SEARCH · Search NASA

Results for “error estimation”

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.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 235 records · Page 13

All sources NASA NTRS DOE OSTI

DOE OSTI2024

Variance-Reduced Accelerated First-Order Methods: Central Limit Theorems and Confidence Statements

In this paper, we consider a strongly convex stochastic optimization problem and propose three classes of variable sample-size stochastic first-order methods: (i) the standard stochastic gradient descent method, (ii) its accelerated variant, and (iii) the stochastic heavy-ball method. In each scheme, the exact gradients are approximated by averaging across an increasing batch size of sampled gradients. We prove that when the sample size increases at a geometric rate, the generated estimates converge in mean to the optimal solution at an analogous geometric rate for schemes (i)–(iii). Based on this result, we provide central limit statements, whereby it is shown that the rescaled estimation errors converge in distribution to a normal distribution with the associated covariance matrix dependent on the Hessian matrix, the covariance of the gradient noise, and the step length. If the sample size increases at a polynomial rate, we show that the estimation errors decay at a corresponding polynomial rate and establish the associated central limit theorems (CLTs). Under certain conditions, we discuss how both the algorithms and the associated limit theorems may be extended to constrained and nonsmooth regimes. As a result, we provide an avenue to construct confidence regions for the optimal solution based on the established CLTs and test the theoretical findings on a stochastic parameter estimation problem.

Lei, Jinlong↗

NASA NTRS1991

Surface and aerosol models for use in radiative transfer codes

Absolute reflectance-based radiometric calibrations of Landsat-5 Thematic Mapper (TM) are improved with the inclusion of a method to invert optical-depth measurements to obtain aerosol-particle size distributions, and a non-Lambertian surface reflectance model. The inverted size distributions can predict radiances varying from the previously assumed jungian distributions by as much as 5 percent, though the reduction in the estimated error is less than one percent. Comparison with measured diffuse-to-global ratios show that neither distribution consistently predicts the ratio accurately, and this is shown to be a large contributor to calibration uncertainties. An empirical model for the surface reflectance of White Sands, using a two-degree polynomial fit as a function of scattering angle, was employed. The model reduced estimated errors in radiance predictions by up to one percent. Satellite calibrations dating from October, 1984 were reprocessed using the improved methods and linear estimations of satellite counts per unit radiance versus time since launch were determined which showed a decrease over time for the first four bands.

Hart, Quinn J.↗

DOE OSTI2024

Comparison of Full-Field and Integrated CFD Convergence Based on Richardson Extrapolation

This work investigated the usefulness of Richardson extrapolation--based discretization error estimates across all points in a solution field to produce a spatial convergence field for a computational fluid dynamics (CFD) simulation. The presented work used previously developed methods for Richardson extrapolation to compute the convergence orders of a CFD simulation at all points of the base (coarsest) mesh solution. Three test cases of increasing complexity were considered: Poiseuille flow, incompressible flow around a sharp corner, and transonic flow over an RAE 2822 airfoil. These test cases highlighted the potential of the proposed method to identify error sources and their relation to the model system-response-quantity convergence orders. However, these test cases also revealed the immaturity of the proposed method stemming from the unreliability of computing observed convergence orders at single points. Nonetheless, the test cases highlighted that the observed convergence orders allow for a more accurate diagnosis of constructive and destructive error transport than mesh pair error estimates. In the long run, the proposed method can be a tool for developing efficient and advanced error management strategies like adaptive mesh refinement.

Weinmeister, Justin↗

NASA NTRS2000

Adjoints and Low-rank Covariance Representation

Quantitative measures of the uncertainty of Earth System estimates can be as important as the estimates themselves. Second moments of estimation errors are described by the covariance matrix, whose direct calculation is impractical when the number of degrees of freedom of the system state is large. Ensemble and reduced-state approaches to prediction and data assimilation replace full estimation error covariance matrices by low-rank approximations. The appropriateness of such approximations depends on the spectrum of the full error covariance matrix, whose calculation is also often impractical. Here we examine the situation where the error covariance is a linear transformation of a forcing error covariance. We use operator norms and adjoints to relate the appropriateness of low-rank representations to the conditioning of this transformation. The analysis is used to investigate low-rank representations of the steady-state response to random forcing of an idealized discrete-time dynamical system.

Tippett, Michael K.↗

NASA NTRS1995

Analysis of filter tuning techniques for sequential orbit determination

This paper examines filter tuning techniques for a sequential orbit determination (OD) covariance analysis. Recently, there has been a renewed interest in sequential OD, primarily due to the successful flight qualification of the Tracking and Data Relay Satellite System (TDRSS) Onboard Navigation System (TONS) using Doppler data extracted onboard the Extreme Ultraviolet Explorer (EUVE) spacecraft. TONS computes highly accurate orbit solutions onboard the spacecraft in realtime using a sequential filter. As the result of the successful TONS-EUVE flight qualification experiment, the Earth Observing System (EOS) AM-1 Project has selected TONS as the prime navigation system. In addition, sequential OD methods can be used successfully for ground OD. Whether data are processed onboard or on the ground, a sequential OD procedure is generally favored over a batch technique when a realtime automated OD system is desired. Recently, OD covariance analyses were performed for the TONS-EUVE and TONS-EOS missions using the sequential processing options of the Orbit Determination Error Analysis System (ODEAS). ODEAS is the primary covariance analysis system used by the Goddard Space Flight Center (GSFC) Flight Dynamics Division (FDD). The results of these analyses revealed a high sensitivity of the OD solutions to the state process noise filter tuning parameters. The covariance analysis results show that the state estimate error contributions from measurement-related error sources, especially those due to the random noise and satellite-to-satellite ionospheric refraction correction errors, increase rapidly as the state process noise increases. These results prompted an in-depth investigation of the role of the filter tuning parameters in sequential OD covariance analysis. This paper analyzes how the spacecraft state estimate errors due to dynamic and measurement-related error sources are affected by the process noise level used. This information is then used to establish guidelines for determining optimal filter tuning parameters in a given sequential OD scenario for both covariance analysis and actual OD. Comparisons are also made with corresponding definitive OD results available from the TONS-EUVE analysis.

Lee, T.↗

NASA NTRS2016

Effect of Satellite Formations and Imaging Modes on Global Albedo Estimation

We confirm the applicability of using small satellite formation flight for multi-angular earth observation to retrieve global, narrow band, narrow field-of-view albedo. The value of formation flight is assessed using a coupled systems engineering and science evaluation model, driven by Model Based Systems Engineering and Observing System Simulation Experiments. Albedo errors are calculated against bi-directional reflectance data obtained from NASA airborne campaigns made by the Cloud Absorption Radiometer for the seven major surface types, binned using MODIS' land cover map - water, forest, cropland, grassland, snow, desert and cities. A full tradespace of architectures with three to eight satellites, maintainable orbits and imaging modes (collective payload pointing strategies) are assessed. For an arbitrary 4-sat formation, changing the reference, nadir-pointing satellite dynamically reduces the average albedo error to 0.003, from 0.006 found in the static reference case. Tracking pre-selected waypoints with all the satellites reduces the average error further to 0.001, allows better polar imaging and continued operations even with a broken formation. An albedo error of 0.001 translates to 1.36 W/sq m or 0.4% in Earth's outgoing radiation error. Estimation errors are found to be independent of the satellites' altitude and inclination, if the nadir-looking is changed dynamically. The formation satellites are restricted to differ in only right ascension of planes and mean anomalies within slotted bounds. Three satellites in some specific formations show average albedo errors of less than 2% with respect to airborne, ground data and seven satellites in any slotted formation outperform the monolithic error of 3.6%. In fact, the maximum possible albedo error, purely based on angular sampling, of 12% for monoliths is outperformed by a five-satellite formation in any slotted arrangement and an eight satellite formation can bring that error down four fold to 3%. More than 70% ground spot overlap between the satellites is possible with 0.5deg of pointing accuracy, 2 Km of GPS accuracy and commands uplinked once a day. The formations can be maintained at less than 1 m/s of monthly (Delta)V per satellite.

BRDF↗

NASA NTRS1983

Error latency estimation using functional fault modeling

A complete modeling of faults at gate level for a fault tolerant computer is both infeasible and uneconomical. Functional fault modeling is an approach where units are characterized at an intermediate level and then combined to determine fault behavior. The applicability of functional fault modeling to the FTMP is studied. Using this model a forecast of error latency is made for some functional blocks. This approach is useful in representing larger sections of the hardware and aids in uncovering system level deficiencies.

Manthani, S. R.↗

NASA NTRS2013

A Single-column Model Ensemble Approach Applied to the TWP-ICE Experiment

Single-column models (SCM) are useful test beds for investigating the parameterization schemes of numerical weather prediction and climate models. The usefulness of SCM simulations are limited, however, by the accuracy of the best estimate large-scale observations prescribed. Errors estimating the observations will result in uncertainty in modeled simulations. One method to address the modeled uncertainty is to simulate an ensemble where the ensemble members span observational uncertainty. This study first derives an ensemble of large-scale data for the Tropical Warm Pool International Cloud Experiment (TWP-ICE) based on an estimate of a possible source of error in the best estimate product. These data are then used to carry out simulations with 11 SCM and two cloud-resolving models (CRM). Best estimate simulations are also performed. All models show that moisture-related variables are close to observations and there are limited differences between the best estimate and ensemble mean values. The models, however, show different sensitivities to changes in the forcing particularly when weakly forced. The ensemble simulations highlight important differences in the surface evaporation term of the moisture budget between the SCM and CRM. Differences are also apparent between the models in the ensemble mean vertical structure of cloud variables, while for each model, cloud properties are relatively insensitive to forcing. The ensemble is further used to investigate cloud variables and precipitation and identifies differences between CRM and SCM particularly for relationships involving ice. This study highlights the additional analysis that can be performed using ensemble simulations and hence enables a more complete model investigation compared to using the more traditional single best estimate simulation only.

numerical weather forecasting↗

NASA NTRS1994

The analysis of star catalogs. 1: An intercomparison among the FK3, the FK4, and the FK5

Progress in the construction of the fundamental catalogs allows one to ask the following questions: 'Now that we have the FK5 with which to measure by, how good was the FK4? The FK3? How realistic were the error estimates they gave for their equatorial coordinates and their proper motions? Have their residual systematic differences continued to decrease in amplitude?' and so forth. Similar questions could be asked of the GC and the N30, and a companion paper will similarly analyze them. Finally, the identical series of questions could be asked of the AGK2, AGK3, AGK3U sequence. In this paper we develop a general method to objectively investigate, post facto, the true quality of star catalog error estimates. We present a complete mathematical formulation of the questions above and delineate the calculations needed to address them. Our initial numerical applications are restricted to a straightforward examination of the mean errors of the coordinates and proper motions in the FK3 (using the FK4 and the FK5 for comparison) and in the FK4 (using the FK5 for comparison). However, we can simply and consistently interpret the results of these computations -- for the FK catalogs fail to follow the predictions of mathematical statistics -- only if the FK3 and the FK4 contain higher angular frequency systematic errors. These errors, at the mean epochs of place of the older catalogs, are larger than the random errors in the FK5 system. We expect that our new ability to discern these features means that we can also prevent them during compilation. Finally, note that the concepts behind our procedures are completely general and can be applied to any set of compiled data -- astrometric, photometric, geodetic, and so forth.

Bucciarelli, B.↗

NASA NTRS2016

Model-Based Engine Control Architecture with an Extended Kalman Filter

This paper discusses the design and implementation of an extended Kalman filter (EKF) for model-based engine control (MBEC). Previously proposed MBEC architectures feature an optimal tuner Kalman Filter (OTKF) to produce estimates of both unmeasured engine parameters and estimates for the health of the engine. The success of this approach relies on the accuracy of the linear model and the ability of the optimal tuner to update its tuner estimates based on only a few sensors. Advances in computer processing are making it possible to replace the piece-wise linear model, developed off-line, with an on-board nonlinear model running in real-time. This will reduce the estimation errors associated with the linearization process, and is typically referred to as an extended Kalman filter. The nonlinear extended Kalman filter approach is applied to the Commercial Modular Aero-Propulsion System Simulation 40,000 (C-MAPSS40k) and compared to the previously proposed MBEC architecture. The results show that the EKF reduces the estimation error, especially during transient operation.

engine control↗

NASA NTRS1992

Submillimeter, millimeter, and microwave spectral line catalogue, revision 3

A computer-accessible catalog of submillimeter, millimeter, and microwave spectral lines in the frequency range between 0 and 10,000 GHz (i.e., wavelengths longer than 30 micrometers) is described. The catalog can be used as a planning or as an aid in the identification and analysis of observed spectral lines. The information listed for each spectral line includes the frequency and its estimated error, the intensity, the lower state energy, and the quantum number assignment. This edition of the catalog has information on 206 atomic and molecular species and includes a total of 630,924 lines. The catalog was constructed by using theoretical least square fits of published spectral lines to accepted molecular models. The associated predictions and their estimated errors are based upon the resultant fitted parameters and their covariances. Future versions of this catalog will add more atoms and molecules and update the present listings as new data appear. The catalog is available as a magnetic data tape recorded in card images, with one card image per spectral line, from the National Space Science Data Center, located at Goddard Space Flight Center.

Pickett, H. M.↗

NASA NTRS2016

Model-Based Engine Control Architecture with an Extended Kalman Filter

This paper discusses the design and implementation of an extended Kalman filter (EKF) for model-based engine control (MBEC). Previously proposed MBEC architectures feature an optimal tuner Kalman Filter (OTKF) to produce estimates of both unmeasured engine parameters and estimates for the health of the engine. The success of this approach relies on the accuracy of the linear model and the ability of the optimal tuner to update its tuner estimates based on only a few sensors. Advances in computer processing are making it possible to replace the piece-wise linear model, developed off-line, with an on-board nonlinear model running in real-time. This will reduce the estimation errors associated with the linearization process, and is typically referred to as an extended Kalman filter. The non-linear extended Kalman filter approach is applied to the Commercial Modular Aero-Propulsion System Simulation 40,000 (C-MAPSS40k) and compared to the previously proposed MBEC architecture. The results show that the EKF reduces the estimation error, especially during transient operation.

engine control↗

NASA NTRS1983

Statistical theory for estimating sampling errors of regional radiation averages based on satellite measurements

The processes which determine the weather and climate are driven by the radiation received by the earth and the radiation subsequently emitted. A knowledge of the absorbed and emitted components of radiation is thus fundamental for the study of these processes. In connection with the desire to improve the quality of long-range forecasting, NASA is developing the Earth Radiation Budget Experiment (ERBE), consisting of a three-channel scanning radiometer and a package of nonscanning radiometers. A set of these instruments is to be flown on both the NOAA-F and NOAA-G spacecraft, in sun-synchronous orbits, and on an Earth Radiation Budget Satellite. The purpose of the scanning radiometer is to obtain measurements from which the average reflected solar radiant exitance and the average earth-emitted radiant exitance at a reference level can be established. The estimate of regional average exitance obtained will not exactly equal the true value of the regional average exitance, but will differ due to spatial sampling. A method is presented for evaluating this spatial sampling error.

Smith, G. L.↗

NASA NTRS2014

Cart3D Simulations for the First AIAA Sonic Boom Prediction Workshop

Simulation results for the First AIAA Sonic Boom Prediction Workshop (LBW1) are presented using an inviscid, embedded-boundary Cartesian mesh method. The method employs adjoint-based error estimation and adaptive meshing to automatically determine resolution requirements of the computational domain. Results are presented for both mandatory and optional test cases. These include an axisymmetric body of revolution, a 69deg delta wing model and a complete model of the Lockheed N+2 supersonic tri-jet with V-tail and flow through nacelles. In addition to formal mesh refinement studies and examination of the adjoint-based error estimates, mesh convergence is assessed by presenting simulation results for meshes at several resolutions which are comparable in size to the unstructured grids distributed by the workshop organizers. Data provided includes both the pressure signals required by the workshop and information on code performance in both memory and processing time. Various enhanced techniques offering improved simulation efficiency will be demonstrated and discussed.

Predictions↗

NASA NTRS1981

Analysis of Meteorological Satellite location and data collection system concepts

A satellite system that employs a spaceborne RF interferometer to determine the location and velocity of data collection platforms attached to meteorological balloons is proposed. This meteorological advanced location and data collection system (MALDCS) is intended to fly aboard a low polar orbiting satellite. The flight instrument configuration includes antennas supported on long deployable booms. The platform location and velocity estimation errors introduced by the dynamic and thermal behavior of the antenna booms and the effects of the presence of the booms on the performance of the spacecraft's attitude control system, and the control system design considerations critical to stable operations are examined. The physical parameters of the Astromast type of deployable boom were used in the dynamic and thermal boom analysis, and the TIROS N system was assumed for the attitude control analysis. Velocity estimation error versus boom length was determined. There was an optimum, minimum error, antenna separation distance. A description of the proposed MALDCS system and a discussion of ambiguity resolution are included.

Wallace, R. G.↗

NASA NTRS2008

Identifying Bearing Rotodynamic Coefficients Using an Extended Kalman Filter

An Extended Kalman Filter is developed to estimate the linearized direct and indirect stiffness and damping force coefficients for bearings in rotor dynamic applications from noisy measurements of the shaft displacement in response to imbalance and impact excitation. The bearing properties are modeled as stochastic random variables using a Gauss-Markov model. Noise terms are introduced into the system model to account for all of the estimation error, including modeling errors and uncertainties and the propagation of measurement errors into the parameter estimates. The system model contains two user-defined parameters that can be tuned to improve the filter's performance; these parameters correspond to the covariance of the system and measurement noise variables. The filter is also strongly influenced by the initial values of the states and the error covariance matrix. The filter is demonstrated using numerically simulated data for a rotor bearing system with two identical bearings, which reduces the number of unknown linear dynamic coefficients to eight. The filter estimates for the direct damping coefficients and all four stiffness coefficients correlated well with actual values, whereas the estimates for the cross-coupled damping coefficients were the least accurate.

Miller, Brad A.↗

NASA NTRS2008

Identifying Bearing Rotordynamic Coefficients using an Extended Kalman Filter

An Extended Kalman Filter is developed to estimate the linearized direct and indirect stiffness and damping force coefficients for bearings in rotor-dynamic applications from noisy measurements of the shaft displacement in response to imbalance and impact excitation. The bearing properties are modeled as stochastic random variables using a Gauss-Markov model. Noise terms are introduced into the system model to account for all of the estimation error, including modeling errors and uncertainties and the propagation of measurement errors into the parameter estimates. The system model contains two user-defined parameters that can be tuned to improve the filter s performance; these parameters correspond to the covariance of the system and measurement noise variables. The filter is also strongly influenced by the initial values of the states and the error covariance matrix. The filter is demonstrated using numerically simulated data for a rotor-bearing system with two identical bearings, which reduces the number of unknown linear dynamic coefficients to eight. The filter estimates for the direct damping coefficients and all four stiffness coefficients correlated well with actual values, whereas the estimates for the cross-coupled damping coefficients were the least accurate.

Miller, Bard A.↗

NASA NTRS2008

Identifying Bearing Rotordynamic Coefficients using an Extended Kalman Filter

Miller, Brad A.↗