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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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NASA NTRS1974

Error analysis of householder transformations as applied to the standard and generalized eigenvalue problems

Backward error analyses of the application of Householder transformations to both the standard and the generalized eigenvalue problems are presented. The analysis for the standard eigenvalue problem determines the error from the application of an exact similarity transformation, and the analysis for the generalized eigenvalue problem determines the error from the application of an exact equivalence transformation. Bounds for the norms of the resulting perturbation matrices are presented and compared with existing bounds when known.

Ward, R. C.↗
NASA NTRS1976

Closed-loop stability of linear quadratic optimal systems in the presence of modeling errors

The well-known stabilizing property of linear quadratic state feedback design is utilized to evaluate the robustness of a linear quadratic feedback design in the presence of modeling errors. Two general conditions are obtained for allowable modeling errors such that the resulting closed-loop system remains stable. One of these conditions is applied to obtain two more particular conditions which are readily applicable to practical situations where a designer has information on the bounds of modeling errors. Relations are established between the allowable parameter uncertainty and the weighting matrices of the quadratic performance index, thereby enabling the designer to select appropriate weighting matrices to attain a robust feedback design.

Toda, M.↗
NASA NTRS1986

Evaluation of a surface/vegetation parameterization using satellite measurements of surface temperature

Ground measurements of surface-sensible heat flux and soil moisture for a wheat-growing area of Beauce in France were compared with the values derived by inverting two boundary layer models with a surface/vegetation formulation using surface temperature measurements made from NOAA-AVHRR. The results indicated that the trends in the surface heat fluxes and soil moisture observed during the 5 days of the field experiment were effectively captured by the inversion method using the remotely measured radiative temperatures and either of the two boundary layer methods, both of which contain nearly identical vegetation parameterizations described by Taconet et al. (1986). The sensitivity of the results to errors in the initial sounding values or measured surface temperature was tested by varying the initial sounding temperature, dewpoint, and wind speed and the measured surface temperature by amounts corresponding to typical measurement error. In general, the vegetation component was more sensitive to error than the bare soil model.

Taconet, O.↗
NASA NTRS1999

Main Geomagnetic Field Models from Oersted and Magsat Data Via a Rigorous General Inverse Theory with Error Bounds

The purpose of the grant was to study how prior information about the geomagnetic field can be used to interpret surface and satellite magnetic measurements, to generate quantitative descriptions of prior information that might be so used, and to use this prior information to obtain from satellite data a model of the core field with statistically justifiable error estimates. The need for prior information in geophysical inversion has long been recognized. Data sets are finite, and faithful descriptions of aspects of the earth almost always require infinite-dimensional model spaces. By themselves, the data can confine the correct earth model only to an infinite-dimensional subset of the model space. Earth properties other than direct functions of the observed data cannot be estimated from those data without prior information about the earth. Prior information is based on what the observer already knows before the data become available. Such information can be "hard" or "soft". Hard information is a belief that the real earth must lie in some known region of model space. For example, the total ohmic dissipation in the core is probably less that the total observed geothermal heat flow out of the earth's surface. (In principle, ohmic heat in the core can be recaptured to help drive the dynamo, but this effect is probably small.) "Soft" information is a probability distribution on the model space, a distribution that the observer accepts as a quantitative description of her/his beliefs about the earth. The probability distribution can be a subjective prior in the sense of Bayes or the objective result of a statistical study of previous data or relevant theories.

Backus, George E.↗
NASA NTRS1999

Adaptive Error Estimation in Linearized Ocean General Circulation Models

Data assimilation methods are routinely used in oceanography. The statistics of the model and measurement errors need to be specified a priori. This study addresses the problem of estimating model and measurement error statistics from observations. We start by testing innovation based methods of adaptive error estimation with low-dimensional models in the North Pacific (5-60 deg N, 132-252 deg E) to TOPEX/POSEIDON (TIP) sea level anomaly data, acoustic tomography data from the ATOC project, and the MIT General Circulation Model (GCM). A reduced state linear model that describes large scale internal (baroclinic) error dynamics is used. The methods are shown to be sensitive to the initial guess for the error statistics and the type of observations. A new off-line approach is developed, the covariance matching approach (CMA), where covariance matrices of model-data residuals are "matched" to their theoretical expectations using familiar least squares methods. This method uses observations directly instead of the innovations sequence and is shown to be related to the MT method and the method of Fu et al. (1993). Twin experiments using the same linearized MIT GCM suggest that altimetric data are ill-suited to the estimation of internal GCM errors, but that such estimates can in theory be obtained using acoustic data. The CMA is then applied to T/P sea level anomaly data and a linearization of a global GFDL GCM which uses two vertical modes. We show that the CMA method can be used with a global model and a global data set, and that the estimates of the error statistics are robust. We show that the fraction of the GCM-T/P residual variance explained by the model error is larger than that derived in Fukumori et al.(1999) with the method of Fu et al.(1993). Most of the model error is explained by the barotropic mode. However, we find that impact of the change in the error statistics on the data assimilation estimates is very small. This is explained by the large representation error, i.e. the dominance of the mesoscale eddies in the T/P signal, which are not part of the 21 by 1" GCM. Therefore, the impact of the observations on the assimilation is very small even after the adjustment of the error statistics. This work demonstrates that simult&neous estimation of the model and measurement error statistics for data assimilation with global ocean data sets and linearized GCMs is possible. However, the error covariance estimation problem is in general highly underdetermined, much more so than the state estimation problem. In other words there exist a very large number of statistical models that can be made consistent with the available data. Therefore, methods for obtaining quantitative error estimates, powerful though they may be, cannot replace physical insight. Used in the right context, as a tool for guiding the choice of a small number of model error parameters, covariance matching can be a useful addition to the repertory of tools available to oceanographers.

Chechelnitsky, Michael Y.↗
NASA NTRS1985

A comparative study of spherical and flat-Earth geopotential modeling at satellite elevations

Flat-Earth modeling is a desirable alternative to the complex spherical-Earth modeling process. These methods were compared using 2 1/2 dimensional flat-earth and spherical modeling to compute gravity and scalar magnetic anomalies along profiles perpendicular to the strike of variably dimensioned rectangular prisms at altitudes of 150, 300, and 450 km. Comparison was achieved with percent error computations (spherical-flat/spherical) at critical anomaly points. At the peak gravity anomaly value, errors are less than + or - 5% for all prisms. At 1/2 and 1/10 of the peak, errors are generally less than 10% and 40% respectively, increasing to these values with longer and wider prisms at higher altitudes. For magnetics, the errors at critical anomaly points are less than -10% for all prisms, attaining these magnitudes with longer and wider prisms at higher altitudes. In general, in both gravity and magnetic modeling, errors increase greatly for prisms wider than 500 km, although gravity modeling is more sensitive than magnetic modeling to spherical-Earth effects. Preliminary modeling of both satellite gravity and magnetic anomalies using flat-Earth assumptions is justified considering the errors caused by uncertainties in isolating anomalies.

Parrott, M. H.↗
NASA NTRS1990

General method for assessing the geographically correlated error for an orbiter with applications to Topex

An estimation based computational algorithm for evaluating geographically dependent orbit determination errors is presented. A derivation is included of the generalized geographically correlated error analysis algorithm and the algorithm is applied to a Topex simulation. Then a general numerical technique which provides the capability to analyze any type of mismodeled parameter with the geopotential as a special case is described. The numerical algorithm is compared with the analytic method of Rosborough (1986) and it is shown that both methods generate consistent geographically dependent orbit error profiles when the ephemeris error is dominated by the mismodeled geopotential.

Wolff, P. J.↗
NASA NTRS2018

Regional Replay: A Unique Reanalysis-Based Tool for Addressing Model Error

Understanding and correcting errors in general circulation and climate models has long been part intuition and part trial and error. Efforts to diagnose the errors and provide some guidance to developers have been of some value, though such efforts, with few exceptions, have been more successful in identifying and documenting the errors in the model simulations rather than the model deficiencies that produced them. Modern atmospheric reanalyses such as MERRA-2 provide much-improved estimates of our climate system at hourly to interannual and longer time scales and have become an important tool for assessing model performance. Here we use MERRA-2 to address biases in the NASA/GMAO GEOS model by employing a "regional replay" approach developed in the GMAO. The regional replay approach constrains the model to remain close to the reanalysis over arbitrary regions and selected model variables, thus allowing us to examine how model error generated over one area is spatially translated across the globe. Several examples are given including an assessment of the global impact of errors produced over the Tibet region.

Tibet Region↗
NASA NTRS1988

A gamma ray observatory ground attitude error analysis study using the generalized calibration system

The Goddard Space Flight Center (GSFC) Flight Dynamics Division (FDD) will be responsible for performing ground attitude determination for Gamma Ray Observatory (GRO) support. The study reported in this paper provides the FDD and the GRO project with ground attitude determination error information and illustrates several uses of the Generalized Calibration System (GCS). GCS, an institutional software tool in the FDD, automates the computation of the expected attitude determination uncertainty that a spacecraft will encounter during its mission. The GRO project is particularly interested in the uncertainty in the attitude determination using Sun sensors and a magnetometer when both star trackers are inoperable. In order to examine the expected attitude errors for GRO, a systematic approach was developed including various parametric studies. The approach identifies pertinent parameters and combines them to form a matrix of test runs in GCS. This matrix formed the basis for this study.

Ketchum, E.↗
NASA NTRS2004

The Impact of Subsampling on MODIS Level-3 Statistics of Cloud Optical Thickness and Effective Radius

The MODIS Level-3 optical thickness and effective radius cloud product is a gridded l deg. x 1 deg. dataset that is derived from aggregation and subsampling at 5 km of 1 km, resolution Level-2 orbital swath data (Level-2 granules). This study examines the impact of the 5 km subsampling on the mean, standard deviation and inhomogeneity parameter statistics of optical thickness and effective radius. The methodology is simple and consists of estimating mean errors for a large collection of Terra and Aqua Level-2 granules by taking the difference of the statistics at the original and subsampled resolutions. It is shown that the Level-3 sampling does not affect the various quantities investigated to the same degree, with second order moments suffering greater subsampling errors, as expected. Mean errors drop dramatically when averages over a sufficient number of regions (e.g., monthly and/or latitudinal averages) are taken, pointing to a dominance of errors that are of random nature. When histograms built from subsampled data with the same binning rules as in the Level-3 dataset are used to reconstruct the quantities of interest, the mean errors do not deteriorate significantly. The results in this paper provide guidance to users of MODIS Level-3 optical thickness and effective radius cloud products on the range of errors due to subsampling they should expect and perhaps account for, in scientific work with this dataset. In general, subsampling errors should not be a serious concern when moderate temporal and/or spatial averaging is performed.

Oreopoulos, Lazaros↗
NASA NTRS1990

A numerical algorithm to propagate navigation error covariance matrices associated with generalized strapdown inertial measurement units

The design and operation of a Strapdown Navigation Analysis Program (SNAP) developed to perform covariance analysis on spacecraft inertial-measurement-unit (IMU) navigation errors are described and demonstrated. Consideration is given to the IMU modeling subroutine (with user-specified sensor characteristics), the data input procedures, state updates and the simulation of instrument failures, the determination of the nominal trajectory, the mapping-matrix and Monte Carlo covariance-matrix propagation methods, and aided-navigation simulation. Numerical results are presented in tables for sample applications involving (1) the Galileo/IUS spacecraft from its deployment from the Space Shuttle to a point 10 to the 8th ft from the center of the earth and (2) the TDRS-C/IUS spacecraft from Space Shuttle liftoff to a point about 2 h before IUS deployment. SNAP is shown to give reliable results for both cases, with good general agreement between the mapping-matrix and Monte Carlo predictions.

Weir, Kent A.↗
NASA NTRS2009

A General Tool for Evaluating High-Contrast Coronagraphic Telescope Performance Error Budgets

This paper describes a general purpose Coronagraph Performance Error Budget (CPEB) tool that we have developed under the NASA Exoplanet Exploration Program. The CPEB automates many of the key steps required to evaluate the scattered starlight contrast in the dark hole of a space-based coronagraph. It operates in 3 steps: first, a CodeV or Zemax prescription is converted into a MACOS optical prescription. Second, a Matlab program calls ray-trace code that generates linear beam-walk and aberration sensitivity matrices for motions of the optical elements and line-of-sight pointing, with and without controlled coarse and fine-steering mirrors. Third, the sensitivity matrices are imported by macros into Excel 2007 where the error budget is created. Once created, the user specifies the quality of each optic from a predefined set of PSDs. The spreadsheet creates a nominal set of thermal and jitter motions and combines them with the sensitivity matrices to generate an error budget for the system. The user can easily modify the motion allocations to perform trade studies.

Terrestrial Planet Finder↗
NASA NTRS2017

Assessment of the Impact of Spatial Heterogeneity on Microwave Satellite Soil Moisture Periodic Error

An accurate temporal and spatial characterization of errors is required for the efficient processing, evaluation, and assimilation of remotely-sensed surface soil moisture retrievals. However, empirical evidence exists that passive microwave soil moisture retrievals are prone to periodic artifacts which may complicate their application in data assimilation systems (which commonly treat observational errors as being temporally white). In this paper, the link between such temporally-periodic errors and spatial land surface heterogeneity is examined. Both the synthetic experiment and site-specified cases reveal that, when combined with strong spatial heterogeneity, temporal periodicity in satellite sampling patterns (associated with exact repeat intervals of the polar-orbiting satellites) can lead to spurious high frequency spectral peaks in soil moisture retrievals. In addition, the global distribution of the most prominent and consistent 8-day spectral peak in the Advanced Microwave Scanning Radiometer - Earth Observing System soil moisture retrievals is revealed via a peak detection method. Three spatial heterogeneity indicators - based on microwave brightness temperature, land cover types, and long-term averaged vegetation index - are proposed to characterize the degree to which the variability of land surface is capable of inducing periodic error into satellite-based soil moisture retrievals. Regions demonstrating 8-day periodic errors are generally consistent with those exhibiting relatively higher heterogeneity indicators. This implies a causal relationship between spatial land surface heterogeneity and temporal periodic error in remotely-sensed surface soil moisture retrievals.

Fangni Lei↗
NASA NTRS2003

Bayes Error Rate Estimation Using Classifier Ensembles

The Bayes error rate gives a statistical lower bound on the error achievable for a given classification problem and the associated choice of features. By reliably estimating th is rate, one can assess the usefulness of the feature set that is being used for classification. Moreover, by comparing the accuracy achieved by a given classifier with the Bayes rate, one can quantify how effective that classifier is. Classical approaches for estimating or finding bounds for the Bayes error, in general, yield rather weak results for small sample sizes; unless the problem has some simple characteristics, such as Gaussian class-conditional likelihoods. This article shows how the outputs of a classifier ensemble can be used to provide reliable and easily obtainable estimates of the Bayes error with negligible extra computation. Three methods of varying sophistication are described. First, we present a framework that estimates the Bayes error when multiple classifiers, each providing an estimate of the a posteriori class probabilities, a recombined through averaging. Second, we bolster this approach by adding an information theoretic measure of output correlation to the estimate. Finally, we discuss a more general method that just looks at the class labels indicated by ensem ble members and provides error estimates based on the disagreements among classifiers. The methods are illustrated for artificial data, a difficult four-class problem involving underwater acoustic data, and two problems from the Problem benchmarks. For data sets with known Bayes error, the combiner-based methods introduced in this article outperform existing methods. The estimates obtained by the proposed methods also seem quite reliable for the real-life data sets for which the true Bayes rates are unknown.

Tumer, Kagan↗
NASA NTRS1991

Radiometric calibration of an airborne multispectral scanner

The absolute radiometric calibration of the NS001 Thematic Mapper Simulator reflective channels was examined based on laboratory tests and in-flight comparisons to ground measurements. The NS001 data are calibrated in-flight by reference to the NS001 internal integrating sphere source. This source's power supply or monitoring circuitry exhibited greater instability in-flight during 1988-1989 than in the laboratory. Extrapolating laboratory behavior to in-flight data resulted in 7-20 percent radiance errors relative to ground measurements and atmospheric modeling. Assuming constancy in the source's output between laboraotry and in-flight resulted in generally smaller errors. Upgrades to the source's power supply and monitoring circuitry in 1990 improved its in-flight stability, though in-flight ground reflectance based calibration tests have not yet been performed.

Markham, Brian L.↗
NASA NTRS1981

A general time element for orbit integration in Cartesian coordinates

Two techniques are discussed for increasing the accuracy of the numerical integration of eccentric orbits in Cartesian coordinates. One involves the use of an independent variable different from time; this increases the efficiency of the numerical integration. The other uses a time element, which reduces the in-track error. A general expression is given of a time element valid for an arbitrary independent variable. It is pointed out that this time element makes it possible to switch the independent variable merely by applying a scaling factor; there is no need to change the differential equations of the motion. Eccentric, true, and elliptic anomalies are used as independent variables in the case of a transfer orbit for a geosynchronous orbit. The elliptic anomaly is shown to perform much better than the other classical anomalies.

Janin, G.↗
NASA NTRS1986

Investigation of scene identification algorithms for radiation budget measurements

The computation of Earth radiation budget from satellite measurements requires the identification of the scene in order to select spectral factors and bidirectional models. A scene identification procedure is developed for AVHRR SW and LW data by using two radiative transfer models. These AVHRR GAC pixels are then attached to corresponding ERBE pixels and the results are sorted into scene identification probability matrices. These scene intercomparisons show that there generally is a higher tendency for underestimation of cloudiness over ocean at high cloud amounts, e.g., mostly cloudy instead of overcast, partly cloudy instead of mostly cloudy, for the ERBE relative to the AVHRR results. Reasons for this are explained. Preliminary estimates of the errors of exitances due to scene misidentification demonstrates the high dependency on the probability matrices. While the longwave error can generally be neglected the shortwave deviations have reached maximum values of more than 12% of the respective exitances.

Diekmann, F. J.↗