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NASA NTRS2019

A comprehensive line spread function error for the Off-plane Grating Rocket Experiment

The Off-plane Grating Rocket Experiment (OGRE) is a soft X-ray grating spectrometer to be flown on a suborbital rocket. The payload is designed to obtain the highest-resolution soft X-ray spectrum of Capella to date with a resolution goal of R(lambda/delta lambda) > 2000 at select wavelengths in its 10 - 55 A bandpass of interest. The optical design of the spectrometer realizes a maximum resolution of R 5000 with all components performing optimally, in perfect alignment, and not considering in-flight pointing errors; however, performance errors, misalignments, and in-flight pointing errors work to degrade this performance. A comprehensive line spread function (LSF) error budget has been constructed for the spectrometer to identify errors contributing to the LSF, to determine how each affects the LSF, and to inform performance requirements and alignment tolerances for the spectrometer. In this document, the comprehensive LSF error budget for the OGRE spectrometer is presented and its implications are discussed.

Benjamin D Donovan↗

NASA NTRSDate not supplied

Logical Shadow Tomography: Efficient Estimation of Error-mitigated Observables

In near-term quantum applications, reducing errors and improving device reliability is an essential task. Towards these ends, various techniques have been introduced in recent literature, collectively referred to as quantum error mitigation techniques, for reducing errors in pre-fault-tolerant devices. Here, we introduce logical shadow tomography as a versatile error mitigation method. Our technique uses a stabilizer code to encode information in a logical state. Instead of doing active error correction, quantum states will be measured at the end of computation via shadow tomography and non-logical errors are projected out in the classical post-processing. Relative to quantum subspace expansion which requires O(2(M-1)L) experiments to estimate an logical Pauli observable encoded by an [[M, L, d]] code, our technique only requires 2L experiments, an important practical reduction in resources.

Hong-Ye Hu↗

NASA NTRS2022

Exploring the Relationship Between Temperature Forecast Errors and Earth System Variables

Accurate subseasonal weather forecasts, from two weeks up to a season, can help reduce costs and impacts related to weather and corresponding extremes. The quality of weather forecasts has improved considerably in recent decades as models represent more details of physical processes, and they benefit from assimilating comprehensive Earth observation data as well as increasing computing power. However, with ever–growing model complexity, it becomes increasingly difficult to pinpoint weaknesses in the forecast models’ process representations which is key to improving forecast accuracy. In this study, we use a comprehensive set of observation–based ecological, hydrological and meteorological variables to study their potential for explaining temperature forecast errors at the weekly time scale. For this purpose, we compute Spearman correlations between each considered variable and the forecast error obtained from the ECMWF subseasonal–to–seasonal (S2S) reforecasts at lead times of 1–6 weeks. This is done across the globe for the time period 2001–2017. The results show that temperature forecast errors globally are most strongly related with climate–related variables such as surface solar radiation and precipitation, which highlights the model’s difficulties in accurately capturing the evolution of the climate–related variables during the forecasting period. At the same time, we find particular regions in which other variables are more strongly related to forecast errors. For instance, in central Europe, eastern North America and southeastern Asia, vegetation greenness and soil moisture are relevant, while in western South America and central North America, circulation–related variables such as surface pressure relate more strongly with forecast errors. Overall, the identified relationships between forecast errors and independent Earth observations reveal promising variables on which future forecasting system development could focus by specifically considering related process representations and data assimilation.

Temperature↗

NASA NTRS2011

Power Spectrum of Uplink Array Signals with Random Phase and Delay Errors

Link Array signals emanating from different antennas must be compensated for Doppler and delay in order to achieve the N(sup 2) array gain predicted by theory. However compensation is never perfect, leaving residual errors that cause losses in array gain and degradation in signal quality. Here we develop a mathematical model for Uplink Array signals in the presence of phase and delay errors, similar to well-known multipath analyses but with features unique to this problem. The resulting losses and distortions are described, and the power spectral density of the array signal derived first conditioned on a given error vector, then averaged over distributions deemed suitable for Uplink Array applications. The impact of phase and delay errors on array gain and signal distortion are addressed, and the maximum data throughput is quantified in terms of the assumed error statistics.

uplinks arrays↗

NASA NTRS2014

Background Error Covariance Estimation Using Information from a Single Model Trajectory with Application to Ocean Data Assimilation

An attractive property of ensemble data assimilation methods is that they provide flow dependent background error covariance estimates which can be used to update fields of observed variables as well as fields of unobserved model variables. Two methods to estimate background error covariances are introduced which share the above property with ensemble data assimilation methods but do not involve the integration of multiple model trajectories. Instead, all the necessary covariance information is obtained from a single model integration. The Space Adaptive Forecast error Estimation (SAFE) algorithm estimates error covariances from the spatial distribution of model variables within a single state vector. The Flow Adaptive error Statistics from a Time series (FAST) method constructs an ensemble sampled from a moving window along a model trajectory.SAFE and FAST are applied to the assimilation of Argo temperature profiles into version 4.1 of the Modular Ocean Model (MOM4.1) coupled to the GEOS-5 atmospheric model and to the CICE sea ice model. The results are validated against unassimilated Argo salinity data. They show that SAFE and FAST are competitive with the ensemble optimal interpolation (EnOI) used by the Global Modeling and Assimilation Office (GMAO) to produce its ocean analysis. Because of their reduced cost, SAFE and FAST hold promise for high-resolution data assimilation applications.

Error Covariance↗

NASA NTRS2014

Background Error Covariance Estimation using Information from a Single Model Trajectory with Application to Ocean Data Assimilation into the GEOS-5 Coupled Model

An attractive property of ensemble data assimilation methods is that they provide flow dependent background error covariance estimates which can be used to update fields of observed variables as well as fields of unobserved model variables. Two methods to estimate background error covariances are introduced which share the above property with ensemble data assimilation methods but do not involve the integration of multiple model trajectories. Instead, all the necessary covariance information is obtained from a single model integration. The Space Adaptive Forecast error Estimation (SAFE) algorithm estimates error covariances from the spatial distribution of model variables within a single state vector. The Flow Adaptive error Statistics from a Time series (FAST) method constructs an ensemble sampled from a moving window along a model trajectory. SAFE and FAST are applied to the assimilation of Argo temperature profiles into version 4.1 of the Modular Ocean Model (MOM4.1) coupled to the GEOS-5 atmospheric model and to the CICE sea ice model. The results are validated against unassimilated Argo salinity data. They show that SAFE and FAST are competitive with the ensemble optimal interpolation (EnOI) used by the Global Modeling and Assimilation Office (GMAO) to produce its ocean analysis. Because of their reduced cost, SAFE and FAST hold promise for high-resolution data assimilation applications.

Data Assimilation↗

NASA NTRS2017

Human Error Assessment and Reduction Technique (HEART) and Human Factor Analysis and Classification System (HFACS)

Research results have shown that more than half of aviation, aerospace and aeronautics mishaps incidents are attributed to human error. As a part of Quality within space exploration ground processing operations, the identification and or classification of underlying contributors and causes of human error must be identified, in order to manage human error.This presentation will provide a framework and methodology using the Human Error Assessment and Reduction Technique (HEART) and Human Factor Analysis and Classification System (HFACS), as an analysis tool to identify contributing factors, their impact on human error events, and predict the Human Error probabilities (HEPs) of future occurrences. This research methodology was applied (retrospectively) to six (6) NASA ground processing operations scenarios and thirty (30) years of Launch Vehicle related mishap data. This modifiable framework can be used and followed by other space and similar complex operations.

human error↗

NASA NTRSDate not supplied

Empirical State Error Covariance Matrix for Batch Estimation

State estimation techniques effectively provide mean state estimates. However, the theoretical state error covariance matrices provided as part of these techniques often suffer from a lack of confidence in their abilities to describe the true uncertainty in the estimated states. By a reinterpretation of the equations involved in the weighted least squares algorithm, it is possible to directly arrive at an empirical state error covariance matrix. This proposed empirical state error covariance matrix will contain the effect of all error sources, known or unknown. Results are presented for a simple, two observer, measurement error only problem.

Estimation↗

NASA NTRSDate not supplied

Effects of Dose Error and Sample Size on Sonic Boom Dose-response Curves

NASA will soon be collecting noise-annoyance community survey data as the X-59 aircraft flies supersonically over several communities in the USA. Sparse measurements of the X-59 sonic thumps will be used together with physics-based simulations to estimate noise doses at survey participant locations. These dose estimates have associated error that affects the accuracy of modeled dose-response curves, which can result in misestimation of annoyance. The precision in dose-response curves is also a consideration in selecting the number of survey participants. To enable pretest studies of dose error and precision, simulated dose-response data were generated based on NASA’s Quiet Supersonic Flights 2018 test. The data included various degrees of dose error and sample size. Frequentist multilevel logistic regression models were fit to the true and perturbed dose-response data. Simple proportional relationships were identified between the model parameters and the perturbation standard deviation. The summary dose-response curves illustrate the impact on accuracy if dose error is not accounted for in the model. The precision in the dose-response curves is also shown as the number of participants and degree of participation is varied. Finally, sampling variability is illustrated by showing the dose-response curves for several replicates with random draws of participants and errors.

X-59↗

NASA NTRSDate not supplied

Effects of Dose Error and Sample Size on Sonic Boom Dose-Response Curves

X-59↗

NASA NTRSDate not supplied

Dose Error Correction Using Simulation Extrapolation for Community Noise Dose-Response Modeling

The objective of this work is to provide a framework to account and correct for dose error in dose-response modeling due to measurement uncertainty. Error in noise measurements, especially in the case of limited monitoring locations in a community, can lead to an attenuation or misestimation of parameters in dose-response models. This error can result in overpredicted annoyance at lower doses and underpredicted annoyance at higher doses. Simulated data in the present work are based on previous NASA community studies and incorporate a notional design for future studies with the X-59 aircraft. Several populations of different annoyance response sensitivities are included. Simulation extrapolation (SIMEX, Cook and Stefanski 1994) is used to correct for the dose error in a simple, fully pooled logistic regression. Results indicate the negative impact of attenuation is greatly diminished for all amounts of dose error considered, regardless of a population’s annoyance sensitivity. Therefore, SIMEX can help produce a more accurate dose-response relationship.

SIMEX↗

NASA NTRSDate not supplied

Modeling Measurement Error in Dose-Response Models of Community Annoyance to Low-Noise Supersonic Flight

The primary research goal of the forthcoming NASA Quesst mission community test campaign is to collect representative community response data in support of the development of supersonic overflight noise certification standards. Beginning in 2026, NASA will fly the novel X-59 demonstrator aircraft over select communities in United States in order to demonstrate the possibility of low-noise supersonic flight over land and to collect objective measurements and subjective data on the perceptual experience of this new noise source. It is believed that a regression of a binary perceptual response (‘highly annoyed’ or ‘not’) on estimated noise levels (doses, measured in decibels) will provide a useful dose-response relationship for regulators. However, as these estimated doses will be subject to measurement error, naïve estimators of regression coefficients are inconsistent and slopes may be subject to attenuation bias. In this presentation, I contrast functional modeling of measurement error via simulation extrapolation (SIMEX) with structural Bayesian measurement error models. These methods are applied to available data collected during two NASA risk reduction studies in California in 2011 and Texas in 2018. I’ll conclude noting that in the presence of nonnegligible measurement errors, probabilities of annoyance may be overpredicted for low noise levels and underpredicted for high noise levels, therefore, methods of correcting for measurement error will be necessary to improve the utility of the dose-response relationship for policy-making purposes.

simulation↗

NASA NTRS1972

A Monte Carlo error analysis program for near-Mars, finite-burn, orbital transfer maneuvers

A computer program was developed which performs an error analysis of a minimum-fuel, finite-thrust, transfer maneuver between two Keplerian orbits in the vicinity of Mars. The method of analysis is the Monte Carlo approach where each off-nominal initial orbit is targeted to the desired final orbit. The errors in the initial orbit are described by two covariance matrices of state deviations and tracking errors. The function of the program is to relate these errors to the resulting errors in the final orbit. The equations of motion for the transfer trajectory are those of a spacecraft maneuvering with constant thrust and mass-flow rate in the neighborhood of a single body. The thrust vector is allowed to rotate in a plane with a constant pitch rate. The transfer trajectory is characterized by six control parameters and the final orbit is defined, or partially defined, by the desired target parameters. The program is applicable to the deboost maneuver (hyperbola to ellipse), orbital trim maneuver (ellipse to ellipse), fly-by maneuver (hyperbola to hyperbola), escape maneuvers (ellipse to hyperbola), and deorbit maneuver.

Green, R. N.↗

NASA NTRS1971

Arithmetic error codes - Cost and effectiveness studies for application in digital system design.

The application of error-detecting or error-correcting codes in digital computer design requires studies of cost and effectiveness tradeoffs to supplement the knowledge of their theoretical properties. General criteria for cost and effectiveness studies of error codes are developed, and results are presented for arithmetic error codes with the low-cost check modulus 2 super a - 1. Both separate (residue) and nonseparate (AN) codes are considered. The class of multiple arithmetic error codes is developed as an extension of low-cost single codes.

Avizienis, A.↗

NASA NTRS1972

Dynamic errors in a tuned flexure-mounted strapdown gyro

Motion induced errors in a tuned, flexure-mounted strapdown gyro are investigated. Analytic expressions are developed for errors induced by linear vibrations, angular motion, and detuning. Sensor-level errors (gyro drift rate) and system-level errors (navigation errors) that are stimulated by an actual dynamic motion environment are computed.

Bortz, J. E., Sr.↗

NASA NTRS1972

Error model for the SAO 1969 standard earth.

A method is developed for estimating an error model for geopotential coefficients using satellite tracking data. A single station's apparent timing error for each pass is attributed to geopotential errors. The root sum of the residuals for each station also depends on the geopotential errors, and these are used to select an error model. The model chosen is 1/4 of the difference between the SAO M1 and the APL 3.5 geopotential.

Martin, C. F.↗

NASA NTRS1973

Effect of photogrammetric reading error on slope-frequency distributions

The effect of reading error on two hypothetical slope frequency distributions and two slope frequency distributions from actual lunar data in order to ensure that these errors do not cause excessive overestimates of algebraic standard deviations for the slope frequency distributions. The errors introduced are insignificant when the reading error is small and the slope length is large. A method for correcting the errors in slope frequency distributions is presented and applied to 11 distributions obtained from Apollo 15, 16, and 17 panoramic camera photographs and Apollo 16 metric camera photographs.

Moore, H. J.↗

NASA NTRS1974

Derivation of formulas for root-mean-square errors in location, orientation, and shape in triangulation solution of an elongated object in space

Formulas are derived for the root-mean-square (rms) displacement, slope, and curvature errors in an azimuth-elevation image trace of an elongated object in space, as functions of the number and spacing of the input data points and the rms elevation error in the individual input data points from a single observation station. Also, formulas are derived for the total rms displacement, slope, and curvature error vectors in the triangulation solution of an elongated object in space due to the rms displacement, slope, and curvature errors, respectively, in the azimuth-elevation image traces from different observation stations. The total rms displacement, slope, and curvature error vectors provide useful measure numbers for determining the relative merits of two or more different triangulation procedures applicable to elongated objects in space.

Long, S. A. T.↗