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At least 343 records · Page 19
All sourcesNASA NTRSDOE OSTI
NASA NTRS1986

On realizations of least-squares estimation and Kalman filtering by systolic arrays

Least-squares (LS) estimation is a basic operation in many signal processing problems. Given y = Ax + v, where A is a m x n coefficient matrix, y is a m x 1 observation vector, and v is a m x 1 zero mean white noise vector, a simple least-squares solution is finding the estimated vector x which minimizes the norm of /Ax-y/. It is well known that for an ill-conditioned matrix A, solving least-squares problems by orthogonal triangular (QR) decomposition and back substitution has robust numerical properties under finite word length effect since 2-norm is preserved. Many fast algorithms have been proposed and applied to systolic arrays. Gentleman-Kung (1981) first presented the trianglular systolic array for a basic Givens reduction. McWhirter (1983) used this array structure to find the least-squares estimation errors. Then by geometric approach, several different systolic array realizations of the recursive least-squares estimation algorithms of Lee et al (1981) were derived by Kalson-Yao (1985). Basic QR decomposition algorithms are considered in this paper and it is found that under a one-row time updating situation, the Householder transformation degenerates to a simple Givens reduction. Next, an improved least-squares estimation algorithm is derived by considering a modified version of fast Givens reduction. From this approach, the basic relationship between Givens reduction and Modified-Gram-Schmidt transformation can easily be understood. This improved algorithm also has simpler computational and inter-cell connection complexities while compared with other known least-squares algorithms and is more realistic for systolic array implementation.

Chen, M. J.↗
NASA NTRS1975

Comparison theorems, numerical integration and satellite orbits

A comparison theorem estimating the difference between solutions of a perturbed and unperturbed equation is obtained. This is then applied to obtain error estimates in numerical integration problems, in particular, those problems involving computation of satellite orbits. The main result is a proof of the intuitive notion that the error in numerically integrating a stable equation grows less rapidly than for an unstable equation.

Stokes, A.↗
NASA NTRS1990

Venus - Improved spin vector from Goldstone radar observations

Twenty-one radar images of the surface of Venus obtained between 1972 and 1982 have been compared to follow the motion of 28 distinct features. The delays and Doppler shifts of these features with respect to the subradar points on the various days were used in a nonlinear least-squares parameter estimation algorithm to refine the period and pole orientation of Venus. The period is found to be -243.022 + or - 0.003 days; the right ascension and declination of the pole are: alpha = 272.816 + or - 0.14 deg; beta = 67.218 + or - 0.05 deg (B1950). These standard error estimates attempt to include effects of systematic errors.

Slade, M. A.↗
NASA NTRS1980

The helium abundance of Jupiter from Voyager

Full disk measurements recorded 31 days before the Voyager 1 encounter with Jupiter by the radiometer of the infrared instrument, IRIS, indicate a geometric albedo of 0.274 + or - 0.013. Combining this measurement with the Pioneer derived phase integral of 1.25 and our error estimate of 0.1 yields a Jovian Bond albedo of 0.343 + or - 0.032. Infrared spectra recorded at the same time by the Michelson interferometer, along with a model extrapolation to low wave numbers not covered by the instrument, yield a thermal emission of (1.359 + or - 0.014) .001 W cm to the (-2) power. As in the case of the albedo measurement, the quoted errors in the emission measurement reflect estimates of systematic effects and are uncertain while the random component is negligible. From these measurements the internal heat flux of Jupiter is estimated to be (5.444 + or - 0.425) .0001 W cm to the (-2) power, and the energy balance defined as the ratio of emitted thermal to absorbed solar energy is 1.668 + or - 0.085.

Gautier, D.↗
NASA NTRSDate not supplied

Characterization of OCO-2 and ACOS-GOSAT biases and errors for flux estimates

We characterize the magnitude of seasonally and spatially varying biases in the National Aeronautics and Space Administration (NASA) Orbiting Carbon Observatory-2 (OCO-2) Version 8 (v8) and the Atmospheric CO2 Observations from Space (ACOS) Greenhouse Gas Observing SATellite (GOSAT) version 7.3 (v7.3) satellite CO2 retrievals by comparisons to measurements collected by the Total Carbon Column Observing Network (TCCON), Atmospheric Tomography (ATom) experiment, and National Oceanic and Atmospheric Administration (NOAA) Earth System Research Laboratory (ESRL) and U. S. Department of Energy (DOE) aircraft, and surface stations. Although the ACOS-GOSAT estimates of the column averaged carbon dioxide (CO2) dry air mole fraction (XCO2) have larger random errors than the OCO-2 XCO2 estimates, and the space-based estimates over land have larger random errors than those over ocean, the systematic errors are similar across both satellites and surface types, 0.6 ± 0.1 ppm. We find similar estimates of systematic error whether dynamic versus geometric coincidences or ESRL/DOE aircraft versus TCCON are used for validation (over land), once validation and co-location errors are accounted for. We also find that areas with sparse throughput of good quality data (due to quality flags and preprocessor selection) over land have ~double the error of regions of high-throughput of good quality data. We characterize both raw and bias-corrected results, finding that bias correction improves systematic errors by a factor of 2 for land observations and improves errors by ~0.2 ppm for ocean. We validate the lowermost tropospheric (LMT) product for OCO-2 and ACOS-GOSAT by comparison to aircraft and surface sites, finding systematic errors of ~1.1 ppm, while having 2-3 times the variability of XCO2. We characterize the time and distance scales of correlations for OCO-2 XCO2 errors, and find error correlations on scales of 0.3 degrees, 5-10 degrees, and 60 days. We find comparable scale lengths for the bias correction term. Assimilation of the OCO-2 bias correction term is used to estimate flux errors resulting from OCO-2 seasonal biases, finding annual flux errors on the order of 0.3 and 0.4 PgC/yr for Transcom-3 ocean and land regions, respectively.

Susan S Kulawik↗
NASA NTRS2008

Estimating Software-Development Costs With Greater Accuracy

COCOMOST is a computer program for use in estimating software development costs. The goal in the development of COCOMOST was to increase estimation accuracy in three ways: (1) develop a set of sensitivity software tools that return not only estimates of costs but also the estimation error; (2) using the sensitivity software tools, precisely define the quantities of data needed to adequately tune cost estimation models; and (3) build a repository of software-cost-estimation information that NASA managers can retrieve to improve the estimates of costs of developing software for their project. COCOMOST implements a methodology, called '2cee', in which a unique combination of well-known pre-existing data-mining and software-development- effort-estimation techniques are used to increase the accuracy of estimates. COCOMOST utilizes multiple models to analyze historical data pertaining to software-development projects and performs an exhaustive data-mining search over the space of model parameters to improve the performances of effort-estimation models. Thus, it is possible to both calibrate and generate estimates at the same time. COCOMOST is written in the C language for execution in the UNIX operating system.

Baker, Dan↗
NASA NTRS2003

Application of a Bank of Kalman Filters for Aircraft Engine Fault Diagnostics

In this paper, a bank of Kalman filters is applied to aircraft gas turbine engine sensor and actuator fault detection and isolation (FDI) in conjunction with the detection of component faults. This approach uses multiple Kalman filters, each of which is designed for detecting a specific sensor or actuator fault. In the event that a fault does occur, all filters except the one using the correct hypothesis will produce large estimation errors, thereby isolating the specific fault. In the meantime, a set of parameters that indicate engine component performance is estimated for the detection of abrupt degradation. The proposed FDI approach is applied to a nonlinear engine simulation at nominal and aged conditions, and the evaluation results for various engine faults at cruise operating conditions are given. The ability of the proposed approach to reliably detect and isolate sensor and actuator faults is demonstrated.

Kobayashi, Takahisa↗
NASA NTRS1987

Numerical analysis of discrete fractional integrodifferential structural dampers

This paper develops solution algorithms enabling the handling of the dynamic response of nonlinear structures contained discretely attached dampers modeled by fractional integrodifferential operators of the Grunwald-Liouville-Riemann type. The development consists of two levels of formulation, namely: (1) numerical approximations of fractional operators and, (2) the establishment of global level implicit schemes enabling the solution to nonlinear structural formulations. To generalize the overall results, error estimates are derived for the fractional operator approximation algorithm. These enable an ongoing optimization of solution efficiency for a given error tolerance. To benchmark the scheme, the results of several numerical experiments are presented. These illustrate the numerical characteristics of the overall formulation.

Padovan, Joseph↗
NASA NTRS2003

Aircraft Engine Sensor/Actuator/Component Fault Diagnosis Using a Bank of Kalman Filters

In this report, a fault detection and isolation (FDI) system which utilizes a bank of Kalman filters is developed for aircraft engine sensor and actuator FDI in conjunction with the detection of component faults. This FDI approach uses multiple Kalman filters, each of which is designed based on a specific hypothesis for detecting a specific sensor or actuator fault. In the event that a fault does occur, all filters except the one using the correct hypothesis will produce large estimation errors, from which a specific fault is isolated. In the meantime, a set of parameters that indicate engine component performance is estimated for the detection of abrupt degradation. The performance of the FDI system is evaluated against a nonlinear engine simulation for various engine faults at cruise operating conditions. In order to mimic the real engine environment, the nonlinear simulation is executed not only at the nominal, or healthy, condition but also at aged conditions. When the FDI system designed at the healthy condition is applied to an aged engine, the effectiveness of the FDI system is impacted by the mismatch in the engine health condition. Depending on its severity, this mismatch can cause the FDI system to generate incorrect diagnostic results, such as false alarms and missed detections. To partially recover the nominal performance, two approaches, which incorporate information regarding the engine s aging condition in the FDI system, will be discussed and evaluated. The results indicate that the proposed FDI system is promising for reliable diagnostics of aircraft engines.

Kobayashi, Takahisa↗
NASA NTRS1994

A geopotential model from satellite tracking, altimeter, and surface gravity data: GEM-T3

An improved model of Earth's gravitational field, Goddard Earth Model T-3 (GEM-T3), has been developed from a combination of satellite tracking, satellite altimeter, and surface gravimetric data. GEM-T3 provides a significant improvement in the modeling of the gravity field at half wavelengths of 400 km and longer. This model, complete to degree and order 50, yields more accurate satellite orbits and an improved geoid representation than previous Goddard Earth Models. GEM-T3 uses altimeter data from GEOS 3 (1975-1976), Seasat (1978) and Geosat (1986-1987). Tracking information used in the solution includes more than 1300 arcs of data encompassing 31 different satellites. The recovery of the long-wavelength components of the solution relies mostly on highly precise satellite laser ranging (SLR) data, but also includes Tracking Network (TRANET) Doppler, optical, and satellite-to-satellite tracking acquired between the ATS 6 and GEOS 3 satellites. The main advances over GEM-T2 (beyond the inclusion of altimeter and surface gravity information which is essential for the resolution of the shorter wavelength geoid) are some improved tracking data analysis approaches and additional SLR data. Although the use of altimeter data has greatly enhanced the modeling of the ocean geoid between 65 deg N and 60 deg S latitudes in GEM-T3, the lack of accurate detailed surface gravimetry leaves poor geoid resolution over many continental regions of great tectonic interest (e.g., Himalayas, Andes). Estimates of polar motion, tracking station coordinates, and long-wavelength ocean tidal terms were also made (accounting for 6330 parameters). GEM-T3 has undergone error calibration using a technique based on subset solutions to produce reliable error estimates. The calibration is based on the condition that the expected mean square deviation of a subset gravity solution from the full set values is predicted by the solutions' error covariances. Data weights are iteratively adjusted until this condition for the error calibration is satisfied. In addition, gravity field tests were performed on strong satellite data sets withheld from the solution (thereby ensuring their independence). In these tests, the performance of the subset models on the withheld observations is compared to error projections based on their calibrated error covariances. These results demonstrate that orbit accuracy projections are reliable for new satellites which were not included in GEM-T3.

Lerch, F. J.↗
NASA NTRS2013

Comparative Analysis of Alternative Spectral Bands of CO2 and O2 for the Sensing of CO2 Mixing Ratios

We performed comparative studies to establish favorable spectral regions and measurement wavelength combinations in alternative bands of CO2 and O2, for the sensing of CO2 mixing ratios (XCO2) in missions such as ASCENDS. The analysis employed several simulation approaches including separate layers calculations based on pre-analyzed atmospheric data from the modern-era retrospective analysis for research and applications (MERRA), and the line-byline radiative transfer model (LBLRTM) to obtain achievable accuracy estimates as a function of altitude and for the total path over an annual span of variations in atmospheric parameters. Separate layer error estimates also allowed investigation of the uncertainties in the weighting functions at varying altitudes and atmospheric conditions. The parameters influencing the measurement accuracy were analyzed independently and included temperature sensitivity, water vapor interferences, selection of favorable weighting functions, excitations wavelength stabilities and other factors. The results were used to identify favorable spectral regions and combinations of on / off line wavelengths leading to reductions in interferences and the improved total accuracy.

Pliutau, Denis↗
NASA NTRS1974

Projection of school district enrollments

The objectives were to provide a better statistical basis for enrollment projections, to attempt to model the school district's enrollment, and to produce a single estimate of enrollment for each grade, grade group, and ethnic group, and for the total by year. Efforts were also made to provide error estimates for the projections, to design a simple, user-oriented computer program for use by school district administrators, and to work with real data from local school districts and aid them in making projections on an experimental basis. The study at Jet Propulsion Laboratory was concerned with projection methodology and production of a generally usable computer program.

Van Dillen, S. L.↗
NASA NTRS1993

Measuring rapid ocean tidal earth orientation variations with very long baseline interferometry

Ocean tidal effects on universal time and polar motion (UTPM) are investigated at four nearly diurnal (K(sub 1), P(sub 1), O(sub 1), and Q(sub 1)) and four nearly semidiurnal (K(sub 2), S(sub 2), M(sub 2), and N(sub 2)) frequencies by analyzing very long baseline interferometry (VLBI) data extending from 1978 to 1992. We discuss limitations of comparisons between experiment and theory for the retograde nearly diurnal polar motion components due to their degeneracy with prograde components of the nutation model. Estimating amplitudes of contributions to the modeled VLBI observables at these eight frequencies produces a statistically highly significant improvement of 7 mm to the residuals of a fit to the observed delays. Use of such an improved UTPM model also reduces the 14-30 mm scatter of baseline lengths about a time-linear model of tectonic motion by 3-14 mm, also withhigh significance levels. A total of 28 UTPM ocean tidal amplitudes can be unambiguously estimated from the data, with resulting UTI and PM magnitudes as large as 21 micro secs and 270 microarc seconds and formal uncertainties of the order of 0.3 micro secs and 5 microarc secs for UTI and PM, respectively. Empirically determined UTPM amplitudes and phases are com1pared to values calculated theoretically by Gross from Seiler's global ocean tide model. The discrepancy between theory and experiment is larger by a factor of 3 for UTI amplitudes (9 micro secs) than for prograde PM amplitudes (42 microarc secs). The 14-year VLBI data span strongly attenuates the influence of mismodeled effects on estimated UTPM amplitudes and phases that are not coherent with the eight frequencies of interest. Magnitudes of coherent and quasi-coherent systematic errors are quantified by means of internal consistency tests. We conclude that coherent systematic effects are many times larger than the formal uncertainties and can be as large as 4 micro secs for UTI and 60 microarc secs for polar motion. On the basis of such ealistic error estimates, 22 of the 31 fitted UTPM ocean tidal amplitudes differ from zero by more than 2 sigma.

Sovers, O. J.↗
NASA NTRS2002

Linear Parameter Varying Control Synthesis for Actuator Failure, Based on Estimated Parameter

The design of a linear parameter varying (LPV) controller for an aircraft at actuator failure cases is presented. The controller synthesis for actuator failure cases is formulated into linear matrix inequality (LMI) optimizations based on an estimated failure parameter with pre-defined estimation error bounds. The inherent conservatism of an LPV control synthesis methodology is reduced using a scaling factor on the uncertainty block which represents estimated parameter uncertainties. The fault parameter is estimated using the two-stage Kalman filter. The simulation results of the designed LPV controller for a HiMXT (Highly Maneuverable Aircraft Technology) vehicle with the on-line estimator show that the desired performance and robustness objectives are achieved for actuator failure cases.

Shin, Jong-Yeob↗
NASA NTRS2003

Three-Dimensional Turbulent RANS Adjoint-Based Error Correction

Engineering problems commonly require functional outputs of computational fluid dynamics (CFD) simulations with specified accuracy. These simulations are performed with limited computational resources. Computable error estimates offer the possibility of quantifying accuracy on a given mesh and predicting a fine grid functional on a coarser mesh. Such an estimate can be computed by solving the flow equations and the associated adjoint problem for the functional of interest. An adjoint-based error correction procedure is demonstrated for transonic inviscid and subsonic laminar and turbulent flow. A mesh adaptation procedure is formulated to target uncertainty in the corrected functional and terminate when error remaining in the calculation is less than a user-specified error tolerance. This adaptation scheme is shown to yield anisotropic meshes with corrected functionals that are more accurate for a given number of grid points then isotropic adapted and uniformly refined grids.

Park, Michael A.↗
NASA NTRS1970

Method of statistical filtering

Minimal formula for bounding the cross correlation between a random forcing function and the state error when this correlation is unknown is used in optimal linear filter theory applications. Use of the bound results in overestimation of the estimation-error covariance.

Battin, R. H.↗
NASA NTRS1989

Control of the errors of discretization and idealization in finite element analysis

Understanding of the basic principles which control errors of discretization in finite element analysis has increased very substantially since 1980. The main milestones were: (1) development of the theoretical basis of p-extensions (1981); (2) understanding of the proper interplay between mesh design and assignment of polynomial degree to elements. Practical realization of exponential convergence rates, independently of the smoothness of the exact solution (1984); and (3) industrial experience with the new finite element technology known as the p- or hp-version of the finite element method: General Dynamics reported thirty- to forty-fold savings in terms of human time and large savings in computer time (1986). Lockheed reported favorably on their evaluation of error estimation and quality control capabilities of the p-version in industrial settings (1987). The gains in our understanding of how to control the errors of discretization represent only half of the control necessary to ensure that a numerical model is in fact an accurate representation of the corresponding physical system. Control of the errors of idealization is equally important. A brief overview of the main ideas of how to ensure the quality and reliability of mathematical models of structural systems is presented.

Szabo, Barna A.↗