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DOE OSTI2020

Black hole spin in X-ray binaries: giving uncertainties an $\mathcal{f}$

The two established techniques for measuring black hole spin in X-ray binaries often yield conflicting results, which must be resolved before either method may be deemed robust. In practice, black hole spin measurements based on fitting the accretion disc continuum effectively do not marginalize over the colour-correction factor f col . This factor parametrizes spectral hardening of the disc continuum by the disc atmosphere, whose true properties are poorly constrained. We incorporate reasonable systematic uncertainties in f col into the eight (non-maximal) black hole spin measurements vetted by the disc continuum fitting community. In most cases, an f col uncertainty of ±0.2–0.3 dominates the black hole spin error budget. We go on to demonstrate that plausible departures in f col values from those adopted by the disc continuum fitting practitioners can bring the discrepant black hole spins into agreement with those from iron line modelling. Systematic uncertainties in f col , such as the effects of strong magnetization, should be better understood before dismissing their potentially dominant impact on the black hole spin error budget.

4U 1543–47↗

NASA NTRS2013

Covariance Analysis Tool (G-CAT) for Computing Ascent, Descent, and Landing Errors

G-CAT is a covariance analysis tool that enables fast and accurate computation of error ellipses for descent, landing, ascent, and rendezvous scenarios, and quantifies knowledge error contributions needed for error budgeting purposes. Because GCAT supports hardware/system trade studies in spacecraft and mission design, it is useful in both early and late mission/ proposal phases where Monte Carlo simulation capability is not mature, Monte Carlo simulation takes too long to run, and/or there is a need to perform multiple parametric system design trades that would require an unwieldy number of Monte Carlo runs. G-CAT is formulated as a variable-order square-root linearized Kalman filter (LKF), typically using over 120 filter states. An important property of G-CAT is that it is based on a 6-DOF (degrees of freedom) formulation that completely captures the combined effects of both attitude and translation errors on the propagated trajectories. This ensures its accuracy for guidance, navigation, and control (GN&C) analysis. G-CAT provides the desired fast turnaround analysis needed for error budgeting in support of mission concept formulations, design trade studies, and proposal development efforts. The main usefulness of a covariance analysis tool such as G-CAT is its ability to calculate the performance envelope directly from a single run. This is in sharp contrast to running thousands of simulations to obtain similar information using Monte Carlo methods. It does this by propagating the "statistics" of the overall design, rather than simulating individual trajectories. G-CAT supports applications to lunar, planetary, and small body missions. It characterizes onboard knowledge propagation errors associated with inertial measurement unit (IMU) errors (gyro and accelerometer), gravity errors/dispersions (spherical harmonics, masscons), and radar errors (multiple altimeter beams, multiple Doppler velocimeter beams). G-CAT is a standalone MATLAB- based tool intended to run on any engineer's desktop computer.

Boussalis, Dhemetrios↗

DOE OSTI2025

Precision measurements of EFT parameters and BAO peak shifts for the Lyman- α forest

We present precision measurements of the bias parameters of the one-loop power spectrum model of the Lyman- α (Ly- α ) forest, derived within the effective field theory (EFT) of large-scale structure. We fit our model to the three-dimensional flux power spectrum measured from the ACCEL 2 hydrodynamic simulations. The EFT model fits the data with an accuracy of below 2% up to k = 2 h Mpc − 1 . Further, we analytically derive how nonlinearities in the three-dimensional clustering of the Ly- α forest introduce biases in measurements of the baryon acoustic oscillations (BAOs) scaling parameters in radial and transverse directions. From our EFT parameter measurements, we obtain a theoretical error budget of Δ α ∥ = − 0.2 % ( Δ α ⊥ = − 0.3 % ) for the radial (transverse) parameters at redshift z = 2.0 . This corresponds to a shift of − 0.3 % (0.1%) for the isotropic (anisotropic) distance measurements. We provide an estimate for the shift of the BAO peak for Ly- α -quasar cross-correlation measurements assuming analytical and simulation-based scaling relations for the nonlinear quasar bias parameters resulting in a shift of − 0.2 % ( − 0.1 % ) for the radial (transverse) dilation parameters, respectively. This analysis emphasizes the robustness of Ly- α forest BAO measurements to the theory modeling. We provide informative priors and an error budget for measuring the BAO feature—a key science driver of the currently observing Dark Energy Spectroscopic Instrument (DESI). Our work paves the way for full-shape cosmological analyses of Ly- α forest data from DESI and upcoming surveys such as the Prime Focus Spectrograph, WEAVE-QSO, and 4MOST. Published by the American Physical Society 2025

de Belsunce, Roger (ORCID:0000000336604028)↗

NASA NTRS1999

Secondary Forest Age and Tropical Forest Biomass Estimation Using TM

The age of secondary forests in the Amazon will become more critical with respect to the estimation of biomass and carbon budgets as tropical forest conversion continues. Multitemporal Thematic Mapper data were used to develop land cover histories for a 33,000 Square kM area near Ariquemes, Rondonia over a 7 year period from 1989-1995. The age of the secondary forest, a surrogate for the amount of biomass (or carbon) stored above-ground, was found to be unimportant in terms of biomass budget error rates in a forested TM scene which had undergone a 20% conversion to nonforest/agricultural cover types. In such a situation, the 80% of the scene still covered by primary forest accounted for over 98% of the scene biomass. The difference between secondary forest biomass estimates developed with and without age information were inconsequential relative to the estimate of biomass for the entire scene. However, in futuristic scenarios where all of the primary forest has been converted to agriculture and secondary forest (55% and 42% respectively), the ability to age secondary forest becomes critical. Depending on biomass accumulation rate assumptions, scene biomass budget errors on the order of -10% to +30% are likely if the age of the secondary forests are not taken into account. Single-date TM imagery cannot be used to accurately age secondary forests into single-year classes. A neural network utilizing TM band 2 and three TM spectral-texture measures (bands 3 and 5) predicted secondary forest age over a range of 0-7 years with an RMSE of 1.59 years and an R(Squared) (sub actual vs predicted) = 0.37. A proposal is made, based on a literature review, to use satellite imagery to identify general secondary forest age groups which, within group, exhibit relatively constant biomass accumulation rates.

Nelson, R. F.↗

NASA NTRS2012

Test Plan for a Calibration Demonstration System for the Reflected Solar Instrument for the Climate Absolute Radiance and Refractivity Observatory

The Climate Absolute Radiance and Refractivity Observatory (CLARREO) mission addresses the need to observe high-accuracy, long-term climate change trends and to use decadal change observations as the most critical method to determine the accuracy of climate change. One of the major objectives of CLARREO is to advance the accuracy of SI traceable absolute calibration at infrared and reflected solar wavelengths. This advance is required to reach the on-orbit absolute accuracy required to allow climate change observations to survive data gaps while remaining sufficiently accurate to observe climate change to within the uncertainty of the limit of natural variability. While these capabilities exist at NIST in the laboratory, there is a need to demonstrate that it can move successfully from NIST to NASA and/or instrument vendor capabilities for future spaceborne instruments. The current work describes the test plan for the Solar, Lunar for Absolute Reflectance Imaging Spectroradiometer (SOLARIS) which is the calibration demonstration system (CDS) for the reflected solar portion of CLARREO. The goal of the CDS is to allow the testing and evaluation of calibration approaches , alternate design and/or implementation approaches and components for the CLARREO mission. SOLARIS also provides a test-bed for detector technologies, non-linearity determination and uncertainties, and application of future technology developments and suggested spacecraft instrument design modifications. The end result of efforts with the SOLARIS CDS will be an SI-traceable error budget for reflectance retrieval using solar irradiance as a reference and methods for laboratory-based, absolute calibration suitable for climate-quality data collections. The CLARREO mission addresses the need to observe high-accuracy, long-term climate change trends and advance the accuracy of SI traceable absolute calibration. The current work describes the test plan for the SOLARIS which is the calibration demonstration system for the reflected solar portion of CLARREO. SOLARIS provides a test-bed for detector technologies, non-linearity determination and uncertainties, and application of future technology developments and suggested spacecraft instrument design modifications. The end result will be an SI-traceable error budget for reflectance retrieval using solar irradiance as a reference and methods for laboratory-based, absolute calibration suitable for climate-quality data collections.

Thome, Kurtis↗

DOE OSTI2020

EXPRES. I. HD 3651 as an Ideal RV Benchmark

The next generation of exoplanet-hunting spectrographs should deliver up to an order of magnitude improvement in radial velocity (RV) precision over the standard 1 m s{sup −1} state-of-the-art spectrographs. This advance is critical for enabling the detection of Earth-mass planets around Sun-like stars. New calibration techniques such as laser frequency combs and stabilized etalons ensure that the instrumental stability is well characterized. However, additional sources of error include stellar noise, undetected short-period planets, and telluric contamination. To understand and ultimately mitigate error sources, the contributing terms in the error budget must be isolated to the greatest extent possible. Here, we introduce a new high-cadence RV program, the Extreme Precision Spectrograph (EXPRES) 100 Earths Survey, which aims to identify rocky planets around bright, nearby G and K dwarfs. We also present a benchmark case: the 62 day orbit of a Saturn-mass planet orbiting the chromospherically quiet star, HD 3651. The combination of high eccentricity (0.6) and a moderately long orbital period ensures significant dynamical clearing of any inner planets. Our Keplerian model for this planetary orbit has a residual rms of 58 cm s{sup −1} over a ∼6 month time baseline. By eliminating significant contributors to the RV error budget, HD 3651 serves as a standard for evaluating the long-term precision of extreme precision RV programs.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS2012

Instrumentation and First Results of the Reflected Solar Demonstration System for the Climate Absolute Radiance and Refractivity Observatory

The Climate Absolute Radiance and Refractivity Observatory (CLARREO) mission key goals include enabling observation of high accuracy long-term climate change trends, use of these observations to test and improve climate forecasts, and calibration of operational and research sensors. The spaceborne instrument suites include a reflected solar spectroradiometer, emitted infrared spectroradiometer, and radio occultation receivers. The requirement for the RS instrument is that derived reflectance must be traceable to Sl standards with an absolute uncertainty of <0.3% and the error budget that achieves this requirement is described in previo1L5 work. This work describes the Solar/Lunar Absolute Reflectance Imaging Spectroradiometer (SOLARIS), a calibration demonstration system for RS instrument, and presents initial calibration and characterization methods and results. SOLARIS is an Offner spectrometer with two separate focal planes each with its own entrance aperture and grating covering spectral ranges of 320-640, 600-2300 nm over a full field-of-view of 10 degrees with 0.27 milliradian sampling. Results from laboratory measurements including use of integrating spheres, transfer radiometers and spectral standards combined with field-based solar and lunar acquisitions are presented. These results will be used to assess the accuracy and repeatability of the radiometric and spectral characteristics of SOLARIS, which will be presented against the sensor-level requirements addressed in the CLARREO RS instrument error budget.

McCorkel, Joel↗

NASA NTRS1991

Differential tracking data types for accurate and efficient Mars planetary navigation

Ways in which high-accuracy differential observations of two or more deep space vehicles can dramatically extend the power of earth-based tracking over conventional range and Doppler tracking are discussed. Two techniques - spacecraft-spacecraft differential very long baseline interferometry (S/C-S/C Delta(VLBI)) and same-beam interferometry (SBI) - are discussed. The tracking and navigation capabilities of conventional range, Doppler, and quasar-relative Delta(VLBI) are reviewed, and the S/C-S/C Delta (VLBI) and SBI types are introduced. For each data type, the formation of the observable is discussed, an error budget describing how physical error sources manifest themselves in the observable is presented, and potential applications of the technique for Space Exploration Initiative scenarios are examined. Requirements for spacecraft and ground systems needed to enable and optimize these types of observations are discussed.

Edwards, C. D., Jr.↗

NASA NTRS2000

Tidal Implications for the GRACE Satellite Mission

A fundamental part of the processing of the GRACE satellite data will be correction for the gravitational effect of tides. This includes solid earth, ocean, and atmospheric tides. The most problematic are ocean tides in shallow seas and in high latitudes (above the 66$^{\circ}$ inclination of Topex). Somewhat smaller, but still important, errors are associated with the S$_1$ air tide and the ocean's dynamic response to it. In this paper we explore several facets of the tidal error budget. The ocean tide error spectrum is estimated (a) by inverse methods and (b) by simple differencing of several of the best tidal models. The tidal error spectrum is flatter than the tidal signal spectrum, and it exceeds 10\% of the signal at degrees 15 and above. The tide errors also exceed the anticipated sensitivity of GRACE for all degrees below 40, and possibly below 50. The assumption of constant seawater density (of about 1035 kg\,M$^{-3}$) is a minor error source. Owing to GRACE's high inclination, solar tides are aliased to long periods, which is potentially problematic for geophysical interpretation of the gravity signal. Simulations of the effect of high-latitude solar-tide errors on gravity estimates around Antarctica will be discussed.

Ray, Richard D.↗

NASA NTRS2012

The Precise Orbit and the Challenge of Long Term Stability

The computation of a precise orbit reference is a fundamental component of the altimetric measurement. Since the dawn of the modern altimeter age, orbit accuracy has been determined by the quality of the GPS, SLR, and DORIS tracking systems, the fidelity of the measurement and force models, and the choice of parameterization for the orbit solutions, and whether a dynamic or a reduced-dynamic strategy is used to calculate the orbits. At the start of the TOPEX mission, the inaccuracies in the modeling of static gravity, dynamic ocean tides, and the nonconservative forces dominated the orbit error budget. Much of the error due to dynamic mismodeling can be compensated by reduced-dynamic tracking techniques depending on the measurement system strength. In the last decade, the launch of the GRACE mission has eliminated the static gravity field as a concern, and the background force models and the terrestrial reference frame have been systematically refined. GPS systems have realized many improvements, including better modeling of the forces on the GPS spacecraft, large increases in the ground tracking network, and improved modeling of the GPS measurements. DORIS systems have achieved improvements through the use of new antennae, more stable monumentation, and of satellite receivers that can track multiple beacons, and as well as through improved modeling of the nonconservative forces. Many of these improvements have been applied in the new reprocessed time series of orbits produced for the ERS satellites, Envisat, TOPEX/Poseidon and the Jason satellites, and as well as for the most recent Cryosat-2 and HY2A. We now face the challenge of maintaining a stable orbit reference for these altimetric satellites. Changes in the time-variable gravity field of the Earth and how these are modelled have been shown to affect the orbit evolution, and the calibration of the altimetric data with tide gauges. The accuracy of the reference frame realizations, and their projection into the future remains a source of error. Other sources of omission error include the geocenter for which no consensus model is as of yet applied. Although progress has been made in nonconservative force modeling through the use of detailed satellite-specific models, radiation pressure modeling, and atmospheric density modeling remain a potential source of orbit error. The longer term influence of variations in the solar and terrestrial radiation fields over annual and solar cycles remains principally untested. Also the long term variation in optical and thermal properties of the space vehicle surfaces would contribute to biases in the orbital frame if ignored. We review the status of altimetric precision orbit determination as exemplified by the recent computations undertaken by the different analysis centers for ERS, Envisat, TOPEX/Poseidon, Jason, Cryosat2 and HY2A, and we provide a perspective on the challenges for future missions such as the Jason-3, SENTINEL-3 and SWOT.

Lemoine, Frank G.↗

NASA NTRS2010

Normalized Point Source Sensitivity for Off-Axis Optical Performance Evaluation of the Thirty Meter Telescope

The Normalized Point Source Sensitivity (PSSN) has previously been defined and analyzed as an On-Axis seeing-limited telescope performance metric. In this paper, we expand the scope of the PSSN definition to include Off-Axis field of view (FoV) points and apply this generalized metric for performance evaluation of the Thirty Meter Telescope (TMT). We first propose various possible choices for the PSSN definition and select one as our baseline. We show that our baseline metric has useful properties including the multiplicative feature even when considering Off-Axis FoV points, which has proven to be useful for optimizing the telescope error budget. Various TMT optical errors are considered for the performance evaluation including segment alignment and phasing, segment surface figures, temperature, and gravity, whose On-Axis PSSN values have previously been published by our group.

optical performance metric↗

NASA NTRS2021

Fundamental Problems In SmallSat Concept Development

The standardization of launch opportunities as secondary payloads, coupled with the miniaturization of digital electronics due to Moore’s law, has enabled a new class of space missions at greatly reduced costs – SmallSat missions. Unfortunately, the desires of concept developers are often in conflict with the limited technical budgets afforded within the constraints of a SmallSat mission. Chief amongst these limited technical budgets, ironically, are the limited mass and volume budgets that enable them in the first place.Mass and volume budgets are consumed in closure of the other technical budgets in space systems: science error budgets, delta-v and propellent budgets, power and energy budgets, and thermal budgets, to name a few. Most aspects of these budgets are unaffected by the miniaturization of digital electronics enabled by modern physics, but are instead governed by the laws of classical physics, worked out by Europeans, long since dead.The fundamental laws of classical physics provide the couplings between these budgets, and provide a way to help potential users realize the practical limitations inherent in SmallSat systems. Understanding the fundamental limitations better positions concept developers to find innovative solutions with these systems and not inefficiently pursue infeasible approaches to their needs.

Austin, Alexander↗

NASA NTRS2008

Radiometric Spacecraft Tracking for Deep Space Navigation

Interplanetary spacecraft navigation relies on three types of terrestrial tracking observables.1) Ranging measures the distance between the observing site and the probe. 2) The line-of-sight velocity of the probe is inferred from Doppler-shift by measuring the frequency shift of the received signal with respect to the unshifted frequency. 3) Differential angular coordinates of the probe with respect to natural radio sources are nominally obtained via a differential delay technique of (Delta) DOR (Delta Differential One-way Ranging). The accuracy of spacecraft coordinate determination depends on the measurement uncertainties associated with each of these three techniques. We evaluate the corresponding sources of error and present a detailed error budget.

ranging↗

NASA NTRS2010

X/Ka Celestial Frame Improvements: Vision to Reality

In order to extend the International Celestial Reference Frame from its S/X-band (2.3/8.4 GHz) basis to a complementary frame at X/Ka-band (8.4/32 GHz), we began in mid-2005 an ongoing series of X/Ka observations using NASA s Deep Space Network (DSN) radio telescopes. Over the course of 47 sessions, we have detected 351 extra-galactic radio sources covering the full 24 hours of right ascension and declinations down to -45 degrees. Angular source position accuracy is at the part-per-billion level. We developed an error budget which shows that the main errors arise from limited sensitivity, mismodeling of the troposphere, uncalibrated instrumental effects, and the lack of a southern baseline. Recent work has improved sensitivity by improving pointing calibrations and by increasing the data rate four-fold. Troposphere calibration has been demonstrated at the mm-level. Construction of instrumental phase calibrators and new digital baseband filtering electronics began in recent months. We will discuss the expected effect of these improvements on the X/Ka frame.

Jacobs, C. S.↗

NASA NTRS2018

Optical Budgeting for LUVOIR

Future large astronomical telescopes in space will have architectures that will have complex and demanding requirements to meet the science goals. The Large UV/Optical/IR Surveyor (LUVOIR) mission concept being assessed by the NASA/Goddard Space Flight Center is expected to be 8 to 16 meters in diameter, have a segmented primary mirror, active control, and be diffraction limited at a wavelength of 500 nanometers. The optical stability is expected to be in the picometer range for minutes to hours. Architecture studies to support the NASA Science and Technology Definition teams (STDTs) are underway to evaluate systems performance. A wave front error budget has been developed to help define the technology needs and assess performance. The budget includes both spatial and temporal domain aspects for the active, adaptive and passive elements in the optical design.

space telescopes↗

DOE OSTI2025

Light and Strange Vector Resonances from Lattice QCD at Physical Quark Masses

We present the first ab initio calculation at physical quark masses of scattering amplitudes describing the lightest pseudoscalar mesons interacting via the strong force in the vector channel. Using lattice quantum chromodynamics, we postdict the defining parameters for two short-lived resonances, the ρ(770) and K*(892) which manifest as complex energy poles in ππ and Kπ scattering amplitudes, respectively. The calculation proceeds by first computing the finite-volume energy spectrum of the two-hadron systems and then determining the amplitudes from the energies using the Lüscher formalism. The error budget includes a data-driven systematic error, obtained by scanning possible fit ranges and fit models to extract the spectrum from Euclidean correlators, as well as the scattering amplitudes from the latter. The final results, obtained by analytically continuing multiple parametrizations into the complex energy plane, are M ρ = 796(5)(50)MeV, Γ ρ = 192(10)(31) MeV, M K* = 893(2)(54) MeV, and Γ K = 51(2)(11) MeV, where the subscript indicates the resonance and M and Γ stand for the mass and width, respectively, and where the first bracket indicates the statistical and the second bracket the systematic uncertainty.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

NASA NTRS1977

Altimeter error sources at the 10-cm performance level

Error sources affecting the calibration and operational use of a 10 cm altimeter are examined to determine the magnitudes of current errors and the investigations necessary to reduce them to acceptable bounds. Errors considered include those affecting operational data pre-processing, and those affecting altitude bias determination, with error budgets developed for both. The most significant error sources affecting pre-processing are bias calibration, propagation corrections for the ionosphere, and measurement noise. No ionospheric models are currently validated at the required 10-25% accuracy level. The optimum smoothing to reduce the effects of measurement noise is investigated and found to be on the order of one second, based on the TASC model of geoid undulations. The 10 cm calibrations are found to be feasible only through the use of altimeter passes that are very high elevation for a tracking station which tracks very close to the time of altimeter track, such as a high elevation pass across the island of Bermuda. By far the largest error source, based on the current state-of-the-art, is the location of the island tracking station relative to mean sea level in the surrounding ocean areas.

Martin, C. F.↗

NASA NTRS1989

A statistical study of radio-source structure effects on astrometric very long baseline interferometry observations

Errors from a number of sources in astrometric very long baseline interferometry (VLBI) have been reduced in recent years through a variety of methods of calibration and modeling. Such reductions have led to a situation in which the extended structure of the natural radio sources used in VLBI is a significant error source in the effort to improve the accuracy of the radio reference frame. In the past, work has been done on individual radio sources to establish the magnitude of the errors caused by their particular structures. The results of calculations on 26 radio sources are reported in which an effort is made to determine the typical delay and delay-rate errors for a number of sources having different types of structure. It is found that for single observations of the types of radio sources present in astrometric catalogs, group-delay and phase-delay scatter in the 50 to 100 psec range due to source structure can be expected at 8.4 GHz on the intercontinental baselines available in the Deep Space Network (DSN). Delay-rate scatter of approx. 5 x 10(exp -15) sec sec(exp -1) (or approx. 0.002 mm sec (exp -1) is also expected. If such errors mapped directly into source position errors, they would correspond to position uncertainties of approx. 2 to 5 nrad, similar to the best position determinations in the current JPL VLBI catalog. With the advent of wider bandwidth VLBI systems on the large DSN antennas, the system noise will be low enough so that the structure-induced errors will be a significant part of the error budget. Several possibilities for reducing the structure errors are discussed briefly, although it is likely that considerable effort will have to be devoted to the structure problem in order to reduce the typical error by a factor of two or more.

Ulvestad, J. S.↗