J.G. De Teixeira da Encarnacao
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13 records found
1
Collision Probability in Geostationary Orbit using Differential Algebra and Gaussian Mixture Elements
Modelled with Solar Radiation Pressure in a 6-DOF regime
Master thesis
(2026)
-
K. Jadhav, E. Mooij, E. Pignacca, J.G. De Teixeira da Encarnacao, E. van Kampen
The geostationary belt has no atmospheric drag to clear it, so the debris from a collision there stays in one of the most valuable regions of near-Earth space. The risk of such a collision is still assessed with methods that are computationally extensive. They propagate the trajectory with a cannonball model of the solar radiation pressure force, carry the uncertainty as a Gaussian covariance through linearised dynamics, and read the probability from a short-term encounter formula. None of the three suits a regime where relative velocities of a few metres per second stretch an encounter over hours, and where solar radiation pressure replaces drag as the largest non-gravitational perturbation. That force depends on the attitude of the object, and the same force drives that attitude. This work extends the hybrid Differential Algebra and Gaussian Mixture Model method with four solar radiation pressure models, from a cannonball to an eight-facet box-wing, and with coupled six degree of freedom orbit-attitude dynamics. The shadow function and the illumination switch of the plate models are reformulated as analytic functions, without which the Taylor expansion does not represent the flow. The angular rate cannot be carried as an expansion variable beyond about one radian of accumulated rotation, so a tumbling body is handled instead by averaging the plate force over its rotation phase. The probability is verified against two published geostationary conjunctions and one real conjunction recorded by an operational system, agreeing with each to better than one percent and at one to two orders of magnitude less computation time than the Monte Carlo reference. For a controlled satellite the fidelity of the force model does not change the answer, since a three degree of freedom cannonball and a coupled six degree of freedom box differ by 0.64 percent at most, and the error is set by the orbit determination. For an uncontrolled fragment of high area-to-mass ratio it decides the answer. A cannonball carrying the reflectivity an operator would assign halves the probability, the same model calibrated to the correct mean force doubles it, and a plate held at one fixed orientation departs by up to two orders of magnitude. Only the phase-averaged model reproduces the six degree of freedom reference, to within four percent. Two further results follow from the geostationary dynamics rather than the force model. The mixture has to be refined along the velocity rather than the position past one day of propagation, and the probability oscillates with a one-day period, so two screenings of the same encounter made twelve hours apart differ by an order of magnitude on identical data.
...
The geostationary belt has no atmospheric drag to clear it, so the debris from a collision there stays in one of the most valuable regions of near-Earth space. The risk of such a collision is still assessed with methods that are computationally extensive. They propagate the trajectory with a cannonball model of the solar radiation pressure force, carry the uncertainty as a Gaussian covariance through linearised dynamics, and read the probability from a short-term encounter formula. None of the three suits a regime where relative velocities of a few metres per second stretch an encounter over hours, and where solar radiation pressure replaces drag as the largest non-gravitational perturbation. That force depends on the attitude of the object, and the same force drives that attitude. This work extends the hybrid Differential Algebra and Gaussian Mixture Model method with four solar radiation pressure models, from a cannonball to an eight-facet box-wing, and with coupled six degree of freedom orbit-attitude dynamics. The shadow function and the illumination switch of the plate models are reformulated as analytic functions, without which the Taylor expansion does not represent the flow. The angular rate cannot be carried as an expansion variable beyond about one radian of accumulated rotation, so a tumbling body is handled instead by averaging the plate force over its rotation phase. The probability is verified against two published geostationary conjunctions and one real conjunction recorded by an operational system, agreeing with each to better than one percent and at one to two orders of magnitude less computation time than the Monte Carlo reference. For a controlled satellite the fidelity of the force model does not change the answer, since a three degree of freedom cannonball and a coupled six degree of freedom box differ by 0.64 percent at most, and the error is set by the orbit determination. For an uncontrolled fragment of high area-to-mass ratio it decides the answer. A cannonball carrying the reflectivity an operator would assign halves the probability, the same model calibrated to the correct mean force doubles it, and a plate held at one fixed orientation departs by up to two orders of magnitude. Only the phase-averaged model reproduces the six degree of freedom reference, to within four percent. Two further results follow from the geostationary dynamics rather than the force model. The mixture has to be refined along the velocity rather than the position past one day of propagation, and the probability oscillates with a one-day period, so two screenings of the same encounter made twelve hours apart differ by an order of magnitude on identical data.
Anomaly Detection in Geostationary Satellites
Unsupervised, Satellite-Agnostic Error Detection & Localisation
Master thesis
(2026)
-
M.C. Bak, N. Yorke-Smith, J.G. De Teixeira da Encarnacao, Erwin Platen, Sytze Andringa
As Eugene Wigner showed in 1939 for the Poincaré algebra, fundamental particles can be classified using symmetry algebras. In a universe including gravity, the Poincaré algebra cannot be the correct symmetry algebra, as this is the symmetry algebra for flat space. Instead, one should consider a symmetry algebra of asymptotic symmetries, which preserve only the asymptotic structure of gravity. Many of these asymptotic symmetries are not physically useful and are therefore considered “trivial.”
In this thesis, we give a new quantum definition of trivial symmetries, namely that a symmetry is trivial if it does not change which fundamental particles are found in a classification. We then specialize to three-dimensional asymptotically Anti-de-Sitter space. To calculate which symmetries are trivial, we first determine the second cohomology group of the asymptotic symmetries. Using the second cohomology group, it is then found that the useful asymptotic symmetry algebra is given by w⊕w⊕Rw \oplus w \oplus \mathbb{R}w⊕w⊕R, where www is the Witt algebra (centerless Virasoro) algebra, whereas the standard definition of trivial symmetry gives w⊕ww \oplus ww⊕w as the useful symmetry algebra. The extra factor of R\mathbb{R}R is interpreted as a kind of center-of-mass momentum.
...
As Eugene Wigner showed in 1939 for the Poincaré algebra, fundamental particles can be classified using symmetry algebras. In a universe including gravity, the Poincaré algebra cannot be the correct symmetry algebra, as this is the symmetry algebra for flat space. Instead, one should consider a symmetry algebra of asymptotic symmetries, which preserve only the asymptotic structure of gravity. Many of these asymptotic symmetries are not physically useful and are therefore considered “trivial.”
In this thesis, we give a new quantum definition of trivial symmetries, namely that a symmetry is trivial if it does not change which fundamental particles are found in a classification. We then specialize to three-dimensional asymptotically Anti-de-Sitter space. To calculate which symmetries are trivial, we first determine the second cohomology group of the asymptotic symmetries. Using the second cohomology group, it is then found that the useful asymptotic symmetry algebra is given by w⊕w⊕Rw \oplus w \oplus \mathbb{R}w⊕w⊕R, where www is the Witt algebra (centerless Virasoro) algebra, whereas the standard definition of trivial symmetry gives w⊕ww \oplus ww⊕w as the useful symmetry algebra. The extra factor of R\mathbb{R}R is interpreted as a kind of center-of-mass momentum.
Master thesis
(2025)
-
G. Valles Valverde, E.J.O. Schrama, B.C. Root, J.G. De Teixeira da Encarnacao
The GRACE/GRACE-FO mission has provided Earth's monthly gravity field data for more than 20 years. It has been a major success and has enabled significant contributions across multiple domains (e.g., water management, cryosphere monitoring, solid Earth sciences). Nonetheless, short-periodic effects are undersampled, and the data is noisy at high spatial frequencies, leading to north-south stripes in gravity field functionals. Future gravity research missions aim at improving both spatial and temporal resolution to fulfil increasingly demanding science and societal needs. In this work, an analytical spectral methodology is employed to study gravity field recovery capabilities of different configurations: GRACE-like, Bender configuration, and multi-satellite pairs configurations. The analytical model underestimates GRACE operational performance by almost one order of magnitude. Application of NGGM performance to a Bender configuration shows the observability of the atmospheric and ocean non-tidal signal with a resolution of 200 km. Moreover, the theoretical feasibility of daily and 3-hour solutions with 3 and 48 satellite pairs, respectively, is demonstrated, with a resolution of roughly 1000 km, assuming CubeSat performance. In this way, future missions might not only improve spatio-temporal resolution but also mitigate other error sources.
...
...
The GRACE/GRACE-FO mission has provided Earth's monthly gravity field data for more than 20 years. It has been a major success and has enabled significant contributions across multiple domains (e.g., water management, cryosphere monitoring, solid Earth sciences). Nonetheless, short-periodic effects are undersampled, and the data is noisy at high spatial frequencies, leading to north-south stripes in gravity field functionals. Future gravity research missions aim at improving both spatial and temporal resolution to fulfil increasingly demanding science and societal needs. In this work, an analytical spectral methodology is employed to study gravity field recovery capabilities of different configurations: GRACE-like, Bender configuration, and multi-satellite pairs configurations. The analytical model underestimates GRACE operational performance by almost one order of magnitude. Application of NGGM performance to a Bender configuration shows the observability of the atmospheric and ocean non-tidal signal with a resolution of 200 km. Moreover, the theoretical feasibility of daily and 3-hour solutions with 3 and 48 satellite pairs, respectively, is demonstrated, with a resolution of roughly 1000 km, assuming CubeSat performance. In this way, future missions might not only improve spatio-temporal resolution but also mitigate other error sources.
The optimization of low-thrust transfer trajectories presents a significant computational challenge due to the vast search space involved. This paper introduces a novel clustering-based successive search space pruning technique to improve low-thrust trajectory optimization. Regions of low ∆V trajectories were extracted from the search space using DBSCAN. Through successive pruning of regions of the search space containing inefficient solutions, effectively zooming in on the most promising areas, the performance of global optimization algorithms was improved. The effectiveness of the search space pruning was evaluated using three interplanetary transfer test cases: Earth-Mars, Earth-Tempel 1, and Earth-Mercury. The performance of three global optimization algorithms, Differential Evolution (DE), Simple Genetic Algorithm (SGA), and Particle Swarm Optimization (PSO) was compared across the original and pruned search spaces. Results show that clustering-based pruning can significantly reduce the search space and subsequently lead to improved optimal transfer trajectories with fewer function evaluations. Differential Evolution outperformed PSO and SGA across all three test cases, demonstrating robustness and efficiency. The results of the optimization highlight the importance of the selection of the population size and number of generations for the optimization algorithms, because insufficient function evaluations resulted in poor convergence for PSO and SGA, including in the reduced search spaces. The results also suggest excessive pruning of the search space can lead to loss of optimal solution. The findings confirmed that clustering-based search space pruning is a promising technique for improving the efficiency of global optimization in low-thrust trajectory design.
...
The optimization of low-thrust transfer trajectories presents a significant computational challenge due to the vast search space involved. This paper introduces a novel clustering-based successive search space pruning technique to improve low-thrust trajectory optimization. Regions of low ∆V trajectories were extracted from the search space using DBSCAN. Through successive pruning of regions of the search space containing inefficient solutions, effectively zooming in on the most promising areas, the performance of global optimization algorithms was improved. The effectiveness of the search space pruning was evaluated using three interplanetary transfer test cases: Earth-Mars, Earth-Tempel 1, and Earth-Mercury. The performance of three global optimization algorithms, Differential Evolution (DE), Simple Genetic Algorithm (SGA), and Particle Swarm Optimization (PSO) was compared across the original and pruned search spaces. Results show that clustering-based pruning can significantly reduce the search space and subsequently lead to improved optimal transfer trajectories with fewer function evaluations. Differential Evolution outperformed PSO and SGA across all three test cases, demonstrating robustness and efficiency. The results of the optimization highlight the importance of the selection of the population size and number of generations for the optimization algorithms, because insufficient function evaluations resulted in poor convergence for PSO and SGA, including in the reduced search spaces. The results also suggest excessive pruning of the search space can lead to loss of optimal solution. The findings confirmed that clustering-based search space pruning is a promising technique for improving the efficiency of global optimization in low-thrust trajectory design.
The modern day growth in satellites and debris in orbit around Earth is resulting in ever increasing requirements for state estimation systems used to avoid collisions and ensure safe operations as part of space situational awareness initiatives. While there are many methods to perform state estimation, the optimal control based estimator (OCBE) provides unique benefits, such as the ability to perform in the presence of mis-modelled accelerations while allowing for reconstruction of unknown maneuvers from the target spacecraft.
However, the method suffers from high computational costs. This thesis covers the implementation of a new variant of the OCBE, focused on propagation and estimation of state in terms of regularized "EDromo" elements.
The method showcases benefits in terms of estimated state error, and reduced sensitivity to the time gaps between measurements, at the cost of further computational complexity. For future work, suggestions to improve efficiency of the method are also presented. ...
However, the method suffers from high computational costs. This thesis covers the implementation of a new variant of the OCBE, focused on propagation and estimation of state in terms of regularized "EDromo" elements.
The method showcases benefits in terms of estimated state error, and reduced sensitivity to the time gaps between measurements, at the cost of further computational complexity. For future work, suggestions to improve efficiency of the method are also presented. ...
The modern day growth in satellites and debris in orbit around Earth is resulting in ever increasing requirements for state estimation systems used to avoid collisions and ensure safe operations as part of space situational awareness initiatives. While there are many methods to perform state estimation, the optimal control based estimator (OCBE) provides unique benefits, such as the ability to perform in the presence of mis-modelled accelerations while allowing for reconstruction of unknown maneuvers from the target spacecraft.
However, the method suffers from high computational costs. This thesis covers the implementation of a new variant of the OCBE, focused on propagation and estimation of state in terms of regularized "EDromo" elements.
The method showcases benefits in terms of estimated state error, and reduced sensitivity to the time gaps between measurements, at the cost of further computational complexity. For future work, suggestions to improve efficiency of the method are also presented.
However, the method suffers from high computational costs. This thesis covers the implementation of a new variant of the OCBE, focused on propagation and estimation of state in terms of regularized "EDromo" elements.
The method showcases benefits in terms of estimated state error, and reduced sensitivity to the time gaps between measurements, at the cost of further computational complexity. For future work, suggestions to improve efficiency of the method are also presented.
Evaluation and Design of the DopTrackBox Concept
Development of a Satellite Doppler Tracking Network Using Commercial Off-the-Shelf Components
Doppler tracking is a widely adopted method of tracking spacecraft for high-profile missions, using networks of vast and expensive dedicated tracking equipment. Though, amateur astronomers are sometimes also capable of tracking these missions using comparatively simple and cheap radio hardware, typically when a spacecraft uses VHF, UHF, LoRa or S-band to communicate with groundstations.
A similar effort is made using the DopTrack project of the Delft University of Technology, with the goal of being able to estimate and predict satellite orbits to similar accuracy as NORAD's TLEs. To this end, a concept was developed to use standardized commercial off-the-shelf components that could be turned into a cheap and reliable tracking network. Preliminary studies showed that this concept is a viable solution, but questions remained regarding the frequency stability of the hardware and the influence of an observation time bias on the estimated orbits. In addition, no design had been made yet that accounted for environmental constraints on the components and the protection thereof.
The aim of this study was to first investigate the frequency stability of the GPS clock and software defined radio that were intended for the concept, in order verify that the desired estimation accuracy could be met. Then, this study investigated what the impact of a time bias in the observations is on the orbit estimation capabilities of the system. Subsequently, a prototype was developed and installed to record satellite passes in a realistic environment. This data was used to provide an estimation of the time bias in the real system, as well as compare its performance with the current DopTrack system.
It was found that the hardware recommended by the preliminary study satisfies the stability requirements of the project. Although it was also found that the system exhibits an observation time bias on the order of one second, the effects of this bias could be mitigated by estimating this bias during the orbit estimation.
The data gathered by operating the prototype revealed two issues with the design. First, even in the Dutch weather, the components occasionally overheated, leading to reduction of the operational period of the system. Further investigation is needed to determine if different hardware components should be used, or if it can be mitigated by redesigning the box with cooling options.
Secondly, the signal-to-noise ratio of the recorded satellites does not meet the expectations set by earlier work, nor does it satisfy the established requirements. Investigations presented in this work show that the likely cause of this is an excess amount of noise picked up by the software defined radio when operated on the roof. Further investigation is needed to find if this can be mitigated by shielding of the equipment, or placing it at locations with less noise.
Doppler tracking is a widely adopted method of tracking spacecraft for high-profile missions, using networks of vast and expensive dedicated tracking equipment. Though, amateur astronomers are sometimes also capable of tracking these missions using comparatively simple and cheap radio hardware, typically when a spacecraft uses VHF, UHF, LoRa or S-band to communicate with groundstations.
A similar effort is made using the DopTrack project of the Delft University of Technology, with the goal of being able to estimate and predict satellite orbits to similar accuracy as NORAD's TLEs. To this end, a concept was developed to use standardized commercial off-the-shelf components that could be turned into a cheap and reliable tracking network. Preliminary studies showed that this concept is a viable solution, but questions remained regarding the frequency stability of the hardware and the influence of an observation time bias on the estimated orbits. In addition, no design had been made yet that accounted for environmental constraints on the components and the protection thereof.
The aim of this study was to first investigate the frequency stability of the GPS clock and software defined radio that were intended for the concept, in order verify that the desired estimation accuracy could be met. Then, this study investigated what the impact of a time bias in the observations is on the orbit estimation capabilities of the system. Subsequently, a prototype was developed and installed to record satellite passes in a realistic environment. This data was used to provide an estimation of the time bias in the real system, as well as compare its performance with the current DopTrack system.
It was found that the hardware recommended by the preliminary study satisfies the stability requirements of the project. Although it was also found that the system exhibits an observation time bias on the order of one second, the effects of this bias could be mitigated by estimating this bias during the orbit estimation.
The data gathered by operating the prototype revealed two issues with the design. First, even in the Dutch weather, the components occasionally overheated, leading to reduction of the operational period of the system. Further investigation is needed to determine if different hardware components should be used, or if it can be mitigated by redesigning the box with cooling options.
Secondly, the signal-to-noise ratio of the recorded satellites does not meet the expectations set by earlier work, nor does it satisfy the established requirements. Investigations presented in this work show that the likely cause of this is an excess amount of noise picked up by the software defined radio when operated on the roof. Further investigation is needed to find if this can be mitigated by shielding of the equipment, or placing it at locations with less noise.
Master thesis
(2025)
-
M. Contarini, D. Dirkx, M. Rovira Navarro, J.G. De Teixeira da Encarnacao, L.L.A. Vermeersen
The ESA Voyage 2050 program has identified Saturn's moon Enceladus as a primary target for
future outer Solar System missions aimed at assessing its potential habitability and internal
structure. To investigate Enceladus' interior, a novel mission concept is proposed, comprising an
orbiter tracked by surface landers. This study quantifies the attainable accuracy in the estimation of
key geophysical parameters by analyzing a range of mission architectures and design
configurations. From the derived uncertainties in selected parameters — including the tidal Love
numbers and libration amplitude — the analysis demonstrates how these observables can constrain
Enceladus' interior, assuming a three-layer structural model. The findings indicate that the proposed
mission architecture enables stringent estimates for Enceladus' geophysical parameters, thereby
yielding refined constraints of its internal properties, including the ice shell thickness, the densities of the core and subsurface ocean, the core radius, and the ice shell shear modulus. ...
future outer Solar System missions aimed at assessing its potential habitability and internal
structure. To investigate Enceladus' interior, a novel mission concept is proposed, comprising an
orbiter tracked by surface landers. This study quantifies the attainable accuracy in the estimation of
key geophysical parameters by analyzing a range of mission architectures and design
configurations. From the derived uncertainties in selected parameters — including the tidal Love
numbers and libration amplitude — the analysis demonstrates how these observables can constrain
Enceladus' interior, assuming a three-layer structural model. The findings indicate that the proposed
mission architecture enables stringent estimates for Enceladus' geophysical parameters, thereby
yielding refined constraints of its internal properties, including the ice shell thickness, the densities of the core and subsurface ocean, the core radius, and the ice shell shear modulus. ...
The ESA Voyage 2050 program has identified Saturn's moon Enceladus as a primary target for
future outer Solar System missions aimed at assessing its potential habitability and internal
structure. To investigate Enceladus' interior, a novel mission concept is proposed, comprising an
orbiter tracked by surface landers. This study quantifies the attainable accuracy in the estimation of
key geophysical parameters by analyzing a range of mission architectures and design
configurations. From the derived uncertainties in selected parameters — including the tidal Love
numbers and libration amplitude — the analysis demonstrates how these observables can constrain
Enceladus' interior, assuming a three-layer structural model. The findings indicate that the proposed
mission architecture enables stringent estimates for Enceladus' geophysical parameters, thereby
yielding refined constraints of its internal properties, including the ice shell thickness, the densities of the core and subsurface ocean, the core radius, and the ice shell shear modulus.
future outer Solar System missions aimed at assessing its potential habitability and internal
structure. To investigate Enceladus' interior, a novel mission concept is proposed, comprising an
orbiter tracked by surface landers. This study quantifies the attainable accuracy in the estimation of
key geophysical parameters by analyzing a range of mission architectures and design
configurations. From the derived uncertainties in selected parameters — including the tidal Love
numbers and libration amplitude — the analysis demonstrates how these observables can constrain
Enceladus' interior, assuming a three-layer structural model. The findings indicate that the proposed
mission architecture enables stringent estimates for Enceladus' geophysical parameters, thereby
yielding refined constraints of its internal properties, including the ice shell thickness, the densities of the core and subsurface ocean, the core radius, and the ice shell shear modulus.
Master thesis
(2025)
-
F. Fructuoso Vidal-Aragón, M.J. Heiligers, J. Guo, J.G. De Teixeira da Encarnacao
Planet-centred solar sailing offers a propellantless way of sustaining non-Keplerian motion for Earth-centred missions. For preliminary mission design and broad trade-space exploration, rapid yet accurate trajectory propagation tools are required. This work evaluates the performance of the Stark model, an analytical formulation that represents the dynamics as two-body motion subject to a uniform perturbing acceleration, applied to controlled solar-sail trajectories and benchmarked against classical numerical integration. Two control strategies for the sail are considered: (i) constant cone-angle laws, for which the Stark solution enables direct state evaluation, and (ii) time-varying locally optimal steering laws designed to target individual Keplerian elements. Performance is assessed in terms of positional accuracy and computational cost over representative one-day propagations. For constant control laws, accuracy is shown to improve with increasing perturbation magnitude, corresponding to larger sail lightness numbers and smaller cone angles. Sensitivity analyses reveal that smaller semi-major axes and larger eccentricities lead to faster dynamical regimes, resulting in increased position error and higher computational cost. For time-varying control laws, the Stark model’s performance depends strongly on the smoothness of the control law: smooth profiles (semi-major axis-, eccentricity-, and argument of periapsis-raising) yield broader regions of superiority in the accuracy-cost trade space compared to numerical integration, whereas abrupt profiles (inclination- and right ascension of the ascending node-raising) significantly reduce these regions. Furthermore, larger lightness numbers diminish the model’s ability to capture rapid dynamics, owing to the restriction of fixed step sizes. Overall, the results demonstrate that the Stark model provides a computationally efficient alternative for preliminary planet-centred solar-sail trajectory design, with advantages over classical numerical integration methods in specific regions of the accuracy-cost trade-off space, particularly for smooth control regimes.
...
Planet-centred solar sailing offers a propellantless way of sustaining non-Keplerian motion for Earth-centred missions. For preliminary mission design and broad trade-space exploration, rapid yet accurate trajectory propagation tools are required. This work evaluates the performance of the Stark model, an analytical formulation that represents the dynamics as two-body motion subject to a uniform perturbing acceleration, applied to controlled solar-sail trajectories and benchmarked against classical numerical integration. Two control strategies for the sail are considered: (i) constant cone-angle laws, for which the Stark solution enables direct state evaluation, and (ii) time-varying locally optimal steering laws designed to target individual Keplerian elements. Performance is assessed in terms of positional accuracy and computational cost over representative one-day propagations. For constant control laws, accuracy is shown to improve with increasing perturbation magnitude, corresponding to larger sail lightness numbers and smaller cone angles. Sensitivity analyses reveal that smaller semi-major axes and larger eccentricities lead to faster dynamical regimes, resulting in increased position error and higher computational cost. For time-varying control laws, the Stark model’s performance depends strongly on the smoothness of the control law: smooth profiles (semi-major axis-, eccentricity-, and argument of periapsis-raising) yield broader regions of superiority in the accuracy-cost trade space compared to numerical integration, whereas abrupt profiles (inclination- and right ascension of the ascending node-raising) significantly reduce these regions. Furthermore, larger lightness numbers diminish the model’s ability to capture rapid dynamics, owing to the restriction of fixed step sizes. Overall, the results demonstrate that the Stark model provides a computationally efficient alternative for preliminary planet-centred solar-sail trajectory design, with advantages over classical numerical integration methods in specific regions of the accuracy-cost trade-off space, particularly for smooth control regimes.
Asteroid missions stand at the forefront of space exploration endeavours. These face a number of challenges, with safe navigation being one of the main issues. The irregular nature of these bodies creates highly perturbed gravity fields that, if modelled incorrectly, can be a danger to the safe navigation of the spacecraft. Therefore, improving the gravity field modelling of asteroids is of key importance.
This research aims to improve the gravity field estimation of asteroids through the use of a satellite constellation consisting of a mothership and a set of CubeSats. In particular, it focuses on the modelling and estimation of the gravity field with spherical harmonics (SH), which makes the research only applicable to the navigation of the spacecraft outside of the Brillouin sphere.
The system design is based on a CubeSat constellation orbiting the asteroid that relays measurements back to a mothership that estimates its state and gravity field through an Unscented Kalman Filter (UKF). The research is centered around 433 Eros asteroid for the model implementation, being an irregular body with known characteristics from the Near-Shoemaker mission.
An end-to-end simulation environment is implemented for the system research. This allows for simulating the orbits of the satellites in a real-world environment considering SH gravity field up to degree and order 15, the perturbation effect of the Sun point mass, and the solar radiation pressure. Additionally, it includes a realistic polyhedral shape of the asteroid including its landmarks. The asteroid model is used together with the modelling of the satellite sensors to estimate the measurements that can be obtained in a realistic scenario including sensor errors, visibility, and communications constraints. Furthermore, the simulation environment contains a UKF filter capable of conducting the gravity-field estimates from the measured states of the constellation satellites.
The research conducts a thorough sensitivity analysis of the scenario evaluating how the constellation design impacts the estimates obtained. This analysis evaluates a number of filter designs, and determines that better performance is achieved when the design models the dynamics of several satellites at the same time. This is followed by an analysis of variance, conducted to obtain a better understanding of the constellation characteristics' effects on the filter estimates.
From the results obtained, a design synthesis is conducted to test the system implemented with an optimised constellation design. Furthermore, the filter design is re-evaluated and improved through the addition of better covariance matrix tuning and the addition of a degree-by-degree estimation procedure that allows to reduce computational load, a main constraint of the system. The results obtained show that the model is capable of accurately estimating the gravity field spherical harmonic coefficients with an error lower than 15% when the filter is tuned properly for SH up to degree and order nine. Additional verification of its applicability has been conducted by testing the system with extreme case asteroids, which show that the system requires a thruster and control system for the satellites to be capable of maintaining stable orbits around the asteroids when these have extremely irregular gravity fields. ...
This research aims to improve the gravity field estimation of asteroids through the use of a satellite constellation consisting of a mothership and a set of CubeSats. In particular, it focuses on the modelling and estimation of the gravity field with spherical harmonics (SH), which makes the research only applicable to the navigation of the spacecraft outside of the Brillouin sphere.
The system design is based on a CubeSat constellation orbiting the asteroid that relays measurements back to a mothership that estimates its state and gravity field through an Unscented Kalman Filter (UKF). The research is centered around 433 Eros asteroid for the model implementation, being an irregular body with known characteristics from the Near-Shoemaker mission.
An end-to-end simulation environment is implemented for the system research. This allows for simulating the orbits of the satellites in a real-world environment considering SH gravity field up to degree and order 15, the perturbation effect of the Sun point mass, and the solar radiation pressure. Additionally, it includes a realistic polyhedral shape of the asteroid including its landmarks. The asteroid model is used together with the modelling of the satellite sensors to estimate the measurements that can be obtained in a realistic scenario including sensor errors, visibility, and communications constraints. Furthermore, the simulation environment contains a UKF filter capable of conducting the gravity-field estimates from the measured states of the constellation satellites.
The research conducts a thorough sensitivity analysis of the scenario evaluating how the constellation design impacts the estimates obtained. This analysis evaluates a number of filter designs, and determines that better performance is achieved when the design models the dynamics of several satellites at the same time. This is followed by an analysis of variance, conducted to obtain a better understanding of the constellation characteristics' effects on the filter estimates.
From the results obtained, a design synthesis is conducted to test the system implemented with an optimised constellation design. Furthermore, the filter design is re-evaluated and improved through the addition of better covariance matrix tuning and the addition of a degree-by-degree estimation procedure that allows to reduce computational load, a main constraint of the system. The results obtained show that the model is capable of accurately estimating the gravity field spherical harmonic coefficients with an error lower than 15% when the filter is tuned properly for SH up to degree and order nine. Additional verification of its applicability has been conducted by testing the system with extreme case asteroids, which show that the system requires a thruster and control system for the satellites to be capable of maintaining stable orbits around the asteroids when these have extremely irregular gravity fields. ...
Asteroid missions stand at the forefront of space exploration endeavours. These face a number of challenges, with safe navigation being one of the main issues. The irregular nature of these bodies creates highly perturbed gravity fields that, if modelled incorrectly, can be a danger to the safe navigation of the spacecraft. Therefore, improving the gravity field modelling of asteroids is of key importance.
This research aims to improve the gravity field estimation of asteroids through the use of a satellite constellation consisting of a mothership and a set of CubeSats. In particular, it focuses on the modelling and estimation of the gravity field with spherical harmonics (SH), which makes the research only applicable to the navigation of the spacecraft outside of the Brillouin sphere.
The system design is based on a CubeSat constellation orbiting the asteroid that relays measurements back to a mothership that estimates its state and gravity field through an Unscented Kalman Filter (UKF). The research is centered around 433 Eros asteroid for the model implementation, being an irregular body with known characteristics from the Near-Shoemaker mission.
An end-to-end simulation environment is implemented for the system research. This allows for simulating the orbits of the satellites in a real-world environment considering SH gravity field up to degree and order 15, the perturbation effect of the Sun point mass, and the solar radiation pressure. Additionally, it includes a realistic polyhedral shape of the asteroid including its landmarks. The asteroid model is used together with the modelling of the satellite sensors to estimate the measurements that can be obtained in a realistic scenario including sensor errors, visibility, and communications constraints. Furthermore, the simulation environment contains a UKF filter capable of conducting the gravity-field estimates from the measured states of the constellation satellites.
The research conducts a thorough sensitivity analysis of the scenario evaluating how the constellation design impacts the estimates obtained. This analysis evaluates a number of filter designs, and determines that better performance is achieved when the design models the dynamics of several satellites at the same time. This is followed by an analysis of variance, conducted to obtain a better understanding of the constellation characteristics' effects on the filter estimates.
From the results obtained, a design synthesis is conducted to test the system implemented with an optimised constellation design. Furthermore, the filter design is re-evaluated and improved through the addition of better covariance matrix tuning and the addition of a degree-by-degree estimation procedure that allows to reduce computational load, a main constraint of the system. The results obtained show that the model is capable of accurately estimating the gravity field spherical harmonic coefficients with an error lower than 15% when the filter is tuned properly for SH up to degree and order nine. Additional verification of its applicability has been conducted by testing the system with extreme case asteroids, which show that the system requires a thruster and control system for the satellites to be capable of maintaining stable orbits around the asteroids when these have extremely irregular gravity fields.
This research aims to improve the gravity field estimation of asteroids through the use of a satellite constellation consisting of a mothership and a set of CubeSats. In particular, it focuses on the modelling and estimation of the gravity field with spherical harmonics (SH), which makes the research only applicable to the navigation of the spacecraft outside of the Brillouin sphere.
The system design is based on a CubeSat constellation orbiting the asteroid that relays measurements back to a mothership that estimates its state and gravity field through an Unscented Kalman Filter (UKF). The research is centered around 433 Eros asteroid for the model implementation, being an irregular body with known characteristics from the Near-Shoemaker mission.
An end-to-end simulation environment is implemented for the system research. This allows for simulating the orbits of the satellites in a real-world environment considering SH gravity field up to degree and order 15, the perturbation effect of the Sun point mass, and the solar radiation pressure. Additionally, it includes a realistic polyhedral shape of the asteroid including its landmarks. The asteroid model is used together with the modelling of the satellite sensors to estimate the measurements that can be obtained in a realistic scenario including sensor errors, visibility, and communications constraints. Furthermore, the simulation environment contains a UKF filter capable of conducting the gravity-field estimates from the measured states of the constellation satellites.
The research conducts a thorough sensitivity analysis of the scenario evaluating how the constellation design impacts the estimates obtained. This analysis evaluates a number of filter designs, and determines that better performance is achieved when the design models the dynamics of several satellites at the same time. This is followed by an analysis of variance, conducted to obtain a better understanding of the constellation characteristics' effects on the filter estimates.
From the results obtained, a design synthesis is conducted to test the system implemented with an optimised constellation design. Furthermore, the filter design is re-evaluated and improved through the addition of better covariance matrix tuning and the addition of a degree-by-degree estimation procedure that allows to reduce computational load, a main constraint of the system. The results obtained show that the model is capable of accurately estimating the gravity field spherical harmonic coefficients with an error lower than 15% when the filter is tuned properly for SH up to degree and order nine. Additional verification of its applicability has been conducted by testing the system with extreme case asteroids, which show that the system requires a thruster and control system for the satellites to be capable of maintaining stable orbits around the asteroids when these have extremely irregular gravity fields.
Two-layer gravity inversion on Mars
Three different inversion methods to obtain a global density model of the crust and upper mantle of Mars
Master thesis
(2024)
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F.M. van den Bogaard, B.C. Root, W. van der Wal, J.G. De Teixeira da Encarnacao
The origin of the Martian dichotomy is subject to question and no substantial evidence exists. Some surface and interior features that are not visible in, e.g., topography data, can show up in gravity data. Therefore, this research inverts gravity data to find a crustal and mantle global density model. Previous research performed a one-layer inversion, assuming equal mass in all columns. Also, missions like InSight do not provide global interior information, but only at the landing site. The aim of this research is to provide a global density model of both the Martian crust and upper mantle. The inversion is performed using a weighted, regularized least-squares algorithm. The gravity input consists of the residual between the MRO120F data set and the state-of-the-art gravity field model of the TU Delft. The design matrix is built using Green’s functions, which define the influence of a mass element in all different directions on a measurement point. Using this least-squares algorithm, three different methods for inversion are used. The separate two-layer inversion, the combined independent two-layer inversion and the combined dependent two-layer inversion. All three inversion methods are performed on synthetic planets as well, for verification purposes. By performing all inversions on the synthetic planets, it was found that the combined independent two-layer inversion results in a strong decoupling of short and long wavelength signals, but is not able to attribute gravity signals to different features in the crust and mantle. The combined dependent two-layer inversion does lead to a result that shows decoupling of crust and mantle features. The hypothesis is that adding different gravity components to the combined dependent two-layer inversion will further increase its accuracy. The results of the inversion methods applied to Mars are in agreement with existing research in terms of standard deviations of the crust and mantle density anomalies. The maps were also analysed geologically, where the most important conclusion is the evidence of potential impact basins in the north polar region. These can be evidence to accept the several impact theory for the origination of the Martian dichotomy. Increasing the resolution and refining the third inversion method with multiple gravity components will increase the potential of gravity inversion to define geological features of Mars.
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The origin of the Martian dichotomy is subject to question and no substantial evidence exists. Some surface and interior features that are not visible in, e.g., topography data, can show up in gravity data. Therefore, this research inverts gravity data to find a crustal and mantle global density model. Previous research performed a one-layer inversion, assuming equal mass in all columns. Also, missions like InSight do not provide global interior information, but only at the landing site. The aim of this research is to provide a global density model of both the Martian crust and upper mantle. The inversion is performed using a weighted, regularized least-squares algorithm. The gravity input consists of the residual between the MRO120F data set and the state-of-the-art gravity field model of the TU Delft. The design matrix is built using Green’s functions, which define the influence of a mass element in all different directions on a measurement point. Using this least-squares algorithm, three different methods for inversion are used. The separate two-layer inversion, the combined independent two-layer inversion and the combined dependent two-layer inversion. All three inversion methods are performed on synthetic planets as well, for verification purposes. By performing all inversions on the synthetic planets, it was found that the combined independent two-layer inversion results in a strong decoupling of short and long wavelength signals, but is not able to attribute gravity signals to different features in the crust and mantle. The combined dependent two-layer inversion does lead to a result that shows decoupling of crust and mantle features. The hypothesis is that adding different gravity components to the combined dependent two-layer inversion will further increase its accuracy. The results of the inversion methods applied to Mars are in agreement with existing research in terms of standard deviations of the crust and mantle density anomalies. The maps were also analysed geologically, where the most important conclusion is the evidence of potential impact basins in the north polar region. These can be evidence to accept the several impact theory for the origination of the Martian dichotomy. Increasing the resolution and refining the third inversion method with multiple gravity components will increase the potential of gravity inversion to define geological features of Mars.
Enhancing Collision Risk Assessment with Deep Learning Models
AI-Driven Satellite Collision Avoidance with Physics-Informed Models
Recent years have seen the exponential growth of the number of artificial objects orbiting the Earth. Since space debris can cause substantial damage, measures are investigated to make space operations more sustainable. Amongst these, there is an interest in the development of methods to detect possible collisions between objects in space. Traditional methods require highly accurate propagations with large computational times, so the focus of this thesis is the modelling of faster and more accurate algorithms to enhance collision risk assessment. To avoid long propagations, neural networks have been trained for orbit prediction and uncertainty estimation, with the main goal of calculating the collision probability between two objects. Different analyses have been made to assess the accuracy, stability, applicability and generalisation of the methods developed. The results show much faster collision risk calculations than traditional methods with a similar level of accuracy. It is also demonstrated how a tool which can generalise to satellites with different geometries can be built.
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Recent years have seen the exponential growth of the number of artificial objects orbiting the Earth. Since space debris can cause substantial damage, measures are investigated to make space operations more sustainable. Amongst these, there is an interest in the development of methods to detect possible collisions between objects in space. Traditional methods require highly accurate propagations with large computational times, so the focus of this thesis is the modelling of faster and more accurate algorithms to enhance collision risk assessment. To avoid long propagations, neural networks have been trained for orbit prediction and uncertainty estimation, with the main goal of calculating the collision probability between two objects. Different analyses have been made to assess the accuracy, stability, applicability and generalisation of the methods developed. The results show much faster collision risk calculations than traditional methods with a similar level of accuracy. It is also demonstrated how a tool which can generalise to satellites with different geometries can be built.
Master thesis
(2024)
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D. Roversi, E. Mooij, K.J. Cowan, J.G. De Teixeira da Encarnacao, T. Lam, R.R. Karimi
The Jovian system is one of the most attractive destinations for scientific space exploration, with many missions having flown to Jupiter and its moons. Among the latter, Io stands out due to its intense volcanic activity, with plumes extending up to hundreds of kilometers above its surface. Scientists believe that sampling, returning, and analyzing the particles ejected from Io’s volcanoes has the potential to unlock valuable information about Earth’s formation, and the history of the Solar System. For this reason, the concept of an Io Sample Return mission was born at the Jet Propulsion Laboratory, California Institute of Technology, where this thesis was carried out.
The project focuses on the mission design and trajectory optimization of a Discovery-class Io Sample Return concept. It investigates which geometry, maneuvers sequence, and flyby trajectories, can enable the sampling of Io’s Prometheus plume through a single flyby, before returning the material back to Earth.
Firstly, a broad-search of feasible patched-conics round-trip trajectories to Jupiter is conducted, using a simplified two-bodies model. The search incorporates launch, entry, time of flight, mission delta-V, and Io encounter constraints. Two algorithms for the reconstruction of ballistic and targeted flybys are developed and integrated within the trajectories-search workflow. This phase highlights the infeasibility of the 14 years flight time constraint and the 8 km/s maximum Io-relative speed during sampling. The two thresholds are increased to 18 years and 10 km/s, respectively. The solutions-space is progressively filtered with the aid of a primer-vector optimizer, and a single candidate trajectory is chosen for further studies. The solutions from the broad-search are also used to conduct a sensitivity study on alternative plume targets, which highlights Prometheus’ ideal position for sampling missions that avoid Jupiter orbit insertion.
The selected patched-conics candidate is used as initial guess for the numerical propagation and optimization of the end-to-end mission. A high-level trade-off is conducted to select the most suitable approach to propagate the trajectory. Two optimization approaches are then compared. An arc-wise scheme, in which each interplanetary transfer is optimized individually, and an all-arcs method, where the Earth-Jupiter and Jupiter-Earth journeys are each optimized in their entirety. Self-Adaptive Differential Evolution (SADE) and Generational Multi-Objective Evolutionary Algorithm by Decomposition (GMOEA/D) are the two optimizers of choice.
Optimization runs conducted using the patched-conics initial guess prove unable to converge to acceptable solutions. Moreover, single-objective optimization struggles to satisfy position discontinuities requirements, when adopting the all-arcs approach. The patched-conics solution is therefore extended to multi-conic, leading to significant performance improvements. Final results show that GMOEA/D outperforms SADE using the all-arcs approach, and finds a solution that satisfies delta-V, launch C3, entry speed, and position discontinuities constraints. It also improves the total delta-V of the baseline multi-conic solution by about 70 m/s, leaving over 700 m/s of margin on the mission delta-V budget.
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The project focuses on the mission design and trajectory optimization of a Discovery-class Io Sample Return concept. It investigates which geometry, maneuvers sequence, and flyby trajectories, can enable the sampling of Io’s Prometheus plume through a single flyby, before returning the material back to Earth.
Firstly, a broad-search of feasible patched-conics round-trip trajectories to Jupiter is conducted, using a simplified two-bodies model. The search incorporates launch, entry, time of flight, mission delta-V, and Io encounter constraints. Two algorithms for the reconstruction of ballistic and targeted flybys are developed and integrated within the trajectories-search workflow. This phase highlights the infeasibility of the 14 years flight time constraint and the 8 km/s maximum Io-relative speed during sampling. The two thresholds are increased to 18 years and 10 km/s, respectively. The solutions-space is progressively filtered with the aid of a primer-vector optimizer, and a single candidate trajectory is chosen for further studies. The solutions from the broad-search are also used to conduct a sensitivity study on alternative plume targets, which highlights Prometheus’ ideal position for sampling missions that avoid Jupiter orbit insertion.
The selected patched-conics candidate is used as initial guess for the numerical propagation and optimization of the end-to-end mission. A high-level trade-off is conducted to select the most suitable approach to propagate the trajectory. Two optimization approaches are then compared. An arc-wise scheme, in which each interplanetary transfer is optimized individually, and an all-arcs method, where the Earth-Jupiter and Jupiter-Earth journeys are each optimized in their entirety. Self-Adaptive Differential Evolution (SADE) and Generational Multi-Objective Evolutionary Algorithm by Decomposition (GMOEA/D) are the two optimizers of choice.
Optimization runs conducted using the patched-conics initial guess prove unable to converge to acceptable solutions. Moreover, single-objective optimization struggles to satisfy position discontinuities requirements, when adopting the all-arcs approach. The patched-conics solution is therefore extended to multi-conic, leading to significant performance improvements. Final results show that GMOEA/D outperforms SADE using the all-arcs approach, and finds a solution that satisfies delta-V, launch C3, entry speed, and position discontinuities constraints. It also improves the total delta-V of the baseline multi-conic solution by about 70 m/s, leaving over 700 m/s of margin on the mission delta-V budget.
...
The Jovian system is one of the most attractive destinations for scientific space exploration, with many missions having flown to Jupiter and its moons. Among the latter, Io stands out due to its intense volcanic activity, with plumes extending up to hundreds of kilometers above its surface. Scientists believe that sampling, returning, and analyzing the particles ejected from Io’s volcanoes has the potential to unlock valuable information about Earth’s formation, and the history of the Solar System. For this reason, the concept of an Io Sample Return mission was born at the Jet Propulsion Laboratory, California Institute of Technology, where this thesis was carried out.
The project focuses on the mission design and trajectory optimization of a Discovery-class Io Sample Return concept. It investigates which geometry, maneuvers sequence, and flyby trajectories, can enable the sampling of Io’s Prometheus plume through a single flyby, before returning the material back to Earth.
Firstly, a broad-search of feasible patched-conics round-trip trajectories to Jupiter is conducted, using a simplified two-bodies model. The search incorporates launch, entry, time of flight, mission delta-V, and Io encounter constraints. Two algorithms for the reconstruction of ballistic and targeted flybys are developed and integrated within the trajectories-search workflow. This phase highlights the infeasibility of the 14 years flight time constraint and the 8 km/s maximum Io-relative speed during sampling. The two thresholds are increased to 18 years and 10 km/s, respectively. The solutions-space is progressively filtered with the aid of a primer-vector optimizer, and a single candidate trajectory is chosen for further studies. The solutions from the broad-search are also used to conduct a sensitivity study on alternative plume targets, which highlights Prometheus’ ideal position for sampling missions that avoid Jupiter orbit insertion.
The selected patched-conics candidate is used as initial guess for the numerical propagation and optimization of the end-to-end mission. A high-level trade-off is conducted to select the most suitable approach to propagate the trajectory. Two optimization approaches are then compared. An arc-wise scheme, in which each interplanetary transfer is optimized individually, and an all-arcs method, where the Earth-Jupiter and Jupiter-Earth journeys are each optimized in their entirety. Self-Adaptive Differential Evolution (SADE) and Generational Multi-Objective Evolutionary Algorithm by Decomposition (GMOEA/D) are the two optimizers of choice.
Optimization runs conducted using the patched-conics initial guess prove unable to converge to acceptable solutions. Moreover, single-objective optimization struggles to satisfy position discontinuities requirements, when adopting the all-arcs approach. The patched-conics solution is therefore extended to multi-conic, leading to significant performance improvements. Final results show that GMOEA/D outperforms SADE using the all-arcs approach, and finds a solution that satisfies delta-V, launch C3, entry speed, and position discontinuities constraints. It also improves the total delta-V of the baseline multi-conic solution by about 70 m/s, leaving over 700 m/s of margin on the mission delta-V budget.
The project focuses on the mission design and trajectory optimization of a Discovery-class Io Sample Return concept. It investigates which geometry, maneuvers sequence, and flyby trajectories, can enable the sampling of Io’s Prometheus plume through a single flyby, before returning the material back to Earth.
Firstly, a broad-search of feasible patched-conics round-trip trajectories to Jupiter is conducted, using a simplified two-bodies model. The search incorporates launch, entry, time of flight, mission delta-V, and Io encounter constraints. Two algorithms for the reconstruction of ballistic and targeted flybys are developed and integrated within the trajectories-search workflow. This phase highlights the infeasibility of the 14 years flight time constraint and the 8 km/s maximum Io-relative speed during sampling. The two thresholds are increased to 18 years and 10 km/s, respectively. The solutions-space is progressively filtered with the aid of a primer-vector optimizer, and a single candidate trajectory is chosen for further studies. The solutions from the broad-search are also used to conduct a sensitivity study on alternative plume targets, which highlights Prometheus’ ideal position for sampling missions that avoid Jupiter orbit insertion.
The selected patched-conics candidate is used as initial guess for the numerical propagation and optimization of the end-to-end mission. A high-level trade-off is conducted to select the most suitable approach to propagate the trajectory. Two optimization approaches are then compared. An arc-wise scheme, in which each interplanetary transfer is optimized individually, and an all-arcs method, where the Earth-Jupiter and Jupiter-Earth journeys are each optimized in their entirety. Self-Adaptive Differential Evolution (SADE) and Generational Multi-Objective Evolutionary Algorithm by Decomposition (GMOEA/D) are the two optimizers of choice.
Optimization runs conducted using the patched-conics initial guess prove unable to converge to acceptable solutions. Moreover, single-objective optimization struggles to satisfy position discontinuities requirements, when adopting the all-arcs approach. The patched-conics solution is therefore extended to multi-conic, leading to significant performance improvements. Final results show that GMOEA/D outperforms SADE using the all-arcs approach, and finds a solution that satisfies delta-V, launch C3, entry speed, and position discontinuities constraints. It also improves the total delta-V of the baseline multi-conic solution by about 70 m/s, leaving over 700 m/s of margin on the mission delta-V budget.
Bridging the GRACE gap
Validation of satellite gravity observations via glacial isostatic adjustment
Master thesis
(2019)
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Sander Vermeulen, B.C. Root, João De Teixeira Da Encarnação, Wouter van der Wal, Pavel Ditmar
The GRACE mission has provided unprecedented insights into mass redistribution processes in the Earth system. Following a strong call for continuation of the mass observations, the GRACE-Follow On (GRACE-FO) mission was launched in May 2018, leaving a coverage gap of ca. 1 year between GRACE and GRACE-FO. Geopotential solutions derived from data of the Swarm mission (2013-present) are candidate data to potentially bridge this gap, as well as bridge the minor discontinuities in the current GRACE time series. This study aims to validate the sensitivity of the Swarm measurement system to mass rates, by comparing GRACE and Swarm observations of the gravity trend induced by glacial isostatic adjustment (GIA). Studies inverting GIA observations (e.g., relative sea level change, surface deformation, [time variable] gravity) into mantle viscosity estimates suggest relatively high viscosity in the Hudson Bay area. This suggests that the North American GIA-induced gravity trend is linear on a multi-decadal time scale, which means we can extrapolate the GRACE-derived GIA observations into the Swarm time period for this area. We find that the Swarm-derived GIA observations correspond well in amplitude and spatial distribution to GRACE observations and conclude that both systems have a similar sensitivity to gravity trends at spatial scales to which Swarm is sensitive to (ca. 1500 km). We validate our findings via geopotential solutions of GRACE-FO and provide a brief analysis of the benefits of adding Swarm-derived information to the combined GRACE / GRACE-FO time series.
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The GRACE mission has provided unprecedented insights into mass redistribution processes in the Earth system. Following a strong call for continuation of the mass observations, the GRACE-Follow On (GRACE-FO) mission was launched in May 2018, leaving a coverage gap of ca. 1 year between GRACE and GRACE-FO. Geopotential solutions derived from data of the Swarm mission (2013-present) are candidate data to potentially bridge this gap, as well as bridge the minor discontinuities in the current GRACE time series. This study aims to validate the sensitivity of the Swarm measurement system to mass rates, by comparing GRACE and Swarm observations of the gravity trend induced by glacial isostatic adjustment (GIA). Studies inverting GIA observations (e.g., relative sea level change, surface deformation, [time variable] gravity) into mantle viscosity estimates suggest relatively high viscosity in the Hudson Bay area. This suggests that the North American GIA-induced gravity trend is linear on a multi-decadal time scale, which means we can extrapolate the GRACE-derived GIA observations into the Swarm time period for this area. We find that the Swarm-derived GIA observations correspond well in amplitude and spatial distribution to GRACE observations and conclude that both systems have a similar sensitivity to gravity trends at spatial scales to which Swarm is sensitive to (ca. 1500 km). We validate our findings via geopotential solutions of GRACE-FO and provide a brief analysis of the benefits of adding Swarm-derived information to the combined GRACE / GRACE-FO time series.