Results for “error estimation and analysis” — Page 7

NASA NTRSDate not supplied

Simultaneous Trajectory Tracking Control and Online Mass Estimation for a Regolith Excavating Robot via Integral Concurrent Learning

An adaptive controller is developed for a regolith excavation robot to determine the mass of excavated material and to account for the effects of gravity and friction while on the surface of other celestial bodies. A data-based integral concurrent learning (ICL) parameter update law accounts for and estimates the unknown mass, gravity, and friction parameters. A Lyapunov-based analysis proves that the trajectory tracking error and the parameter estimate errors exponentially converge to zero. An estimation of the mass of regolith excavated by the robot is calculated from the estimated parameters. A simulation study is performed to show the performance of the developed technique. Simulation results show that for 3 kilograms of excavated material, the mass estimate has an error of 4.9 grams.

Max L. Greene↗

NASA NTRS2019

Multilevel Monte Carlo Estimation of Unbiased Expectation via Sample Reuse and the Low Variance Estimation of Asymptotic Rates

A new variant of the multilevel Monte Carlo estimator [5, 3, 9, 12] is presented for the estimation of expectation statistics that utilizes sample reuse in specified levels, explicitly removes approximation error bias associated with numerically computed output quantities of interest that have an asymptotic limit behavior, and permits a low variance estimate of the asymptotic rate of convergence to that limit. In addition, it is shown that this new multilevel Monte Carlo variant can yield a computational cost savings. A review of Monte Carlo and multilevel Monte Carlo estimators is presented that includes analysis of expected value, expected mean squared error, and the calculation of optimized multilevel sample size parameters. The multilevel Monte Carlo estimator produces estimates of expectation for numerically approximated output quantities of interest that are biased by approximation error. When the quantity of interest can be modeled as the asymptotic limit of numerically approximated output quantities of interest, it is theoretically possible to remove this approximation error bias in the multilevel Monte Carlo estimator. In actual implementations, however, this procedure is unreliable due to statistical variability and inaccuracy in estimating the needed asymptotic limit. Analysis and numerical experiment show that the proposed variant of the multilevel Monte Carlo method greatly reduces (in some cases eliminates) the statistical variability in this limit estimation.

Barth, Timothy↗

NASA NTRS1970

Neutron ages computed from experimental activation data

Computer program reduces time manually required to compute neutron age and to provide definite plan of procedural choices. Program allows convenient comparison of several fitting and error analysis procedures. Program code provides for error estimation of various integration options.

Semler, T. T.↗

NASA NTRS1976

A simulation for gravity fine structure recovery from high-low GRAVSAT SST data

Covariance error analysis techniques were applied to investigate estimation strategies for the high-low SST mission for accurate local recovery of gravitational fine structure, considering the aliasing effects of unsolved for parameters. Surface density blocks of 5 deg x 5 deg and 2 1/2 deg x 2 1/2 deg resolution were utilized to represent the high order geopotential with the drag-free GRAVSAT configured in a nearly circular polar orbit at 250 km. altitude. GEOPAUSE and geosynchronous satellites were considered as high relay spacecraft. It is demonstrated that knowledge of gravitational fine structure can be significantly improved at 5 deg x 5 deg resolution using SST data from a high-low configuration with reasonably accurate orbits for the low GRAVSAT. The gravity fine structure recoverability of the high-low SST mission is compared with the low-low configuration and shown to be superior.

Estes, R. H.↗

NASA NTRS1984

Specular reflectance of optical-black coatings in the far infrared

Far-infrared specular reflectance spectra of seven optically black coatings near normal incidence are presented. Seven photometric spectra were obtained using eleven bandpass transmission filters in the wavelength range between 12 and 500 microns, and three interferometric spectra were obtained for corroboration. Data on the construction, thickness, and rms surface roughness of the coatings are also presented. The chemical composition of three coatings can be distinguished from that of the others by a strong absorption feature between 20 and 40 microns, which can be largely attributed to amorphous silicate material. At 100 microns, the most and least reflective coatings differ by nearly 3 orders of magnitude. Inverse relationships observed between the spectra and the roughness and thickness of the coatings led to development of a reflecting-layer model for the measured reflectance. The model successfully describes the spectra at wavelengths outside the silicate absorption, and optical constants are deduced from a nonlinear least squares fit to the data. Parametric errors are estimated by chi-square analysis, and sensitivity tests are performed to determine which parameters control reflectance in different spectral regions.

Smith, S. M.↗

NASA NTRS1985

Application of laser anemometry to turbomachinery flow field measurements

The application of laser anemometry to the measurement of turbomachinery flow fields is reviewed. Choices of optical configuration, seed particle generation, and seed injection techniques are discussed. The modification of experimental facilities to gain optical access is considered. The efficiency of data acquisition schemes is analyzed and issues related to data integrity and error estimation are addressed. Data reduction and analysis techniques for extracting and understanding the flow physics from laser anemometer measurements are presented.

Strazisar, A. J.↗

NASA NTRS1988

The NBS scale of radiance temperature

The measurement methods and instrumentation used in the realization and transfer of the International Practical Temperature Scale (IPTS-68) above the temperature of freezing gold are described. The determination of the ratios of spectral radiance of tungsten-strip lamps to a gold-point blackbody at a wavelength of 654.6 nm is detailed. The response linearity, spectral responsivity, scattering error, and polarization properties of the instrumentation are described. The analysis of the sources of error and estimates of uncertainty are presented. The assigned uncertainties (three standard deviations) in radiance temperature range from + or - 2 K at 2573 K to + or - 0.5 K at 1073 K.

Waters, William R.↗

NASA NTRS1988

Relative error covariance analysis techniques and application

A technique for computing the error covariance of the difference between two estimators derived from different (possibly overlapping) data arcs is presented. The relative error covariance is useful for predicting the achievable consistency between Kalman-Bucy filtered estimates generated from two (not necessarily disjoint) data sets. The relative error covariance analysis technique is then applied to a Venus Orbiter simulation.

Wolff, Peter, J.↗

NASA NTRS1993

Attitude determination using vector observations: A fast optimal matrix algorithm

The attitude matrix minimizing Wahba's loss function is computed directly by a method that is competitive with the fastest known algorithm for finding this optimal estimate. The method also provides an estimate of the attitude error covariance matrix. Analysis of the special case of two vector observations identifies those cases for which the TRIAD or algebraic method minimizes Wahba's loss function.

Markley, F. Landis↗

NASA NTRS1993

Attitude determination using vector observations - A fast optimal matrix algorithm

The attitude matrix minimizing Wahba's loss function is computed directly by a method that is competitive with the fastest known algorithm for finding this optimal estimate. The method also provides an estimate of the attitude error covariance matrix. Analysis of the special case of two vector observations identifies those cases for which the TRIAD or algebraic method minimizes Wahba's loss function.

Markley, F. L.↗

NASA NTRS1983

Estimating regression coefficients from clustered samples: Sampling errors and optimum sample allocation

A number of surveys were conducted to study the relationship between the level of aircraft or traffic noise exposure experienced by people living in a particular area and their annoyance with it. These surveys generally employ a clustered sample design which affects the precision of the survey estimates. Regression analysis of annoyance on noise measures and other variables is often an important component of the survey analysis. Formulae are presented for estimating the standard errors of regression coefficients and ratio of regression coefficients that are applicable with a two- or three-stage clustered sample design. Using a simple cost function, they also determine the optimum allocation of the sample across the stages of the sample design for the estimation of a regression coefficient.

Kalton, G.↗

NASA NTRS2010

Improving Forecast Skill by Assimilation of AIRS Temperature Soundings

AIRS was launched on EOS Aqua on May 4, 2002, together with AMSU-A and HSB, to form a next generation polar orbiting infrared and microwave atmospheric sounding system. The primary products of AIRS/AMSU-A are twice daily global fields of atmospheric temperature-humidity profiles, ozone profiles, sea/land surface skin temperature, and cloud related parameters including OLR. The AIRS Version 5 retrieval algorithm, is now being used operationally at the Goddard DISC in the routine generation of geophysical parameters derived from AIRS/AMSU data. A major innovation in Version 5 is the ability to generate case-by-case level-by-level error estimates delta T(p) for retrieved quantities and the use of these error estimates for Quality Control. We conducted a number of data assimilation experiments using the NASA GEOS-5 Data Assimilation System as a step toward finding an optimum balance of spatial coverage and sounding accuracy with regard to improving forecast skill. The model was run at a horizontal resolution of 0.5 deg. latitude X 0.67 deg longitude with 72 vertical levels. These experiments were run during four different seasons, each using a different year. The AIRS temperature profiles were presented to the GEOS-5 analysis as rawinsonde profiles, and the profile error estimates delta (p) were used as the uncertainty for each measurement in the data assimilation process. We compared forecasts analyses generated from the analyses done by assimilation of AIRS temperature profiles with three different sets of thresholds; Standard, Medium, and Tight. Assimilation of Quality Controlled AIRS temperature profiles significantly improve 5-7 day forecast skill compared to that obtained without the benefit of AIRS data in all of the cases studied. In addition, assimilation of Quality Controlled AIRS temperature soundings performs better than assimilation of AIRS observed radiances. Based on the experiments shown, Tight Quality Control of AIRS temperature profile performs best on the average from the perspective of improving Global 7 day forecast skill.

Susskind, Joel↗

NASA NTRS2010

Use of Quality Controlled AIRS Temperature Soundings to Improve Forecast Skill

AIRS was launched on EOS Aqua on May 4, 2002, together with AMSU-A and HSB, to form a next generation polar orbiting infrared and microwave atmospheric sounding system. The primary products of AIRS/AMSU-A are twice daily global fields of atmospheric temperature-humidity profiles, ozone profiles, sea/land surface skin temperature, and cloud related parameters including OLR. Also included are the clear column radiances used to derive these products which are representative of the radiances AIRS would have seen if there were no clouds in the field of view. All products also have error estimates. The sounding goals of AIRS are to produce 1 km tropospheric layer mean temperatures with an rms error of 1K, and layer precipitable water with an rms error of 20 percent, in cases with up to 90 percent effective cloud cover. The products are designed for data assimilation purposes for the improvement of numerical weather prediction, as well as for the study of climate and meteorological processes. With regard to data assimilation, one can use either the products themselves or the clear column radiances from which the products were derived. The AIRS Version 5 retrieval algorithm is now being used operationally at the Goddard DISC in the routine generation of geophysical parameters derived from AIRS/AMSU data. A major innovation in Version 5 is the ability to generate case-by-case level-by-level error estimates for retrieved quantities and clear column radiances, and the use of these error estimates for Quality Control. The temperature profile error estimates are used to determine a case-by-case characteristic pressure pbest, down to which the profile is considered acceptable for data assimilation purposes. The characteristic pressure p(sub best) is determined by comparing the case dependent error estimate (delta)T(p) to the threshold values (Delta)T(p). The AIRS Version 5 data set provides error estimates of T(p) at all levels, and also profile dependent values of pbest based on use of a Standard profile dependent threshold (Delta)T(p). These Standard thresholds were designed as a compromise between optimal use for data assimilation purposes, which requires highest accuracy (tighter Quality Control), and climate purposes, which requires more spatial coverage (looser Quality Control). Subsequent research using Version 5 sounding and error estimates showed that tighter Quality Control performs better for data assimilation proposes, while looser Quality Control better spatial coverage) performs better for climate purposes. We conducted a number of data assimilation experiments using the NASA GEOS-5 Data Assimilation System as a step toward finding an optimum balance of spatial coverage and sounding accuracy with regard to improving forecast skill. The model was run at a horizontal resolution of 0.5 degree latitude x 0.67 degree longitude with 72 vertical levels. These experiments were run during four different seasons, each using a different year. The AIRS temperature profiles were presented to the GEOS-5 analysis as rawinsonde profiles, and the profile error estimates (delta)T(p) were used as the uncertainty for each measurement in the data assimilation process.

Susskind, Joel↗

NASA NTRS1990

Consistency and convergence for numerical radiation conditions

The problem of imposing radiation conditions at artificial boundaries for the numerical simulation of wave propagation is considered. Emphasis is on the behavior and analysis of the error which results from the restriction of the domain. The theory of error estimation is briefly outlined for boundary conditions. Use is made of the asymptotic analysis of propagating wave groups to derive and analyze boundary operators. For dissipative problems this leads to local, accurate conditions, but falls short in the hyperbolic case. A numerical experiment on the solution of the wave equation with cylindrical symmetry is described. A unified presentation of a number of conditions which have been proposed in the literature is given and the time dependence of the error which results from their use is displayed. The results are in qualitative agreement with theoretical considerations. It was found, however, that for this model problem it is particularly difficult to force the error to decay rapidly in time.

Hagstrom, Thomas↗

NASA NTRS2001

A Canonical Ensemble Correlation Prediction Model for Seasonal Precipitation Anomaly

This report describes an optimal ensemble forecasting model for seasonal precipitation and its error estimation. Each individual forecast is based on the canonical correlation analysis (CCA) in the spectral spaces whose bases are empirical orthogonal functions (EOF). The optimal weights in the ensemble forecasting crucially depend on the mean square error of each individual forecast. An estimate of the mean square error of a CCA prediction is made also using the spectral method. The error is decomposed onto EOFs of the predictand and decreases linearly according to the correlation between the predictor and predictand. This new CCA model includes the following features: (1) the use of area-factor, (2) the estimation of prediction error, and (3) the optimal ensemble of multiple forecasts. The new CCA model is applied to the seasonal forecasting of the United States precipitation field. The predictor is the sea surface temperature.

Shen, Samuel S. P.↗

NASA NTRS1999

Data Assimilation in the Presence of Forecast Bias: The GEOS Moisture Analysis

We describe the application of the unbiased sequential analysis algorithm developed by Dee and da Silva (1998) to the GEOS DAS moisture analysis. The algorithm estimates the persistent component of model error using rawinsonde observations and adjusts the first-guess moisture field accordingly. Results of two seasonal data assimilation cycles show that moisture analysis bias is almost completely eliminated in all observed regions. The improved analyses cause a sizable reduction in the 6h-forecast bias and a marginal improvement in the error standard deviations.

Dee, Dick P.↗

NASA NTRS2003

Estimation of Model Error Variances During Data Assimilation

Data assimilation is all about understanding the error characteristics of the data and models that are used in the assimilation process. Reliable error estimates are needed to implement observational quality control, bias correction of observations and model fields, and intelligent data selection. Meaningful covariance specifications are obviously required for the analysis as well, since the impact of any single observation strongly depends on the assumed structure of the background errors. Operational atmospheric data assimilation systems still rely primarily on climatological background error covariances. To obtain error estimates that reflect both the character of the flow and the current state of the observing system, it is necessary to solve three problems: (1) how to account for the short-term evolution of errors in the initial conditions; (2) how to estimate the additional component of error caused by model defects; and (3) how to compute the error reduction in the analysis due to observational information. Various approaches are now available that provide approximate solutions to the first and third of these problems. However, the useful accuracy of these solutions very much depends on the size and character of the model errors and the ability to account for them. Model errors represent the real-world forcing of the error evolution in a data assimilation system. Clearly, meaningful model error estimates and/or statistics must be based on information external to the model itself. The most obvious information source is observational, and since the volume of available geophysical data is growing rapidly, there is some hope that a purely statistical approach to model error estimation can be viable. This requires that the observation errors themselves are well understood and quantifiable. We will discuss some of these challenges and present a new sequential scheme for estimating model error variances from observations in the context of an atmospheric data assimilation system.

Dee, Dick↗

NASA NTRS1995

Partitioning of ocean and land uptake of CO2 as inferred by delta C-13 measurements from the NOAA Climate Monitoring and Diagnostics Laboratory Global Air Sampling Network

Using delta C-13 measurements in atmospheric CO2 from a cooperative global air sampling network, we determined the partitioning of the net uptake of CO2 between ocean and land as a function of latitude and time. The majority of delta C-13 measurements were made at the Institute of Arctic and Alpine Research (INSTAAR) of the University of Colorado. We perform an inverse deconvolution of both CO2 and delta C-13 observations, using a two-dimensional model of atmospheric transport. Also, the discrimination against C-13 by plant photosynthesis, as a function of latitude and time, is calculated from global runs of the simple biosphere (SiB) model. Uncertainty due to the longitudinal structure of the data, which is not represented by the model, is studied through a bootstrap analysis by adding and omitting measurement sites. The resulting error estimates for our inferred sources and sinks are of the order of 1 GTC (1 GTC = 10(exp 15) gC). Such error bars do not reflect potential systematic errors arising from our estimates of the isotopic disequilibria between the atmosphere and the oceans and biosphere, which are estimated in a separate sensitivity analysis. With respect to global totals for 1992 we found that 3.2 GTC of carbon dissolved into the ocean and that 1.5 GTC were sequestered by land ecosystems. Northern hemisphere ocean gyres north of 15 deg N absorbed 2.7 GTC. The equatorial oceans between 10 deg S and 10 deg N were a net source to the atmosphere of 0.9 GTC. We obtained a sink of 1.6 GTC in southern ocean gyres south of 20 deg S, although the deconvolution is poorly constrained by sparse data coverage at high southern latitudes. The seasonal uptake of CO2 in the northern gyres appears to be correlated with a bloom of phytoplankton in surface waters. On land, northern temperate and boreal ecosystems between 35 deg N and 65 deg N were found to be a major sink of CO2 in 1992, as large as 3.5 GTC. Northern tropical ecosystems (equator-30 deg N) appear to be a net source to the source to the atmosphere of 2 GTC which could reflect biomass burning. A small sink, 0.3 GTC, was inferred for southern tropical ecosystems (30 deg S-equator).

Ciais, Philippe↗