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Temporal aliasing is currently the largest error contributor to time-variable satellite gravity field models. Therefore, the evolution of sensor technologies has to be complemented by strategies to reduce temporal aliasing errors. The most straightforward way to improve temporal aliasing is through extended satellite constellations because they improve the observation geometry and increase the achievable temporal resolution. Therefore, strategies to optimize the design of larger satellite constellations are investigated in this contribution. A complete constellation modeling procedure is presented, starting from primary design variables (such as the required targeted resolutions) and concluding with concrete orbital elements for the individual satellites. In parallel, it is evaluated if improved instrument sensitivities based on quantum technologies (cold atom interferometry) can be fully exploited in the case of larger constellations. For this, future quantum satellite gravity missions adopting the gradiometry concept (similar to the GOCE mission) and the low-low satellite-to-satellite tracking concept (similar to GRACE/-FO) are simulated on optimized constellations with up to 6 satellites/pairs. The retrieval performance of a 6-pair mission in terms of the global equivalent water height RMS can be improved by a factor of roughly 3 compared to an inclined double-pair mission. 3D-gradiometry intrinsically has a better de-aliasing behavior but has extremely high accuracy requirements for the gradiometer (about 10 µEotvos) and the attitude reconstruction to be of any benefit. All simulations show that when incorporating improved sensor technologies, such as future quantum sensing instruments in extended constellations, temporal aliasing will remain the dominant error source by far, up to five orders of magnitude larger than the instrument errors. Therefore, improving sensor technologies has to go hand in hand with larger satellite constellations and improved space–time parameterization strategies to further reduce temporal aliasing effects. Graphical Abstract

The Linked Autonomous Interplanetary Satellite Orbit Navigation (LiAISON) technique enables autonomous absolute orbit determination through satellite-to-satellite tracking (SST) range measurements between two satellites when one is located in an asymmetric gravitational field.While traditional LiAISON studies assume a precise lunar ephemeris, this paper investigates the feasibility of autonomously estimating the lunar ephemeris (lunar orbit relative to the Earth) and satellite orbits simultaneously.The proposed approach utilizes an extended Kalman filter to process SST measurements in cislunar space, specifically involving distant-retrograde-orbit (DRO) satellites, and this paper evaluates lunar ephemeris estimation performance across SST scenarios and compares observability.Numerical simulations demonstrate that in an SST scenario involving two DRO satellites and a low-Earth-orbit (LEO) satellite using 90 d of SST simulated data with 0.5-m range noise, the lunar ephemeris achieves meter-level position accuracy.Additionally, the satellite orbit accuracy reaches 0.1 m for LEO and approximately 5 m for DRO satellites.Although the simulation results were obtained with several simplifications, these findings nevertheless demonstrate the efficacy of the proposed method for lunar ephemeris estimation and its potential to enhance the autonomy of satellite navigation in cislunar space.

Effective ocean management and the conservation of highly migratory species depend on resolving the overlap between animal movements and distributions, and fishing effort. However, this information is lacking at a global scale. Here we show, using a big-data approach that combines satellite-tracked movements of pelagic sharks and global fishing fleets, that 24% of the mean monthly space used by sharks falls under the footprint of pelagic longline fisheries. Space-use hotspots of commercially valuable sharks and of internationally protected species had the highest overlap with longlines (up to 76% and 64%, respectively), and were also associated with significant increases in fishing effort. We conclude that pelagic sharks have limited spatial refuge from current levels of fishing effort in marine areas beyond national jurisdictions (the high seas). Our results demonstrate an urgent need for conservation and management measures at high-seas hotspots of shark space use, and highlight the potential of simultaneous satellite surveillance of megafauna and fishers as a tool for near-real-time, dynamic management. A global dataset of the satellite-tracked movements of pelagic sharks and fishing fleets show that sharks—and, in particular, commercially important species—have limited spatial refuge from fishing effort.

The Martian gravity field serves as the primary constraint for modeling the interior structure and changes in the surface mass. Currently, the determination of the Martian gravity field relies on ground-based tracking measurements, such as range and Doppler, conducted between Earth stations and Mars orbiters. However, these tracking methods encounter limitations in terms of observation accuracy and signal attenuation. Given the successful application of the satellite-to-satellite tracking technique in determining Earth's gravity field, as well as improving the resolution of the lunar gravity field, this paper explores its potential application to the determination of the Martian static gravity field. The objective of this research is to employ numerical simulation to assess the improvement in the precision of the Martian static gravity field achievable with the low–low satellite-to-satellite tracking (ll-SST) technique, considering various conditions, including observation durations, measurement noises, and orbital altitudes. The findings show that the intersatellite ranging system considerably enhances the global resolution of the gravity field, using the ll-SST technique at an orbital altitude of 300 km and a SST measurement noise of 1 μm s−1, the global resolution can reach at least degree 120. Reducing the measurement noise by an order of magnitude can increase the global resolution of the gravity field by 20 degrees for 300 km altitudes, and 16 degrees for 400 km altitudes. Reducing the orbital altitude by 100 km (from 400 to 300 km) results in a 20 degrees improvement in the global resolution of the gravity field.

Mars gravity field models are critical data sets for studying the planet’s internal structure. Currently, Mars gravity field determination is primarily based on modeling of tracking data from spacecraft such as Mars Reconnaissance Orbiter, Mars Odyssey, and Mars Global Surveyor. The Tianwen-1 mission has now been operational in orbit for over 3 yr. In this study, we construct a degree and order 120 gravity field model using Tianwen-1 spacecraft tracking data from 2021 June to 2024 October and perform a data fusion with the MRO120D gravity field model. Thereafter, we evaluate the contribution of Tianwen-1 tracking data to the improvement of the Martian gravity field modeling. Results indicate that the tracking data from Tianwen-1 provide limited enhancement to the low-degree terms of the gravity field. The relative errors in low-degree terms up to degree 10 of the fused model range from 10−6 to 10−4, and the formal uncertainties up to degree 6 are consistent with those of MRO120F model. The maximum difference in gravity anomalies at the Mars surface reaches 4.5 mGal, while the maximum discrepancy in gravity anomaly errors is approximately 0.65 mGal. The orbit determination performance for the Tianwen-1 spacecraft remains consistent between the two models. Currently, the accuracy improvement in the Martian static gravity field modeling achieved through Earth-based tracking data is relatively modest. Future significant advancements in Martian static gravity field modeling should focus on novel measurement techniques, such as satellite-to-satellite tracking, gravity gradiometry, and an accelerometer on board the spacecraft.

This study aims to assess the autonomous navigation performance of an asteroid orbiter enhanced using an inter-satellite link to a beacon satellite. Autonomous navigation includes the orbit determination of the orbiter and beacon, and asteroid gravity estimation without any ground station support. Navigation measurements were acquired using satellite-to-satellite tracking (SST) and optical observation of asteroid surface landmarks. This study presents a new orbiter–beacon SST scheme, in which the orbiter circumnavigates the asteroid in a low-altitude strongly-perturbed orbit, and the beacon remains in a high-altitude weakly-perturbed orbit. We used Asteroid 433 Eros as an example, and analyzed and designed low- and high-altitude orbits for the orbiter and beacon. The navigation measurements were precisely modeled, extended Kalman filters were devised, and observation configuration was analyzed using the Cramer–Rao lower bound (CRLB). Monte Carlo simulations were carried out to assess the effects of the orbital inclination and altitudes of the orbiter and beacon as key influencing factors. The simulation results showed that the proposed SST scheme was an effective solution for enhancing the autonomous navigation performance of the orbiter, particularly for improving the accuracy of gravity estimation.

High-precision inertial sensors or accelerometers can provide references for free-falling motion in gravitational fields in space. They serve as the key payloads for gravity recovery missions such as CHAMP, the GRACE-type missions, and the planned Next-Generation Gravity Missions. In this work, a systematic method for electrostatic inertial sensor calibration of gravity recovery satellites is suggested, which is applied to and verified with the Taiji-1 mission. With this method, the complete operating parameters including the scale factors, the center of mass offset vector, and the intrinsic biased acceleration can be precisely calibrated with only two sets of short-term in-orbit experiments. This could reduce the gaps in data that are caused by necessary in-orbit calibrations during the lifetime of related missions. Taiji-1 is the first technology-demonstration satellite of the “Taiji Program in Space”, which, in its final extended phase in 2022, could be viewed as operating in the mode of a high–low satellite-to-satellite tracking gravity mission. Based on the principles of calibration, swing maneuvers with time spans of approximately 200 s and rolling maneuvers for 19 days were conducted by Taiji-1 in 2022. Given the data of the actuation voltages of the inertial sensor, satellite attitude variations, precision orbit determinations, the inertial sensor’s operating parameters are precisely re-calibrated with Kalman filters and are relayed to the Taiji-1 science team. The relative errors of the calibrations are <1% for the linear scale factors, <3% for center of mass, and <0.1% for biased accelerations. Data from one of the sensitive axes are re-processed with the updated operating parameters, and the resulting performance is found to be slightly improved over the former results. This approach could be of high reference value for the accelerometer or inertial sensor calibrations of the GFO, the Chinese GRACE-type mission, and the Next-Generation Gravity Missions. This could also create some insight into the in-orbit calibrations of the ultra-precision inertial sensors for future GW space antennas because of the technological inheritance between these two generations of inertial sensors.

Gravity Recovery and Climate Experiment (GRACE) data are a valuable source of information for estimating hydrological mass changes. Several approaches have been conducted to investigate surface density changes from satellite-based observations. The traditional approaches are mainly based on the Stokes coefficients, related to a spherical harmonic representation of the gravitational potential. This study aims to develop an alternative method to estimate the temporal variations in water storage. It is based on a specific type of mascon technique that investigates the possibility of obtaining a solution without Stokes coefficients. The method uses a piecewise constant surface density function to estimate surface density changes based on the GRACE satellite-to-satellite tracking (SST) data. The surface density changes are directly obtained from the variations in positions and velocities of the two GRACE satellites. We therefore avoid the series truncation and aim to improve the leakage problem at the price of higher numerical burden. The proposed method is numerically tested on synthetic data similar to level-1 GRACE data for a period of one month. Two regularization methods, the well-known Tikhonov solution and a method that accounts for the areas of different patches, are employed to obtain a stable solution. The accuracy assessment over the Greenland area indicates that the estimated values are reliable and statistically significant, a further confirmation of the efficacy and stability of the method.

As the first in-orbit formation satellites equipped with a Laser Ranging Interferometer (LRI) instrument, Gravity Recovery and Climate Experiment Follow-on (GRACE-FO) satellites are designed to evaluate the effective ability of the new LRI ranging system applied to satellite-to-satellite tracking. To evaluate the application of LRI in GRACE-FO, a relative kinematic orbit determination scheme for formation satellites integrating Kalman filters and GPS/LRI is proposed. The observation equation is constructed by combining LRI and spaceborne GPS data, and the intersatellite baselines of GRACE-FO formation satellites are calculated with Kalman filters. The combination of GPS and LRI techniques can limit the influence of GPS observation errors and improve the stability of orbit determination of the GRACE-FO satellites formation. The linearization of the GPS/LRI observation model and the process of the GPS/LRI relative kinematic orbit determination are provided. Relative kinematic orbit determination is verified by actual GPS/LRI data of GRACE-FO-A and GRACE-FO-B satellites. The quality of relative kinematic orbit determination is evaluated by reference orbit check and K-Band Ranging (KBR) check. The result of the reference orbit check indicates that the accuracy of GRACE-FO relative kinematic orbit determination along X, Y, and Z (components of the baseline vector) directions is better than 2.9 cm. Compared with the relative kinematic orbit determination by GPS only, GPS/LRI improves the accuracy of the relative kinematic orbit determination by approximately 1cm along with X, Y and Z directions, and by about 1.8 cm in 3D directions. The overall accuracy of relative kinematic orbit determination is improved by 25.9%. The result of the KBR check indicates that the accuracy of the intersatellite baseline determination is about +/−10.7 mm.

The Earth’s time-variable gravity field is of great significance to study mass change within the Earth’s system. Since 2002, the NASA-DLR Gravity Recovery and Climate Experiment (GRACE) and its successor GRACE follow-on mission provide observations of monthly changes in the Earth gravity field with unprecedented accuracy and resolution by employing low-low satellite-to-satellite tracking (LLSST) measurements. In addition to LLSST, monthly gravity field models can be acquired from satellite laser ranging (SLR) and high-low satellite-to-satellite tracking (HLSST). The monthly gravity field solutions HLSST+SLR were derived by combining HLSST observations of low earth orbiting (LEO) satellites with SLR observations of geodetic satellites. Bandpass filtering was applied to the harmonic coefficients of HLSST+SLR solutions to reduce noise. In this study, we analyzed the performance of the monthly HLSST+SLR solutions in the spectral and spatial domains. The results show that: (1) the accuracies of HLSST+SLR solutions are comparable to those from GRACE for coefficients below degree 10, and significantly improved compared to those of SLR-only and HLSST-only solutions; (2) the effective spatial resolution could reach 1000 km, corresponding to the spherical harmonic coefficient degree 20, which is higher than that of the HLSST-only solutions. Compared with the GRACE solutions, the global mass redistribution features and magnitudes can be well identified from HLSST+SLR solutions at the spatial resolution of 1000 km, although with much noise. In the applications of regional mass recovery, the seasonal variations over the Amazon Basin and the long-term trend over Greenland derived from HLSST+SLR solutions truncated to degree 20 agree well with those from GRACE solutions without truncation, and the RMS of mass variations is 282 Gt over the Amazon Basin and 192 Gt in Greenland. We conclude that HLSST+SLR can be an alternative option to estimate temporal changes in the Earth gravity field, although with far less spatial resolution and lower accuracy than that offered by GRACE. This approach can monitor the large-scale mass transport during the data gaps between the GRACE and the GRACE follow-on missions.