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At least 559 records · Page 31

Late Breaking Results: COPPER: Computation Obfuscation by Producing Permutations for Encoding Randomly

Deployed embedded devices face security risks due to increased ease of physical access to the devices by unauthorized users. Capable adversaries can intercept a device to recover the data in memory, including results of performed sensitive computations. Device owners require data confidentiality on their physically insecure devices. To satisfy this goal we implement a novel method, COPPER (Computation Obfuscation by Producing Permutations for Encoding Randomly), to create data which never exists on the device digitally in plaintext format and which is subsequently used for computation. In this paper we utilize COPPER to calculate a moving average computation on encoded data.

embedded systems↗

Neutron Time-of-Flight Measurements of Charged-Particle Energy Loss in Inertial Confinement Fusion Plasmas

Neutron spectra from secondary 3 H(d,n)α reactions produced by an implosion of a deuterium-gas capsule at the National Ignition Facility have been measured with order-of-magnitude improvements in statistics and resolution over past experiments. Furthermore, these new data and their sensitivity to the energy loss of fast tritons emitted from thermal 2 H(d,p) 3 H reactions enable the first statistically significant investigation of charged-particle stopping via the emitted neutron spectrum. Radiation-hydrodynamic simulations, constrained to match a number of observables from the implosion, were used to predict the neutron spectra while employing two different energy loss models. This analysis represents the first test of stopping models under inertial confinement fusion conditions, covering plasma temperatures of k B T ≈ 1–4 keV and particle densities of n ≈ (12–2) × 10 24 cm –3 . Under these conditions, we find significant deviations of our data from a theory employing classical collisions whereas the theory including quantum diffraction agrees with our data.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Low-dose x-ray tomography through a deep convolutional neural network

Synchrotron-based X-ray tomography offers the potential of rapid large-scale reconstructions of the interiors of materials and biological tissue at fine resolution. However, for radiation sensitive samples, there remain fundamental trade-offs between damaging samples during longer acquisition times and reducing signals with shorter acquisition times. We present a deep convolutional neural network (CNN) method that increases the acquired X-ray tomographic signal by at least a factor of 10 during low-dose fast acquisition by improving the quality of recorded projections. Short exposure time projections enhanced with CNN show similar signal to noise ratios as compared with long exposure time projections and much lower noise and more structural information than low-dose fats acquisition without CNN. We optimized this approach using simulated samples and further validated on experimental nano-computed tomography data of radiation sensitive mouse brains acquired with a transmission X-ray microscopy. We demonstrate that automated algorithms can reliably trace brain structures in datasets collected with low dose-CNN. As a result, this method can be applied to other tomographic or scanning based X-ray imaging techniques and has great potential for studying faster dynamics in specimens.

60 APPLIED LIFE SCIENCES↗

Ground-based Spectroscopy of the Exoplanet XO-2b Using a Systematic Wavelength Calibration

Exoplanets orbiting close to their host star are expected to support a large ionosphere, which extends to larger pressures than witnessed in our solar system. These ionospheres can be investigated with ground-based transit observations of the optical signatures of alkali metals, which are the source of the ions. However, most ground-based transit spectra do not systematically resolve the wings of the features and continuum, as needed to constrain the alkali abundances. Here we present new observations and analyses of optical transit spectra that cover the Na doublet in the atmosphere of the exoplanet XO-2b. To assess the consistency of our results, observations were obtained from two separate platforms: Gemini/GMOS and Mayall/KOSMOS. To mitigate the systematic errors, we chose XO-2, because it has a binary companion of the same brightness and stellar type, which provides an ideal reference star to model Earth’s atmospheric effects. We find that interpretation of the data is highly sensitive to time-varying translations along the detector, which change according to wavelength and differ between the target and reference star. It was necessary to employ a time-dependent cross-correlation to align our wavelength bins and correct for atmospheric differential refraction. This approach allows us to resolve the wings of the Na line across five wavelength bins at a resolution of ∼1.6 nm and limit the abundance of Na. We obtain consistent results from each telescope with an Na amplitude of 521 ± 161 and 403 ± 186 ppm for GMOS and KOSMOS, respectively. The results are analyzed with a radiative transfer model that includes the effects of ionization. The data are consistent with a clear atmosphere between ∼1 and 100 mbar that establishes a lower limit on Na at 0.4{sub −0.3}{sup +2} ppm ([Na/H] = −0.64{sub −0.6}{sup +0.78}), consistent with solar. However, we cannot rule out the presence of clouds at ∼10 mbar that allow for higher Na abundances, which would be consistent with the stellar metallicity measured for the host star ([Na/H] = 0.485 ± 0.043).

79 ASTRONOMY AND ASTROPHYSICS↗

Recent Advancements in the Infrared Flow Visualization System for the NASA Ames Unitary Plan Wind Tunnels

The following details recent efforts undertaken at the NASA Ames Unitary Plan wind tunnels to design and deploy an advanced, production-level infrared (IR) flow visualization data system. Highly sensitive IR cameras, coupled with in-line image processing, have enabled the visualization of wind tunnel model surface flow features as they develop in real-time. Boundary layer transition, shock impingement, junction flow, vortex dynamics, and buffet are routinely observed in both transonic and supersonic flow regimes all without the need of dedicated ramps in test section total temperature. Successful measurements have been performed on wing-body sting mounted test articles, semi-span floor mounted aircraft models, and sting mounted launch vehicle configurations. The unique requirements of imaging in production wind tunnel testing has led to advancements in the deployment of advanced IR cameras in a harsh test environment, robust data acquisition storage and workflow, real-time image processing algorithms, and evaluation of optimal surface treatments. The addition of a multi-camera IR flow visualization data system to the Ames UPWT has demonstrated itself to be a valuable analyses tool in the study of new and old aircraft/launch vehicle aerodynamics and has provided new insight for the evaluation of computational techniques.

Infrared Thermography↗

Confronting interacting dark radiation scenarios with cosmological data

Dark radiation (DR) is generally predicted in new physics scenarios that address fundamental puzzles of the Standard Model or tensions in the cosmological data. Cosmological data have the sensitivity to constrain not only the energy density of DR but also whether it is interacting. In this paper, we present a systematic study of five types of interacting DR (free-streaming, fluid, decoupling, instantaneous decoupling, and recoupling DR) and their impact on cosmological observables. We modify the Boltzmann hierarchy to describe all these types of interacting DR under the relaxation time approximation. We, for the first time, robustly calculate the collision terms for recoupling scalar DR and provide a better estimation of the recoupling transition redshift. We demonstrate the distinct features of each type of DR on the cosmic microwave background and matter power spectra. We perform Markov-chain Monte Carlo scans using the Planck 2018 data and baryon acoustic oscillation data. Assuming no new physics in the standard model neutrino sector, we find no statistically significant constraints on the couplings of DR, although there is a slight preference for the fluidlike limit of all the cases. In the case of instantaneous decoupling DR, this limit corresponds to a late transition redshift around recombination. Furthermore, the ΔN eff constraint varies marginally depending on the type of DR.

79 ASTRONOMY AND ASTROPHYSICS↗

Energy dependence of cosmic ray composition above 10(15) GeV/nucleus

It is argued that above 10 to the 5th power GeV/nucleus, in the range where charge-resolved spectra have not yet been determined, the appropriate measures of equal-energy composition are 1nA and 1nA , the mean value and dispersion relative to the mean value and dispersion relative to the mean of 1nA, where A is the mass number. Experimental data which are sensitive to changes in 1nA with increasing energy are examined. It is found that, taken as a whole, they show no change (+ or 0.5) between 10 to the 5th power and 10 to the 6th power GeV, and a decrease of 1.5 + or - 0.5 between 10 to the 6th power and 10 to the 8th power GeV, with no further change + or - 0.5) above 10 to the 8th power GeV. Taken as a whole, the various indirect estimates of the absolute value of 1nA above 10 to the 5th power GeV/nucleus are also consistent with this pattern. For a wide range of astrophysically plausible composition models the value of the other measure, 1nA is insensitive to changes in 1nA . Because of this the existing data on 1nA can likewise easily be reconciled with this pattern.

Linsley, J.↗

A Monte Carlo Sensitivity Analysis of CF2 and CF Radical Densities in a c-C4F8 Plasma

A Monte Carlo sensitivity analysis is used to build a plasma chemistry model for octacyclofluorobutane (c-C4F8) which is commonly used in dielectric etch. Experimental data are used both quantitatively and quantitatively to analyze the gas phase and gas surface reactions for neutral radical chemistry. The sensitivity data of the resulting model identifies a few critical gas phase and surface aided reactions that account for most of the uncertainty in the CF2 and CF radical densities. Electron impact dissociation of small radicals (CF2 and CF) and their surface recombination reactions are found to be the rate-limiting steps in the neutral radical chemistry. The relative rates for these electron impact dissociation and surface recombination reactions are also suggested. The resulting mechanism is able to explain the measurements of CF2 and CF densities available in the literature and also their hollow spatial density profiles.

Bose, Deepak↗

Nuclear Data and Benchmarking Program: Nuclear Data Performance Assessment for Advanced Reactors

Over the last several Evaluated Nuclear Data File (ENDF)/B releases, many updates have been introduced to the nuclear data libraries that can significantly change computational results. These changes can be particularly important for advanced reactor concepts, which are not as thoroughly investigated as those used in light water reactor (LWR) systems. Therefore, a performance assessment of the ENDF/B libraries using the SCALE 6.2.3 code package was conducted under the auspices of the U.S., Department of Energy Office of Nuclear Energy (DOE-NE). The following systems relevant to the advanced reactor community were chosen as subject for investigation in this report: sodium cooled fast reactor systems, graphite moderated high temperature gas-cooled reactors, and several molten salt reactor models. At first, the similarity of the integral performance of the ENDF/B-VII.1 and ENDF/B-VIII.0 nuclear data libraries caused by compensating errors in important differential data was demonstrated. In calculations for a shipping container of high-assay low enriched uranium, the data of individual isotopes were systematically swapped between the two ENDF/B libraries. An eigenvalue difference of up to 450 pcm was found due to the use of 235 U and 238 U from one library and 1 H and 16 O from the other library. This clearly demonstrates a cross-correlation between reaction data sets of different isotopes within a library that should be reported in the evaluations. For sodium-cooled fast reactor (SFR) fuel assemblies, significant eigenvalue (k inf ) differences (200– 450 pcm) were found between calculations using the 2011 ENDF/B-VII.1 data and 2018 ENDF/B-VIII.0 data. These differences were mainly caused by updates of 238 U and 239 Pu neutron cross sections. Results from the multigroup (MG) calculations further revealed that the group structure of the applied MG library strongly influences the MG bias due to the importance of an appropriate energy resolution of the resonances in higher energy ranges. The application of previously used MG libraries requires new verification for advanced reactor simulation in comparisons with reference continuous-energy calculations. Nuclear data uncertainty analyses of these SFR systems resulted in eigenvalue uncertainties between 1,400 and 1,800 pcm, which are three to four times higher than corresponding uncertainties in light water reactor (LWR) systems. The main contributor to this uncertainty was found to be inelastic scattering on 238 U, which shows an uncertainty of up to 50% in the fast energy range. Other important contributors are the scattering reactions of 56 Fe and 23 Na which have so far not appeared in LWR analysis. Since the largest contribution to the eigenvalue uncertainty of SFR systems is coming from scattering reactions, it is expected that uncertainties in the angular scattering distributions also have a significant impact. Those uncertainties are, however, not available for the majority of nuclides, and the capabilities to determine sensitivities to this data are currently underdeveloped. For two graphite moderated high temperature gas-cooled reactor (HTGR) benchmarks, only the ENDF/BVII. 1 calculations resulted in consistent eigenvalues (k eff ) with the corresponding experimental measurements. Eigenvalue differences of about 1,000 pcm were found between the 2006 ENDF/B-VII.0 data and the 2011 ENDF/B-VII.1 data, primarily due to an updated carbon capture cross section in the thermal energy range in the later ENDF/B release. The ENDF/B-VIII.0 eigenvalue was larger than the ENDF/B-VII.1 eigenvalue by about 300 pcm mainly due to updates in multiple 235 U neutron cross sections, with offsetting updates in the 238 U cross sections. With ENDF/B-VIII.0, graphite can be modeled as perfect crystal or with two different porosities. The choice of the graphite evaluation can have a significant influence of the eigenvalue. For a HTGR benchmark, maximum eigenvalue differences as high as 650 pcm due to different porosities were observed. More detailed studies of the impact of the porosity are necessary while considering that the graphite porosity can vary between the used materials and changes as a function of neutron fluence. xii The uncertainty of the HTGR eigenvalues due to nuclear data uncertainties was found between 500 and 600 pcm, with the top contributor being the neutron multiplicity of 235 U. A gap in the form of missing uncertainties in graphite thermal scattering data, that might have significant impact on HTGR reactors, was identified. This gap is being investigated by the DOE-NE Nuclear Data and Benchmarking Program, as documented in a separate report The fast spectrum molten salt reactor calculations revealed similar comparisons as for the SFR assemblies. The eigenvalue uncertainties were significantly influenced by inelastic scattering on 238 U, while the impact of angular scattering distributions is unknown. For the graphite and zirconium hydride moderated system, eigenvalue uncertainties of up to 700 pcm were observed, requiring in depth analyses of the cross sections and corresponding uncertainties of the included materials. In general, it was observed that the flux spectra of the various molten salt reactor systems show significant differences, even between a fresh state and a depleted state. The choice of the energy group structure of MG calculations is therefore highly relevant; the applicability of previously used MG libraries needs to be verified. Due the unavailability of pin power measurements of advanced reactor systems, pin power calculations with both ENDF/B-VII.1 and VIII.0 data were performed for a light water reactor and compared to corresponding measurements. Both calculations show good agreement with the measurements. A comparison between the ENDF/B-VII.1 and VIII.0 results revealed small differences, mostly in the range of about 0.2%.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

The effects of random errors in rawinsonde data on derived kinematic quantities

The sensitivity of kinematic parameters to random errors contained in rawinsonde data is assessed. Parameters under consideration include relative vorticity, vorticity advection, horizontal divergence, kinematic vertical motion, and temperature advection. It is shown that horizontal divergence is the most affected, with reliability a function of height. Vorticity advection is the next most altered by random error, and in this case, the effects of wind errors are greater on the gradient of vorticity than on the vorticity itself. Vertical motions are most affected by random perturbations at 300 mb and above, and temperature advection is found to be the least sensitive to random perturbations.

Belt, C. L.↗

Parametric analysis of synthetic aperture radar data acquired over truck garden vegetation

An airborne X-band SAR acquired multipolarization and multiflight pass SAR images over a truck garden vegetation area. Based on a variety of land cover and row crop direction variations, the vertical (VV) polarization data contain the highest contrast, while cross polarization contains the least. When the radar flight path is parallel to the row direction, both horizontal (HH) and VV polarization data contain very high return which masks out the specific land cover that forms the row structure. Cross polarization data are not that sensitive to row orientation. The inclusion of like and cross polarization data help delineate special surface features (e.g., row crop against non-row-oriented land cover, very-rough-surface against highly row-oriented surface).

Wu, S. T.↗

Comparison of measured and calculated forces on the RE-1000 free-piston Stirling engine displacer

The NASA Lewis Research Center has tested a 1 kW free-piston Stirling engine at the NASA Lewis test facilities. The tests performed over the past several years on the RE-1000 single cylinder engine are known as the sensitivity tests. This report presents an analysis of some of the data published in the sensitivity test report. A basic investigation into the measured forces acting on the unconstrained displacer of the engine is presented. These measured forces are then correlated with the values predicted by the NASA Lewis Stirling engine computer simulation. The results of the investigation are presented in the form of phasor diagrams. Possible future work resulting from this investigation is outlined.

Schreiber, Jeffrey G.↗

TPSAS-NF1676L-20351-DND

Characterization of atmospheric variability is crucial to the design of the Entry, Descent, and Landing (EDL) activities at Mars. The distribution of dust in the Martian atmosphere has a significant impact on the atmospheric structure and variability. Information obtained through reconstruction of EDL data from past missions can be used in studying the performance of a model used in preflight atmospheric characterization for future missions. We use the Mars Weather Research and Forecasting (MarsWRF) General Circulation Model to simulate the atmospheric temperature during the landing time periods of Mars Exploration Rovers MER-A and MER-B in 2004. The multi-scale capability of MarsWRF is useful for conducting high- resolution nested simulation centered at the landing site. This version of MarsWRF includes a high spectral accuracy k-distribution radiative transfer model. We use the IR dust opacity profile data from the Thermal Emission spectrometer (TES) limb scan data as well as the TES Nadir data to prescribe the dust opacity distribution. Data from MY 26, which corresponds to the year of MER landing, and data from a climatology based on the median of 4 years (MY24 to MY27) of TES data are used. Model temperature profiles are compared with the reconstructions from EDL data and TES observations. Sensitivity of the model simulation to variations in the input opacity data are shown.

Murali Natarajan↗

Comparison of SAR and CYNSS surface water extent metrics over the Yucatan Lake wetland site

Wetlands have a major role in the carbon cycle, outgassing large quantities of carbon dioxide and methane through processes that are directly and strongly influenced by the duration and timing of inundation. Therefore, understanding the seasonal pattern of inundation can be a component for regional to global scale carbon models. Measurement of inundation extent also establishes a benchmark for the current status of wetland areas, useful in assessing the future impacts of climate change. The incorporation of frequent measurements of inundation extent into large-scale hydrological models would permit the evaluation of more detailed seasonal and longer-term floodplain dynamics and their associated management implications.The Cyclone GNSS (CYGNSS) constellation of satellites launched in 2016, and carries receivers capable of receiving data from L-band GNSS reflections. Delay Doppler maps (DDM) are generated on board and telemetered to the ground, along with a small number of raw data takes that can be used for special processing on the ground for evaluation purposes. It has been previously shown that these data can be sensitive to inundation.The NASA ISRO Synthetic Aperture Radar, currently planned for launch in January 2023, has both an L-band and S-band SAR for earth imaging. The L-band SAR, which will image the Earth's land mass twice every 12 days, has a requirement for measuring wetland inundation extent at the 1 ha scale. One of the sites that will be used to validate this requirement is Yucatan Lake, Louisiana. This oxbow lake and surrounding area located adjacent to the Mississippi river experiences periodic and extensive flooding in the surrounding forest areas.In 2019, NASA's UAVSAR fully polarimetric airborne L-band SAR conducted a flight campaign to image a dozen sites in the SE USA at approximately 12-day intervals and both in the morning and evening, to simulate the type of data NISAR will obtain. One site imaged during this campaign was the Yucatan Lake area, spanning water stages from low to high flood conditions.It has been demonstrated previously that GNSS reflectometry such as that measured by CYGNSS may be used to characterize surface inundation. It has also been known for decades that L-band SAR may be used to characterize not only the presence of open water, but also the presence of subcanopy inundation in forested areas. In this paper we will present results comparing data from these two types of instruments.

Lavalle, Marco↗

An ALMA+ACA measurement of the shock in the Bullet Cluster

Context: The thermal Sunyaev-Zeldovich (SZ) effect presents a relatively new tool for characterizing galaxy cluster merger shocks, traditionally studied through X-ray observations. Widely regarded as the “textbook example” of a cluster merger bow shock, the western, most-prominent shock front in the Bullet Cluster (1E0657-56) represents the ideal test case for such an SZ study. Aims: We aim to characterize the shock properties using deep, high-resolution interferometric SZ effect observations in combination with priors from an independent X-ray analysis. Methods: Our analysis technique relies on the reconstruction of a parametric model for the SZ signal by directly and jointly fitting data from the Atacama Large Millimeter/submillimeter Array (ALMA) and Atacama Compact Array (ACA) in Fourier space. Results: The ALMA+ACA data are primarily sensitive to the electron pressure difference across the shock front. To estimate the shock Mach number M, this difference can be combined with the value for the upstream electron pressure derived from an independent Chandra X-ray analysis. In the case of instantaneous electron-ion temperature equilibration, we find M = 2.08 (+0.12,−0.12), in ≈ 2.4σ tension with the independent constraint from Chandra, M(X)= 2.74 ± 0.25. The assumption of purely adiabatic electron temperature change across the shock leads to M = 2.53 (+0.33,−0.25), in better agreement with the X-ray estimate M(X) = 2.57 ± 0.23 derived for the same heating scenario. Conclusion: We have demonstrated that interferometric observations of the thermal SZ effect provide constraints on the properties of the shock in the Bullet Cluster that are highly complementary to X-ray observations. The combination of X-ray and SZ data yields a powerful probe of the shock properties, capable of measuring M and addressing the question of electron-ion equilibration in cluster shocks. Our analysis is however limited by systematics related to the overall cluster geometry and the complexity of the post-shock gas distribution. To overcome these limitations, a simultaneous, joint-likelihood analysis of SZ and X-ray data is needed.

Luca Di Mascolo↗

Sampling and Analysis Plan for Supplemental Environmental Project: Aquatic Life Surveys

As part of a settlement agreement for nuclear waste incidents in 2014, several supplemental environment projects (SEPs) were initiated at Los Alamos National Laboratory (LANL or the Laboratory) between the U.S. Department of Energy and the state of New Mexico. One SEP from this agreement consists of performing aquatic life surveys and will be used to assess the applicability of using generic ambient water-quality criteria (AWQC) for aquatic life. AWQC are generic criteria developed by the U.S. Environmental Protection Agency (EPA) to cover a broad range of aquatic species and are not unique to a specific region or state. AWQC are established by a composition of toxicity data, called species sensitivity distributions (SSDs), and are determined by LC50 (lethal concentration of 50% of the organisms studied) acute toxicity experiments for chemicals of interest. It is of interest to determine whether aquatic species inhabiting waters on the Pajarito Plateau are adequately protected using the current generic AWQC. The focus of this study will determine which aquatic species are present in ephemeral, intermittent, and perennial waters within LANL boundaries and from reference waters adjacent to LANL. If the species identified from these waters do not generally represent species used in the SSDs, then SSDs may need to be modified and AWQC may need to be updated. This sampling and analysis plan details the sampling methodology, surveillance locations, temporal scheduling, and analytical approaches that will be used to complete aquatic life surveys. A significant portion of this sampling and analysis plan was formalized by referring to Appendix E: SEP Aquatic Life Surveys DQO (Data Quality Objectives).

54 ENVIRONMENTAL SCIENCES↗

Unraveling the 2021 Central Tennessee flood event using a hierarchical multi-model inundation modeling framework

Flood prediction systems need hierarchical atmospheric, hydrologic, and hydraulic models to predict rainfall, runoff, streamflow, and floodplain inundation. The accuracy of such systems depends on the error propagation through the modeling chain, sensitivity to input data, and choice of models. In this study, we used multiple precipitation forcings (hindcast and forecast) to drive hydrologic and hydrodynamic models to analyze the impacts of various drivers on the estimates of flood inundation depth and extent. We implement this framework to unravel the August 2021 extreme flooding event that occurred in Central Tennessee, USA. We used two radar-based quantitative precipitation estimates (STAGE4 and MRMS) as well as quantitative precipitation forecasts (QPF) from the National Weather Service Weather Prediction Center (WPC) to drive a series of models in the hierarchical framework, including the Variable Infiltration Capacity (VIC) land surface model, the Routing Application for Parallel Computation of Discharge (RAPID) river routing model, and the AutoRoute and TRITON inundation models. An evaluation with observed high-water marks demonstrates that the framework can reasonably simulate flood inundation. Despite the complex error propagation mechanism of the modeling chain, we show that inundation estimates are most sensitive to rainfall estimates. Most notably, QPF significantly underestimates flood magnitudes and inundations leading to unanticipated severe flooding for all stakeholders involved in the event. Finally, we discuss the implications of the hydrodynamic modeling framework for real-time flood forecasting.

54 ENVIRONMENTAL SCIENCES↗

Deep-space navigation with differenced data types. Part 3: An expanded information content and sensitivity analysis

An approximate six-parameter analytic model for Earth-based differential range measurements is presented and is used to derive a representative analytic approximation for differenced Doppler measurements. The analytical models are tasked to investigate the ability of these data types to estimate spacecraft geocentric angular motion, Deep Space Network station oscillator (clock/frequency) offsets, and signal-path calibration errors over a period of a few days, in the presence of systematic station location and transmission media calibration errors. Quantitative results indicate that a few differenced Doppler plus ranging passes yield angular position estimates with a precision on the order of 0.1 to 0.4 micro-rad, and angular rate precision on the order of 10 to 25 x 10(exp -12) rad/sec, assuming no a priori information on the coordinate parameters. Sensitivity analyses suggest that troposphere zenith delay calibration error is the dominant systematic error source in most of the tracking scenarios investigated; as expected, the differenced Doppler data were found to be much more sensitive to troposphere calibration errors than differenced range. By comparison, results computed using wideband and narrowband (delta) VLBI under similar circumstances yielded angular precisions of 0.07 to 0.4 micro-rad, and angular rate precisions of 0.5 to 1.0 x 10(exp -12) rad/sec.

Estefan, J. A.↗