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At least 91 records · Page 5

Characterization of frequency standard instability by estimation of their covariance matrix

The popular 3-cornered hat method used for evaluating the noise contributions of individual frequency standards is revisited. This method is used in several cases, but sometimes the results are not consistent because one or more estimated clock variances turn out to be negative. Different causes of this unacceptable result have been conjectured: among them one regards the hypothesis of uncorrelated clocks, essential in this method. Since recently realistic cases of correlation between clocks, mainly due to the environmental conditions, have been observed, this paper proposes an entirely revisited version of the 3-cornered hat method which permits to evaluate the individual variances and also the possible covariances between clocks, by relaxing the hypothesis of uncorrelation. The uncertainty and the lack of contemporaneity of the measurement series are assumed to be negligible. The lack of the uncorrelation hypothesis calls for a more general mathematical model leading to an underdetermined linear system. The estimates of the (co)variances of the measurement series us well us those of the individual clocks are introduced by means of the scalar product of the related time series and arranged in the respective covariance matrices S and R. Since covariance matrix is positive definite by definition, the problem consists in estimating the unknown R, subject to the constraint of positive definiteness, from the known S. Unfortunately, this constraint is not sufficient to estimate R. Therefore a suitable optimization criterion is proposed, which assures the positive definiteness of R and, at the same time, minimizes the global correlation among clocks. Examples of frequency instability measurements processed by the "classical" 3-cornered hat method and the here-revisited method are presented showing that the solutions are identical only when the uncorrelation hypothesis doesn't violate the positive definiteness of R.

PatriziaTravella↗

Gravity field improvement using global positioning system data from TOPEX/Poseidon - A covariance analysis

The TOPEX/Poseidon satellite data can be used to improve the knowledge of the earth's gravitational field. The GPS data are especially useful for improving the gravity field over the world's oceans, where the current tracking data are sparse. Using realistic scenario for processing 10 days of GPS data, a covariance analysis is performed to obtain the expected improvement to the GEM-T2 gravity field. The large amount of GPS data and the large number of parameters (1979 parameters for the gravity field, plus carrier-phase biases, etc.) required special filtering techniques for efficient solution. The gravity-bin technique is used to compute the covariance matrix associated with the spherical harmonic gravity field. The covariance analysis shows that the GPS data from one 10-day arc of TOPEX/Poseidon with no a priori constraints can resolve medium degree and order (3-26) parameters with sigmas (standard deviations) that are an order of magnitude smaller than the corresponding sigmas of GEM-T2. When the information from GEM-T2 is combined with the TOPEX/Poseidon GPS measurements, an order-of-magnitude improvement is observed in low- and medium-degree terms with significant improvements spread over a wide range of degree and order.

Bertiger, Willy I.↗

Baryon acoustic oscillations in thin redshift shells from BOSS DR12 and eBOSS DR16 galaxies

ABSTRACT In an age of large astronomical data sets and severe cosmological tensions, the case for model independent analyses is compelling. We present a set of 14 baryon acoustic oscillations measurements in thin redshift shells with $3\,\mathrm{ per} \,\mathrm{ cent}$ precision that were obtained by analysing BOSS DR12 and eBOSS DR16 galaxies in the redshift range 0.32 < z < 0.66. Thanks to the use of thin shells, the analysis is carried out using just redshifts and angles so that the fiducial model is only introduced when considering the mock catalogues, necessary for the covariance matrix estimation and the pipeline validation. We compare our measurements, with and without supernova data, to the corresponding constraints from Planck 2018, finding good compatibility. A Monte Python module for this likelihood is available at github.com/ranier137/angularBAO.

79 ASTRONOMY AND ASTROPHYSICS↗

Cross-correlating radial peculiar velocities and CMB lensing convergence

We study, for the first time, the cross correlation between the angular distribution of radial peculiar velocities (PV) and the lensing convergence of cosmic microwave background (CMB) photons. We derive theoretical expectations for the signal and its covariance and assess its detectability with existing and forthcoming surveys. We find that such cross-correlations are expected to improve constraints on different gravitational models by partially breaking degeneracies with the matter density. We identify in the distance-scaling dispersion of the peculiar velocities the most relevant source of noise in the cross correlation. For this reason, we also study how the above picture changes assuming a redshift-independent scatter for the PV, obtained for example using a reconstruction technique. Our results show that the cross correlation might be detected in the near future combining PV measurements from DESI and the convergence map from CMB-S4. Using realistic direct PV measurements we predict a cumulative signal-to-noise ratio of approximately 3.8σ using data on angular scales 3 ≤ ℓ ≤ 200. For an idealized reconstructed peculiar velocity map extending up to redshift z = 0.15 and a smoothing scale of 4 Mpc h -1 we predict a cumulative signal-to-noise ratio of approximately 27σ from angular scales 3 ≤ ℓ ≤ 200. We conclude that currently reconstructed peculiar velocities have more constraining power than directly observed ones, even though they are more cosmological-model dependent.

79 ASTRONOMY AND ASTROPHYSICS↗

Multiobjective insensitive design of airplane control systems with uncertain parameters

A multiobjective computer-aided design algorithm has been developed which minimizes the sensitivity of the design objectives to uncertainties in system parameters. The more important uncertain parameters are described by a gaussian random vector with known covariance matrix, and a vector sensitivity objective function is defined as the probabilities that the design objectives will violate specified requirements constraints. Control system parameters are found which minimize the sensitivity vector in a Pareto-optimal sense, using constrained minimization algorithms. Example results are shown for lateral stability augmentation system (SAS) design for three Shuttle flight conditions.

Schy, A. A.↗

Rapid Development of the Seeker Free-Flying Inspector Guidance, Navigation, and Control System

Seeker is an automated extravehicular free-flying inspector CubeSat designed and built in-house at the Johnson Space Center (JSC). As a Class 1E project funded by the International Space Station (ISS) Program, Seeker had a streamlined process to flight certification, but the vehicle had to be designed, developed, tested, and delivered within approximately one year after authority to pro-ceed (ATP) and within a $1.8 million budget. These constraints necessitated an expedited Guidance, Navigation, and Control (GNC) development schedule, development began with a navigation sensor trade study using Linear Covariance (LinCov) analysis and a rapid sensor downselection process, resulting in the use of commercial off-the-shelf (COTS) sensors which could be procured quickly and subjected to in-house environmental testing to qualify them for flight. A neural network was used to enable a COTS camera to provide bearing measurements for visual navigation. The GNC flight software (FSW) algorithms utilized lean development practices and leveraged the Core Flight Software (CFS) architecture to rapidly develop the GNC system, tune the system parameters, and verify performance in simulation. This pace was anchored by several Hardware-Software Integration (HSI) milestones, which forced the Seeker GNC team to develop the interfaces both between hardware and software and between the GNC domains early in the project and to enable a timely delivery.

Sullivan, Jacob↗

Rapid Development of the Seeker Free-Flying Inspector Guidance, Navigation, and Control System

Seeker is an automated extravehicular free-flying inspector CubeSat designed and built in-house at the Johnson Space Center (JSC). As a Class 1E project funded by the International Space Station (ISS) Program, Seeker had a stream-lined process to flight certification, but the vehicle had to be designed, developed, tested, and delivered within approximately one year after authority to proceed (ATP) and within a $1.8 million budget. These constraints necessitated an expedited Guidance, Navigation, and Control (GNC) development schedule. Development began with a navigation sensor trade study using Linear Covariance (LinCov) analysis and a rapid sensor down-selection process, resulting in the use of commercial off-the-shelf (COTS) sensors which could be procured quickly and subjected to in-house environmental testing to qualify them for flight. A neural network was used to enable a COTS camera to provide bearing measure-ments for visual navigation. The GNC flight software (FSW) algorithms utilized lean development practices and leveraged the Core Flight Software (CFS) architecture to rapidly develop the GNC system, tune the system parameters, and verify performance in simulation. This pace was anchored by several Hardware-Software Integration (HSI) milestones, which forced the Seeker GNC team to develop the interfaces both between hardware and software and between the GNC domains early in the project and to enable a timely delivery.

Sullivan, Jake↗

Towards a self-consistent analysis of the anisotropic galaxy two- and three-point correlation functions on large scales: application to mock galaxy catalogues

We establish a practical method for the joint analysis of anisotropic galaxy two- and three-point correlation functions (2PCF and 3PCF, respectively) on the basis of the decomposition formalism of the 3PCF using tripolar spherical harmonics. We perform such an analysis with MultiDark-Patchy mock catalogues to demonstrate and understand the benefit of the anisotropic 3PCF. We focus on scales above $80\, h^{-1}\, {\rm Mpc}$, and use information from the shape and the baryon acoustic oscillation (BAO) signals of the 2PCF and 3PCF. We also apply density field reconstruction to increase the signal-to-noise ratio of BAO in the 2PCF measurement, but not in the 3PCF measurement. In particular, we study in detail the constraints on the angular diameter distance and the Hubble parameter. We build a model of the bispectrum or 3PCF that includes the non-linear damping of the BAO signal in redshift space. We carefully account for various uncertainties in our analysis including theoretical models of the 3PCF, window function corrections, biases in estimated parameters from the fiducial values, the number of mock realizations to estimate the covariance matrix, and bin size. The joint analysis of the 2PCF and 3PCF monopole and quadrupole components shows a $30{{\ \rm per\ cent}}$ and $20{{\ \rm per\ cent}}$ improvement in Hubble parameter constraints before and after reconstruction of the 2PCF measurements, respectively, compared to the 2PCF analysis alone. Furthermore, this study clearly shows that the anisotropic 3PCF increases cosmological information from galaxy surveys and encourages further development of the modelling of the 3PCF on smaller scales than we consider.

79 ASTRONOMY AND ASTROPHYSICS↗

Capturing non-Gaussianity of the large-scale structure with weighted skew-spectra

The forthcoming generation of wide-field galaxy surveys will probe larger volumes and galaxy densities, thus allowing for a much larger signal-to-noise ratio for higher-order clustering statistics, in particular the galaxy bispectrum. Extracting this information, however, is more challenging than using the power spectrum due to more complex theoretical modeling, as well as significant computational cost of evaluating the bispectrum signal and the error budget. To overcome these challenges, several proxy statistics have been proposed in the literature, which partially or fully capture the information in the bispectrum, while being computationally less expensive than the bispectrum. One such statistics are weighted skew-spectra, which are cross-spectra of the density field and appropriately weighted quadratic fields. Using Fisher forecasts, we show that the information in these skew-spectra is equivalent to that in the bispectrum for parameters that appear as amplitudes in the bispectrum model, such as galaxy bias parameters or the amplitude of primordial non-Gaussianity. We consider three shapes of the primordial bispectrum: local, equilateral and that due to massive particles with spin two during inflation. In conclusion, to obtain constraints that match those from a measurement of the full bispectrum, we find that it is crucial to account for the full covariance matrix of the skew-spectra.

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Predictive Attitude Estimation Using Global Positioning System Signals

In this paper, a new algorithm is developed for attitude estimation using Global Positioning System (GPS) signals. The new algorithm is based on a predictive filtering scheme designed for spacecraft without rate measuring devices. The major advantage of this new algorithm over traditional Kalman filter approaches is that the model error is not assumed to represented by an unbiased Gaussian noise process with known covariance, but instead is determined during the estimation process. This is achieved by simultaneously solving system optimality conditions and an output error constraint. This approach is well suited for GPS attitude estimation since some error sources that contribute to attitude inaccuracy, such as signal multipath, are known to be non-Gaussian processes. Also, the predictive filter scheme can use either GPS signals or vector observations or a combination of both for attitude estimation, so that performance characteristics can be maintained during periods of GPS attitude sensor outage. The performance of the new algorithm is tested using flight data from the REX-2 spacecraft. Results are shown using the predictive filter to estimate the attitude from both GPS signals and magnetometer measurements, and comparing that solution to a magnetometer-only based solution. Results using the new estimation algorithm indicate that GPS-based solutions are verified to within 2 degrees using the magnetometer cross-check for the REX-2 spacecraft. GPS attitude accuracy of better than 1 degree is expected per axis, but cannot be reliably proven due to inaccuracies in the magnetic field model.

Crassidis, John L.↗

IGM damping wing constraints on the tail end of reionization from the enlarged XQR-30 sample

ABSTRACT The attenuation of Lyα photons by neutral hydrogen in the intergalactic medium (IGM) at z ≳ 5 continues to be a powerful probe for studying the epoch of reionization. Given a framework to estimate the intrinsic (true) Lyα emission of high-z sources, one can infer the ionization state of the IGM during reionization. In this work, we use the enlarged XQR-30 sample of 42 high-resolution and high signal-to-noise quasar spectra between $5.8\lesssim \, z\lesssim \, 6.6$ obtained with VLT/X-shooter to place constraints on the IGM neutral fraction. This is achieved using our existing Bayesian QSO reconstruction framework which accounts for uncertainties such as the: (i) posterior distribution of predicted intrinsic Lyα emission profiles (obtained via covariance matrix reconstruction of the Lyα and N v emission lines from unattenuated high-ionization emission line profiles; C iv, Si iv + O iv], and C iii]) and (ii) distribution of ionized regions within the IGM using synthetic damping wing profiles drawn from a 1.63 Gpc3 reionization simulation. Following careful quality control, we used 23 of the 42 available QSOs to obtain constraints/limits on the IGM neutral fraction during the tail-end of reionization. Our median and 68th percentile constraints on the IGM neutral fraction are: $0.20\substack{+0.14 -0.12}$ and $0.29\substack{+0.14 -0.13}$ at z = 6.15 and 6.35. Further, we also report 68th percentile upper limits of $\bar{x}_{\mathrm{H\, {\small I}}{}} \lt 0.21$, 0.20, 0.21, and 0.18 at z = 5.8, 5.95, 6.05, and 6.55. These results imply reionization is still ongoing at $5.8\lesssim \, z\lesssim \, 6.55$, consistent with previous results from XQR-30 (dark fraction and Lyα forest) along with other observational probes considered in the literature.

Greig, B. (ORCID:0000000240852094)↗

A Computational Framework to design 3D stiffness gradient acoustic metamaterials for impedance matching

Acoustic waves play a crucial role in various applications, including medical imaging, non-destructive testing, and sonar systems. One of the significant challenges in these applications is impedance matching, which is essential for minimizing reflections and maximizing the transfer of acoustic energy between different media. Acoustic metamaterials offer a promising solution to this challenge. In addition to impedance control, gradient stiffness can enhance structural efficiency and enable spatial control of wave propagation, making it a valuable feature in acoustic metamaterial design. In this pa- per, we present our developed computational method to design 3D stiffness gradient acoustic metamaterials for impedance matching. The key steps in our approach include generating initial designs using a periodic covariance function to provide unit cells that are both periodic on the boundaries and randomly formed inside the unit cell. Furthermore, we integrated manufacturing constraints into the design process, ensuring that the structures are interconnected for fabrication. We propose two computational optimization algorithms: GenUnit, based on a non-dominated sorting genetic algorithm (NSGA-II), and MLMatch, which leverages differentiable machine learning. The two approaches are not separate contributions but complementary com- ponents of a unified framework. GenUnit requires no training data and directly interfaces with physics-based simulations, making it highly accurate but slower for large-scale exploration. In contrast, MLMatch is data-hungry during training but, once trained, enables near-instantaneous inference and broad design-space coverage. Together, they form a hybrid strategy: ML- Match rapidly explores the global design space, and GenUnit provides local refinement with high-fidelity accuracy. This balance between training cost, inference time, and precision is the motivation for including both methods in the same study. We applied this dual-algorithm framework to generate two metallic-based metamaterial designs that match the acoustic impedance of water while exhibiting a controlled gradient in stiffness (from stiff to soft). The stiffness gradient is particularly advantageous in applications where one side of the structure must interface with soft or sensitive surfaces, such as human tissue or delicate components. Here, this work paves the way for improved materials in various acoustic applications, particularly in ultrasound devices, by providing better impedance.

Metamaterial↗

Multivariate Error Covariance Estimates by Monte-Carlo Simulation for Assimilation Studies in the Pacific Ocean

One of the most difficult aspects of ocean state estimation is the prescription of the model forecast error covariances. The paucity of ocean observations limits our ability to estimate the covariance structures from model-observation differences. In most practical applications, simple covariances are usually prescribed. Rarely are cross-covariances between different model variables used. Here a comparison is made between a univariate Optimal Interpolation (UOI) scheme and a multivariate OI algorithm (MvOI) in the assimilation of ocean temperature. In the UOI case only temperature is updated using a Gaussian covariance function and in the MvOI salinity, zonal and meridional velocities as well as temperature, are updated using an empirically estimated multivariate covariance matrix. Earlier studies have shown that a univariate OI has a detrimental effect on the salinity and velocity fields of the model. Apparently, in a sequential framework it is important to analyze temperature and salinity together. For the MvOI an estimation of the model error statistics is made by Monte-Carlo techniques from an ensemble of model integrations. An important advantage of using an ensemble of ocean states is that it provides a natural way to estimate cross-covariances between the fields of different physical variables constituting the model state vector, at the same time incorporating the model's dynamical and thermodynamical constraints as well as the effects of physical boundaries. Only temperature observations from the Tropical Atmosphere-Ocean array have been assimilated in this study. In order to investigate the efficacy of the multivariate scheme two data assimilation experiments are validated with a large independent set of recently published subsurface observations of salinity, zonal velocity and temperature. For reference, a third control run with no data assimilation is used to check how the data assimilation affects systematic model errors. While the performance of the UOI and MvOI is similar with respect to the temperature field, the salinity and velocity fields are greatly improved when multivariate correction is used, as evident from the analyses of the rms differences of these fields and independent observations. The MvOI assimilation is found to improve upon the control run in generating the water masses with properties close to the observed, while the UOI failed to maintain the temperature and salinity structure.

Borovikov, Anna↗

TDRSS Augmentation for Launch and Ascent High Speed Navigation Filter

An investigation was performed to evaluate the feasibility and possible advantages of augmenting the High Speed Trajectory Determination (HSTD) ground navigation filter with measurements from the Tracking & Data Relay Satellite System (TDRSS) constellation. The proposed communications system strategy for Constellation uses TDRSS rather than ground S-band, so the capability of replacing the S-band navigation capability with TDRSS was considered. HSTD simulations were performed with combinations of S-band, C-band, and TDRSS measurements. Several assumptions are made with regard to measurement biases and signal noise characteristics to produce first-look level accuracies. Preliminary results show that solutions using TDRSS instead of S-band have similar or improved performance from the view of filter covariance and may be a feasible alternative. These results also show that TDRSS tracking alone gives poorer observations and resulting performance Operational and other constraints to the use of TDRSS in a high-speed ground navigation filter are not addressed.

Holt, Greg .↗

High-degree Gravity Models from GRAIL Primary Mission Data

We have analyzed Ka‒band range rate (KBRR) and Deep Space Network (DSN) data from the Gravity Recovery and Interior Laboratory (GRAIL) primary mission (1 March to 29 May 2012) to derive gravity models of the Moon to degree 420, 540, and 660 in spherical harmonics. For these models, GRGM420A, GRGM540A, and GRGM660PRIM, a Kaula constraint was applied only beyond degree 330. Variance‒component estimation (VCE) was used to adjust the a priori weights and obtain a calibrated error covariance. The global root‒mean‒square error in the gravity anomalies computed from the error covariance to 320×320 is 0.77 mGal, compared to 29.0 mGal with the pre‒GRAIL model derived with the SELENE mission data, SGM150J, only to 140×140. The global correlations with the Lunar Orbiter Laser Altimeter‒derived topography are larger than 0.985 between l = 120 and 330. The free‒air gravity anomalies, especially over the lunar farside, display a dramatic increase in detail compared to the pre‒GRAIL models (SGM150J and LP150Q) and, through degree 320, are free of the orbit‒track‒related artifacts present in the earlier models. For GRAIL, we obtain an a posteriori fit to the S‒band DSN data of 0.13 mm/s. The a posteriori fits to the KBRR data range from 0.08 to 1.5 micrometers/s for GRGM420A and from 0.03 to 0.06 micrometers/s for GRGM660PRIM. Using the GRAIL data, we obtain solutions for the degree 2 Love numbers, k20=0.024615+/-0.0000914, k21=0.023915+/-0.0000132, and k22=0.024852+/-0.0000167, and a preliminary solution for the k30 Love number of k30=0.00734+/-0.0015, where the Love number error sigmas are those obtained with VCE.

Primary 1↗

Combination of cluster number counts and two-point correlations: validation on mock Dark Energy Survey

ABSTRACT We present a method of combining cluster abundances and large-scale two-point correlations, namely galaxy clustering, galaxy–cluster cross-correlations, cluster autocorrelations, and cluster lensing. This data vector yields comparable cosmological constraints to traditional analyses that rely on small-scale cluster lensing for mass calibration. We use cosmological survey simulations designed to resemble the Dark Energy Survey Year 1 (DES-Y1) data to validate the analytical covariance matrix and the parameter inferences. The posterior distribution from the analysis of simulations is statistically consistent with the absence of systematic biases detectable at the precision of the DES-Y1 experiment. We compare the χ2 values in simulations to their expectation and find no significant difference. The robustness of our results against a variety of systematic effects is verified using a simulated likelihood analysis of DES-Y1-like data vectors. This work presents the first-ever end-to-end validation of a cluster abundance cosmological analysis on galaxy catalogue level simulations.

79 ASTRONOMY AND ASTROPHYSICS↗

X-BASE: the first terrestrial carbon and water flux products from an extended data-driven scaling framework, FLUXCOM-X

Mapping in situ eddy covariance measurements of terrestrial land–atmosphere fluxes to the globe is a key method for diagnosing the Earth system from a data-driven perspective. We describe the first global products (called X-BASE) from a newly implemented upscaling framework, FLUXCOM-X, representing an advancement from the previous generation of FLUXCOM products in terms of flexibility and technical capabilities. The X-BASE products are comprised of estimates of CO 2 net ecosystem exchange (NEE), gross primary productivity (GPP), evapotranspiration (ET), and for the first time a novel, fully data-driven global transpiration product (ETT), at high spatial (0.05°) and temporal (hourly) resolution. X-BASE estimates the global NEE at −5.75 ± 0.33 Pg C yr −1 for the period 2001–2020, showing a much higher consistency with independent atmospheric carbon cycle constraints compared to the previous versions of FLUXCOM. The improvement of global NEE was likely only possible thanks to the international effort to increase the precision and consistency of eddy covariance collection and processing pipelines, as well as to the extension of the measurements to more site years resulting in a wider coverage of bioclimatic conditions. However, X-BASE global net ecosystem exchange shows a very low interannual variability, which is common to state-of-the-art data-driven flux products and remains a scientific challenge. With 125 ± 2.1 Pg C yr −1 for the same period, X-BASE GPP is slightly higher than previous FLUXCOM estimates, mostly in temperate and boreal areas. X-BASE evapotranspiration amounts to 74.7×10 3 ± 0.9×10 3 km 3 globally for the years 2001–2020 but exceeds precipitation in many dry areas, likely indicating overestimation in these regions. On average 57 % of evapotranspiration is estimated to be transpiration, in good agreement with isotope-based approaches, but higher than estimates from many land surface models. Despite considerable improvements to the previous upscaling products, many further opportunities for development exist. Pathways of exploration include methodological choices in the selection and processing of eddy covariance and satellite observations, their ingestion into the framework, and the configuration of machine learning methods. For this, the new FLUXCOM-X framework was specifically designed to have the necessary flexibility to experiment, diagnose, and converge to more accurate global flux estimates.

Nelson, Jacob A.↗

TDCOSMO - XVI. Measurement of the Hubble constant from the lensed quasar WGD 2038–4008

Time-delay cosmography is a powerful technique to constrain cosmological parameters, particularly the Hubble constant (H0). The TDCOSMO Collaboration is performing an ongoing analysis of lensed quasars to constrain cosmology using this method. In this work, we obtain constraints from the lensed quasar WGD 2038−4008 using new time-delay measurements and previous mass models by TDCOSMO. This is the first TDCOSMO lens to incorporate multiple lens modeling codes and the full time-delay covariance matrix into the cosmological inference. The models are fixed before the time delay is measured, and the analysis is performed blinded with respect to the cosmological parameters to prevent unconscious experimenter bias. We obtain DΔ t = 1.68−0.38+0.40 Gpc using two families of mass models, a power-law describing the total mass distribution, and a composite model of baryons and dark matter, although the composite model is disfavored due to kinematics constraints. In a flat ΛCDM cosmology, we constrain the Hubble constant to be H0 = 65−14+23 km s−1 Mpc−1. The dominant source of uncertainty comes from the time delays, due to the low variability of the quasar. Future long-term monitoring, especially in the era of the Vera C. Rubin Observatory’s Legacy Survey of Space and Time, could catch stronger quasar variability and further reduce the uncertainties. This system will be incorporated into an upcoming hierarchical analysis of the entire TDCOSMO sample, and improved time delays and spatially-resolved stellar kinematics could strengthen the constraints from this system in the future.Key words: gravitational lensing: strong / cosmological parameters / distance scale⋆ Corresponding author; kcwong19@gmail.com.⋆⋆ NHFP Einstein fellow.

79 ASTRONOMY AND ASTROPHYSICS↗