporal aliasing errors. Given the fact that future missions will likely continue to use the low-low satellite-to-satellite tracking formation with laser ranging interferometry, it is expected that the residual acceleration noise will become one of the largest error contributor for the time-variable gravity field solution. We evaluate three different levels of residual acceleration noise based on demonstrated drag-free systems to find a suitable drag-free performance target for upcoming geodesy missions. We analyze both a single collinear polar pair and the optimal double collinear pair of drag-free satellites and assume the use of a laser ranging interferometer. A partitioned best linear unbiased estimator that was developed, incorporating several novel features from the ground up is used to compute the solutions in terms of spherical harmonics. It was found that the suitable residual acceleration noise level is around 2?×?10^?12?ms^?2?Hz^?1/2. Decreasing the acceleration noise below this level did not result in more accurate gravity field solutions for the chosen mission architecture.     

深空卫星重力测量计划研究综述

地球卫星重力测量计划CHAMP(CHAllenging Minisatellite Payload)、GRACE(Gravity Recovery and Climate Experiment)、GOCE(Gravity field and steady-state Ocean Circulation Explorer)和月球卫星重力测量计划(Gravity Recovery and Interior Laboratory,GRAIL)的成功实施,以及下一代地球重力卫星(GRACE Follow-On)的即将发射昭示着我们将迎来一个前所未有的高精度和高空间分辨的深空卫星重力探测时代。围绕深空卫星重力测量的研究背景、必要性、可行性、卫星重力反演软件平台构建、轨道摄动和未来研究方向开展了研究论证。研究表明:深空卫星重力测量作为新世纪重力探测技术,在精化量体重力场、提高惯性导航精度、天体动力学、天体物理学和军事技术的研究,以及促进国民经济发展和提高社会效益等方面具有广泛的应用前景。     

Recovery of the Earth’s gravity field from formation-flying satellites: Temporal aliasing issues

Temporal and mean gravity field models derived from the twin-satellite, leader–follower mission GRACE have provided a new type of information for Earth sciences. In this contribution, we study the potential of various alternative satellite formations for gravity field determination in the post-GRACE era in a simulation environment. In particular, the effects of spherical harmonic truncation and of temporal aliasing in the processing of gravity products from such future formations are investigated.     

Mapping mean lake surface from satellite altimetry and GPS kinematic surveys

Lake water height is a key variable in water cycle and climate change studies, which is achievable using satellite altimetry constellation. A method based on data processing of altimetry from several satellites has been developed to interpolate mean lake surface (MLS) over a set of 22 big lakes distributed on the Earth. It has been applied on nadir radar altimeters in Low Resolution Mode (LRM: Jason-3, Saral/AltiKa, CryoSat-2) in Synthetic Aperture Radar (SAR) mode (Sentinel-3A), and in SAR interferometric (SARin) mode (CryoSat-2), and on laser altimetry (ICESat). Validation of the method has been performed using a set of kinematic GPS height profiles from 18 field campaigns over the lake Issykkul, by comparison of altimetry’s height at crossover points for the other lakes and using the laser altimetry on ICESat-2 mission. The precision reached ranges from 3 to 7 cm RMS (Root Mean Square) depending on the lakes. Currently, lake water level inferred from satellite altimetry is provided with respect to an ellipsoid. Ellipsoidal heights are converted into orthométric heights using geoid models interpolated along the satellite tracks. These global geoid models were inferred from geodetic satellite missions coupled with absolute and regional anomaly gravity data sets spread over the Earth. However, the spatial resolution of the current geoid models does not allow capturing short wavelength undulations that may reach decimeters in mountaineering regions or for rift lakes (Baikal, Issykkul, Malawi, Tanganika). We interpolate in this work the geoid height anomalies with three recent geoid models, the EGM2008, XGM2016 and EIGEN-6C4d, and compare them with the Mean Surface of 22 lakes calculated using satellite altimetry. Assuming that MLS mimics the local undulations of the geoid, our study shows that over a large set of lakes (in East Africa, Andean mountain and Central Asia), short wavelength undulations of the geoid in poorly sampled areas can be derived using satellite altimetry. The models used in this study present very similar geographical patterns when compared to MLS. The precision of the models largely depends on the location of the lakes and is about 18 cm, in average over the Earth. MLS can serve as a validation dataset for any future geoid model. It will also be useful for validation of the future mission SWOT (Surface Water and Ocean Topography) which will measure and map water heights over the lakes with a high horizontal resolution of 250 by 250 m.     

Earth gravity model improvement: An alternative method for Doppler-tracked satellites

A new method of Earth gravity model improvement based on an analytical formulation of Doppler residuals is presented here in prospect of future geodetic and altimetric missions (DORIS, TOPEX/POSEIDON, ERS1). After an intermediate step of orbit improvement, disturbing forces due to gravity field mismodeling are recovered above tracking stations at satellite altitude. Some significant simulation results for SEASAT and DORIS are presented.     

Improved kHz-SLR tracking techniques and orbit quality analysis for LEO missions

Satellite gravity field missions such as CHAMP, GRACE and GOCE are designed as low Earth orbiting spacecraft (LEO) with orbit heights of about 250–500 km. The challenging mission objectives require a very precise knowledge of the satellite orbit position in space. For these missions precise orbit information is typically provided by GPS satellite-to-satellite tracking (SST) observations supported by satellite laser ranging (SLR).     

Modeling and analysis of Earth’s gravity field measurement performance by inner-formation flying system

The Earth’s gravity field can be measured with high precision by constructing the purely gravitational orbit of the inner-satellite in Inner-formation Flying System (IFS), which is independently proposed by Chinese scholars and offers a new way to carry out gravity field measurement by satellite without accelerometers. In IFS, for the purpose of quickly evaluating the highest degree of recovered gravity field model and geoid error as well as analyzing the influence of system parameters on gravity field measurement, an analytical formula was established by spectral analysis method. The formula can reflect the analytical relationship between gravity field measurement performance and system parameters such as orbit altitude, the inner-satellite orbit determination error, the inner-satellite residual disturbances, data sampling interval and total measurement time. This analytical formula was then corrected by four factors introduced from numerical simulation of IFS gravity field measurement. By comparing computation results from corrected analytical formula and the actual gravity field measurement performance by CHAMP, the correctness and rationality of this analytical formula were verified. Based on this analytical formula, the influences of system parameters on IFS gravity field measurement were analyzed. It is known that gravity field measurement performance is a monotone decreasing function of orbit altitude, the inner-satellite orbit determination error, the inner-satellite residual disturbances, data sampling interval and the reciprocal of total measurement time. There is a match relationship between the inner-satellite orbit determination error and residual disturbances, in other words, the change rate of gravity field measurement performance with one of them is seriously restricted by their relative size. The analytical formula can be used to quantitatively evaluate gravity field measurement performance fast and design IFS parameters optimally. It is noted that the analytical formula and corresponding conclusions are applied to any gravity satellite which measures gravity field by satellite perturbation orbit.     

一种基于时间梳技术的高频正弦信号相位差测量方法

本文研究了一种基于时间梳原理的高频正弦信号相位差测量方法,给出了时间梳原理的数学模型,并详细分析了其特点,并将此原理首次应用于高频信号的数据采集中,可以用低频和被测信号构建一种高频等效采样技术,可以在不满足乃奎斯特采样定理下,对被测两路正弦信号进行同步采样,避免了高频信号采样的高采样率,结合多重互相关技术,实现了对高频正弦信号的相位差的高精度测量,实验结果表明本文算法对高频信号对高频正弦信号的相位差测量具有很高的测量精度,尤其在低信噪比下也有较高的测量精度,具有较高的工程实用价值。     

Exploiting the Sentinel-3 tandem phase dataset and azimuth oversampling to better characterize the sensitivity of SAR altimeter sea surface height to long ocean waves

Being the very first SAR mode altimeter tandem phase, the Sentinel-3 A/B tandem phase has provided an unprecedented opportunity to better characterize the sensitivity of SAR altimetry retrievals to high-frequency processes, such as long ocean waves. In this paper, we show that for some sea-state conditions, that are still to be precisely characterized, long ocean waves are responsible for high-frequency (spatial and temporal) coherent Sea Level Anomaly (SLA) signals. It is found that the peak wavelength corresponds to the dominant swell wavelength. Furthermore, the short time lag between S3-A and S3-B acquisitions allows performing cross-spectral analyses that reveal phase shifts consistent with waves travelling according to the wave dispersion relation. It is also demonstrated that the classical 20 Hz sampling frequency is insufficient to properly sample most swell-induced SLA signals and that aliasing can generate errors over the entire frequency spectrum, including at long wavelengths. These results advocate for the use of azimuth oversampling (40 Hz or 80 Hz). Low-pass filtering should be applied prior to any down-sampling to 20 Hz, in order to prevent long-wavelength errors induced by spectral leakage.     

Enhanced multipath mitigation method based on multi-resolution CNR model and adaptive statistical test strategy for real-time kinematic PPP

This study proposes an enhanced multipath mitigation method based on multi-resolution carrier-to-noise-ratio (CNR) model and adaptive statistical test strategy for real-time kinematic precise point positioning (PPP) applications. The multi-resolution CNR model is established with GPS observation data collected from DOY 152 to 181 of 2019 by 230 globally distributed IGS stations, which used to analyze the relevant factors affecting CNR. Statistical results indicate that the CNR is not only related to the satellite elevation, but also closely related to the receiver types and specific satellite. The maximum difference between different receivers can reach 20 dB for the same satellite at the same elevation. In addition, the performance of the CNR is also obviously different between each satellite, and the maximum difference between different satellites is about 10 dB for the same receiver at the same elevation. Hence, in terms of the method which is based on CNR information for multipath detection and mitigation, the independence of receiver types, satellite and frequency must be considered. With the above analysis, this study developed a multi-resolution CNR model based on different receiver types, different satellites and different elevation firstly. Then, combined with the adaptive statistical test strategy which is based on the difference of CNR between inter-frequency and the difference of CNR between adjacent epochs, the multipath can be detected effectively. For the epoch which affected by multipath, the down-weighted strategy based on CNR is adopted to mitigate the influence of multipath on positioning. Real-time kinematic PPP data are collected to assess the proposed method, and the results demonstrate that the proposed method can detect the multipath effectively, and the detection rate can reach 90.28%. Moreover, after adopting the mitigation strategy, the RMS bias of the east, north and up components are improved about 19.95%, 17.89% and 23.07% compared to the original results, respectively. It is worth noting that this proposed method is also suitable for other GNSS, such as GLONASS and BDS, but the corresponding CNR model must be established simultaneously.     

Magnetic torquer induced disturbing signals within GRACE accelerometer data

The GRACE (Gravity Recovery And Climate Experiment) gravity field satellite mission was launched in 2002. Although many investigations have been carried out, not all disturbances and perturbations upon satellite instruments and sensors are resolved yet. In this work the issue of acceleration disturbances onboard of GRACE due to magnetic torquers is investigated and discussed. Each of the GRACE satellites is equipped with a three-axes capacitive accelerometer to measure non-gravitational forces acting on the spacecraft. We used 10 Hz Level 1a raw accelerometer data in order to determine the impact of electric current changes on the accelerometer. After reducing signals which are induced by highly dominating processes in the low frequency range, such as thermospheric drag and solar radiation pressure, which can easily be done by applying a high-pass filter, disturbing signals from onboard instruments such as thruster firing events or heater switch events need to be removed from the previously filtered data. Afterwards the spikes which are induced by the torquers can be very well observed. Spikes vary in amplitude with respect to an increasing or decreasing current used for magnetic torquers, and can be as large as 20 nm/s². Furthermore, we were able to set up a model for the spikes of each scenario with which we were able to compute model spike time series. With these time series the spikes can successfully be removed from the 10 Hz raw accelerometer data. Spectral analysis of the time series reveal that an influence onto gravity field determination due to these effects is very unlikely, but can theoretically not be excluded.     

GPS-only gravity field recovery with GOCE,CHAMP, and GRACE

Gravity missions such as the Gravity field and steady-state Ocean Circulation Explorer (GOCE) are equipped with onboard Global Positioning System (GPS) receivers for precise orbit determination (POD), instrument time-tagging, and the extraction of the long wavelength part of the Earth’s gravity field. The very low orbital altitude of the GOCE satellite and the availability of dense 1 s GPS tracking data are ideal characteristics to exploit the contribution of GPS high-low Satellite-to-Satellite Tracking (hl-SST) to gravity field determination. We present gravity field solutions based on about 8 months of GOCE GPS hl-SST data from 2009 and compare the results with those obtained from the CHAllenging Minisatellite Payload (CHAMP) and Gravity Recovery And Climate Experiment (GRACE) missions. The very low orbital altitude of GOCE significantly improves gravity field recovery from GPS hl-SST data above degree 20, but not for the degrees below 20, where the quality of the spherical harmonic coefficients remains essentially unchanged. Despite the limited time span of GOCE data used, the gravity field of the Earth can be resolved up to about degree 115 using GPS data only. Empirically determined phase center variations (PCVs) of the GOCE onboard GPS helix antenna are, however, mandatory to achieve this performance.     

Atomic clocks for astrophysical measurements

Recently developed atomic hydrogen masers have achieved stability well into the 10^?16 domain for averaging time intervals beyond 1000 sec and future devices promise further improvements. These devices are very adaptable for space use in very high precision measurements of angle through Very Long Baseline Interferometry (VLBI) and range and range-rate through Doppler techniques. Proposed space missions using these clocks will be discussed for the measurement of the sun's gravity field distribution and tests of gravitation and relativity including a search for pulsed low frequency (～0.001 Hz) gravitational waves, and orbiting VLBI stations. Estimates of system performance capability will be discussed and the accuracy capability of relativistic measurements evaluated in terms of results from the 1976 NASA/SAO spaceborne clock test of the Einstein Equivalence Principle.     

Strategies for detection of putative life on Europa

Planned future exploration missions to the Jovian satellite Europa have a strong astrobiological motivation. Characterization of the potential habitability of the liquid water environments, and searching for life signals are the main astrobiological objectives of these missions. To meet these objectives specific strategies and instrumentation are required. Here we discuss some scenarios for the development of Europa potential biospheres. These scenarios are based on assumptions of the life similarity concept and knowledge about terrestrial life in extreme environments. Since the potential habitable environments on Europa are in the interior of the satellite it is not possibly to directly detect life. However, there are processes that link aqueous sub-surface environments with the near-surface environment, such as tectonism or magmatism. Therefore, by analysing endogenous materials that arise from the interior it is possible to make predictions about what is in the sub-surface. We propose some measurements and instrumentation for future missions to detect biosignatures on the upper layers of Europa, including the simple physico-chemical traces of metabolism to complex biomolecules or biostructures. Raman spectroscopy or biosensor technologies are the future for in situ exploration of the Solar System.     

Mapping the earth's magnetic and gravity fields from space: Current status and future prospects

Orbital potential field measurements are sensitive to regional variations in earth density and magnetization that occur over scales of a few hundred kilometers or greater. Global field models currently available are able to distinguish gravity variations of ±5 milligal over distances of ～1,000 km and magnetic variations of ±6 gamma over distances of ～300 km at the earth's surface. Regional variations in field strength have been detected in orbital measurements that are not apparent in higher resolution, low altitude surveys. NASA is presently studying a spacecraft mission known as GRAVSAT/MAGSAT, which would be the first satellite mission to perform a simultaneous survey of the earth's gravity and magnetic fields at low orbital altitudes. GRAVSAT/MAGSAT has been proposed for launch during the latter nineteen-eighties, and it would measure gravity field strength to an accuracy of 1 milligal and magnetic field strength to an accuracy of 2 gamma (scalar)/5 gamma (vector components) over a distance of roughly 100 km. Even greater improvements in the accuracy and spatial resolution of orbital surveys are anticipated during the nineteen-nineties with the development of potential field gradiometers and a tethered satellite system that can be deployed from the Space Shuttle to altitudes of 120 km above the earth's surface.     

航天器应急姿态捕获中GPS信号的应用

星载全球定位系统（GPS）卫星接收机在测量接收各GPS卫星信号时,可同时得到接收信号的信号强度测量辅助数据E。理论分析表明,接收信号的强度E与信号入射天线的法向夹角α强相关。如建立E与α稳定的先验模型,E就可以作为测量值,计算入射天线的角度α。在同一时刻,通过三个以上GPS卫星信号入射天线的角度α,可计算星载GPS卫星接收机接收天线的空间姿态。确定姿态的精度取决于E与α相关先验模型的稳定性。利用CHAMP卫星星载接收机在轨实测数据检验,估算的初始姿态精度为2°~3°。该方法可作为航天器故障状态下应急姿态捕获的一种辅助手段,也可为携带星载GPS而无高精度定姿要求的简易航天器提供一种新的无附加成本的定姿途径。     

An alternative computation of a gravity field model from GOCE

GOCE is the first satellite with a gravitational gradiometer (SGG). This allows to determine a gravity field model with high spatial resolution and high accuracy. Four of the six independent components of the gravitational gradient tensors (GGT) are measured with high accuracy in the so-called measurement band (MB) from 5 to 100 mHz by the GOCE gradiometer. Based on more than 1 year of GOCE measurements, two gravity field models have been derived. Here, we introduce a strategy for spherical harmonic analysis (SHA) from GOCE measurements, with a bandpass filter applied to the SGG data, combined with orbit analysis based on the integral equation approach, and additional constraints (or stabilization) in the polar areas where no observation is available due to the orbit geometry. In addition, we combined the GOCE SGG part with a set of GRACE normal equations. This improves the accuracy of the gravity field in the long-wavelength parts, due to the complementarity of GOCE and GRACE. Comparison with other models and with external data shows that our results are rather close to the GPS-levelling data in well-selected test regions, with an uncertainty of 4–7 cm, for truncation at degree 200.     

A method in near-surface estimation of air temperature (NEAT) in times following the satellite passing time using MODIS images

Air temperature is one of the most important parameters in environmental, agricultural and water resources studies. This information is not usually always available at the required temporal and spatial resolution. The air temperature is measured at a fixed point in the meteorological stations which are dispersed and may not have the appropriate spatial resolution needed for many applications. On the other hand, MODIS satellite images have relatively acceptable spatial resolution specially for use in environmental studies. There is a methodology with which the near surface air temperature can be extracted from MODIS images at the satellite passing time with an acceptable accuracy. The goal in this study is to find a way to predict the air temperature in times after/before the satellite passing time. The procedure consists of two steps. In the first step, the relationship between the air temperature at a time in a synoptic station and the air temperature in other times up to 5 h later were modeled. In the second step, using these built up relationships, the air temperature extracted from the satellite image at the passing time was extrapolated to the next hours. Finally, the results of this extrapolation method were evaluated using the air temperatures measured at those hours and in the pixels containing some other meteorological stations. The error of the method when applied to a relatively homogeneous surface cover was about 1.5 °C. This error when applied to the next hours, was below 2 °C up to 5 h after satellite passing time. This method can be useful in some agricultural and horticultural applications in which both the spatial and temporal resolution are needed simultaneously. This product is a useful tool for frost prediction, a phenomenon that usually happens at night or early in the morning.