Search NASA⌕ Search

SEARCH · Search NASA

Results for “error vector”

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.

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

At least 487 records · Page 27
All sourcesNASA NTRSDOE OSTI
NASA NTRS2004

Multivariate Error Covariance Estimates by Monte-Carlo Simulation for Assimilation Studies in the Pacific Ocean

One of the most difficult aspects of ocean state estimation is the prescription of the model forecast error covariances. The paucity of ocean observations limits our ability to estimate the covariance structures from model-observation differences. In most practical applications, simple covariances are usually prescribed. Rarely are cross-covariances between different model variables used. Here a comparison is made between a univariate Optimal Interpolation (UOI) scheme and a multivariate OI algorithm (MvOI) in the assimilation of ocean temperature. In the UOI case only temperature is updated using a Gaussian covariance function and in the MvOI salinity, zonal and meridional velocities as well as temperature, are updated using an empirically estimated multivariate covariance matrix. Earlier studies have shown that a univariate OI has a detrimental effect on the salinity and velocity fields of the model. Apparently, in a sequential framework it is important to analyze temperature and salinity together. For the MvOI an estimation of the model error statistics is made by Monte-Carlo techniques from an ensemble of model integrations. An important advantage of using an ensemble of ocean states is that it provides a natural way to estimate cross-covariances between the fields of different physical variables constituting the model state vector, at the same time incorporating the model's dynamical and thermodynamical constraints as well as the effects of physical boundaries. Only temperature observations from the Tropical Atmosphere-Ocean array have been assimilated in this study. In order to investigate the efficacy of the multivariate scheme two data assimilation experiments are validated with a large independent set of recently published subsurface observations of salinity, zonal velocity and temperature. For reference, a third control run with no data assimilation is used to check how the data assimilation affects systematic model errors. While the performance of the UOI and MvOI is similar with respect to the temperature field, the salinity and velocity fields are greatly improved when multivariate correction is used, as evident from the analyses of the rms differences of these fields and independent observations. The MvOI assimilation is found to improve upon the control run in generating the water masses with properties close to the observed, while the UOI failed to maintain the temperature and salinity structure.

Borovikov, Anna↗
NASA NTRS1997

Planar Doppler Velocimetry for Large-Scale Wind Tunnel Testing

Recently, Planar Doppler Velocimetry (PDV) has been shown by several laboratories to offer an attractive means for measuring three-dimensional velocity vectors everywhere in a light sheet placed in a flow. Unlike other optical means of measuring flow velocities, PDV is particularly attractive for use in large wind tunnels where distances to the sample region may be several meters, because it does not require the spatial resolution and tracking of individual scattering particles or the alignment of crossed beams at large distances. To date, demonstrations of PDV have been made either in low speed flows without quantitative comparison to other measurements, or in supersonic flows where the Doppler shift is large and its measurement is relatively insensitive to instrumental errors. Moreover, most reported applications have relied on the use of continuous-wave lasers, which limit the measurement to time-averaged velocity fields. This work summarizes the results of two previous studies of PDV in which the use of pulsed lasers to obtain instantaneous velocity vector fields is evaluated. The objective has been to quantitatively define and demonstrate PDV capabilities for applications in large-scale wind tunnels that are intended primarily for the production testing of subsonic aircraft. For such applications, the adequate resolution of low-speed flow fields requires accurate measurements of small Doppler shifts that are obtained at distances of several meters from the sample region. The use of pulsed lasers provides the unique capability to obtain not only time-averaged fields, but also their statistical fluctuation amplitudes and the spatial excursions of unsteady flow regions such as wakes and separations. To accomplish the objectives indicated, the PDV measurement process is first modeled and its performance evaluated computationally. The noise sources considered include those related to the optical and electronic properties of Charge-Coupled Device (CCD) arrays and to speckle effects associated with coherent illumination from pulsed lasers. The signal noise estimates are incorporated into the PDV signal analysis process and combined with computed scattering signals using a Mie scattering theory for polydisperse smoke particles. The relevant parameters incorporate a range of practical aerodynamic test conditions and facility sizes. The results define the optimum instrument configurations, show that the expected signal levels from a practical PDV system are sufficiently large to allow its useful application in large facilities, and show that the expected velocity measurement uncertainties are small compared to the mean velocities of interest for most subsonic, large-scale wind tunnel testing. Experimental studies using several experimental bench-top setups are then described that validate the physics of the PDV model and to calibrate its computed results. The validated model allows estimates of the uncertainties of PDV measurements and a complete definition of the PDV capabilities to be made with sufficient confidence to decide the viability of PDV for large-scale wind tunnel applications.

McKenzie, Robert L.↗
NASA NTRS1971

An analysis of approach navigation accuracy and guidance requirements for the grand tour mission to the outer planets

The navigation and guidance process for the Jupiter, Saturn and Uranus planetary encounter phases of the 1977 Grand Tour interior mission was simulated. Reference approach navigation accuracies were defined and the relative information content of the various observation types were evaluated. Reference encounter guidance requirements were defined, sensitivities to assumed simulation model parameters were determined and the adequacy of the linear estimation theory was assessed. A linear sequential estimator was used to provide an estimate of the augmented state vector, consisting of the six state variables of position and velocity plus the three components of a planet position bias. The guidance process was simulated using a nonspherical model of the execution errors. Computation algorithms which simulate the navigation and guidance process were derived from theory and implemented into two research-oriented computer programs, written in FORTRAN.

Jones, D. W.↗
NASA NTRS1983

A Covariance Analysis for the Determination of Baseline Observing GPS Satellites

Results of covariance analyses are presented for the determination of baseline vectors of length from 150 m to 4000 km. The data are doubly differenced ranges derived from the signals transmitted by the satellites of the Global Positioning System. The modeling of various error sources is described. The results indicate the low cost baseline determination system is capable of subdecimeter accuracy for baselines up to 1000 km in length.

Wu, S. C.↗
NASA NTRS1985

Spline Curves, Wire Frames and Bvalue

The methods that were developed for wire-frame design are described. The principal tools for control of a curve during interactive design are mathematical ducks. The simplest of these devices is an analog of the draftsman's lead weight that he uses to control a mechanical spline also create Ducks for controlling differential and integral properties of curves were created. Other methods presented include: constructing the end of a Bezier polygon to gain quick and reasonably confident control of the end tangent vector, end curvature and end torsion; keeping the magnitude of unwanted curvature oscillations within tolerance; constructing the railroad curves that appear in many engineering design problems; and controlling the frame to minimize errors at mesh points and to optimize the shapes of the curve elements.

Smith, L.↗
NASA NTRS1991

Ascent performance of an air-breathing horizontal-takeoff launch vehicle

Simulations are conducted to investigate a proposed NASA launch vehicle that is fully reusable, takes off horizontally, and uses airbreathing propulsion in a single stage. The propulsion model is based on a cycle analysis method, and the vehicle is assumed to be a rigid structure with distributed fuel, operating under a range of atmospheric conditions. The program to optimize simulated trajectories (POST) is modified to include a predictor-corrector guidance capability and then used to generate the trajectories. Significant errors are encountered during the unpowered coast phase due to uncertainty in the atmospheric density profile. The amount of ascent propellant needed is shown to be directly related to the thrust-vector angle and the location of the center of gravity of the vehicle because of the importance of aim-drag losses to total ideal velocity.

Powell, Richard W.↗
NASA NTRS1993

Aircraft measurement of electric field - Self-calibration

Aircraft measurement of electric fields is difficult as the electrically conducting surface of the aircraft distorts the electric field. Calibration requires determining the relations between the undistorted electric field in the absence of the vehicle and the signals from electric field meters that sense the local distorted fields in their immediate vicinity. This paper describes a generalization of a calibration method which uses pitch and roll maneuvers. The technique determines both the calibration coefficients and the direction of the electric vector. The calibration of individual electric field meters and the elimination of the aircraft's self-charge are described. Linear combinations of field mill signals are examined and absolute calibration and error analysis are discussed. The calibration method was applied to data obtained during a flight near thunderstorms.

Winn, W. P.↗
NASA NTRS1997

A Predictive Attitude Determination Algorithm

In this paper, a new and efficient algorithm is developed for attitude determination from vector observations. The new algorithm, called the Predictive Attitude Determination (PAD) algorithm, is derived from a general nonlinear predictive filter approach. Traditional deterministic algorithms are shown to be suboptimal for anisotropic measurement errors. The major advantage of the PAD algorithm is that it can be easily applied to the case where anisotropic measurement errors exist. Also, an analytical expression is derived for the steady-state attitude error covariance, which is shown to be equivalent to the optimal covariance derived from maximum likelihood techniques. Simulation studies indicate that the new algorithm is able to accurately determine the attitude of a spacecraft, even for radically anisotropic measurement errors.

Markley, F. Landis↗
NASA NTRS1971

The pointing errors of geosynchronous satellites

A study of the correlation between cloud motion and wind field was initiated. Cloud heights and displacements were being obtained from a ceilometer and movie pictures, while winds were measured from pilot balloon observations on a near-simultaneous basis. Cloud motion vectors were obtained from time-lapse cloud pictures, using the WINDCO program, for 27, 28 July, 1969, in the Atlantic. The relationship between observed features of cloud clusters and the ambient wind field derived from cloud trajectories on a wide range of space and time scales is discussed.

Sikdar, D. N.↗
NASA NTRS1997

Measurement Capabilities of Planar Doppler Velocimetry in Large-Scale Wind Tunnels

Over the past few years, Planar Doppler Velocimetry (PDT) has been shown by several laboratories to offer an attractive means for measuring three-dimensional velocity vectors everywhere in a light sheet placed in a flow. Unlike some other optical means of measuring flow velocities, PDT is particularly attractive for use in large wind tunnels where distances to the sample region may be several meters, because it does not require the spatial resolution and tracking of individual scattering particles or the alignment of crossed beams at large distances. To date, demonstrations of PDT (also called Doppler Global Velocimetry by some authors) have been made either in low speed flows without quantitative comparison to other measurements, or in supersonic flows where the Doppler shift is large and its measurement is relatively insensitive to instrumental errors. Moreover, most reported applications have relied on the use of continuous-wave lasers, which limit the measurement to time-averaged velocity fields. This work summarizes the results of two previous studies of PDT in which the use of pulsed lasers to obtain instantaneous velocity vector fields is evaluated. The objective has been to quantitatively define and demonstrate PDT capabilities for applications in large-scale wind tunnels that are intended primarily for the testing of rotorcraft and subsonic aircraft at speeds typically less than 100 m/s. For such applications, the adequate resolution of low-speed flow fields requires accurate measurements of small Doppler shifts that are obtained at distances of several meters from the sample region and with a field of view that is sufficient to encompass the entire region of interest. The use of pulsed lasers provides the unique capability to obtain not only time-averaged fields, but also their statistical fluctuation amplitudes and the spatial excursions of unsteady flow regions such as wakes, separations, and rotor-tip vortices. To accomplish the objectives of these studies, the PDT measurement process was first modeled and its performance evaluated computationally. The noise sources considered included those related to the optical and electronic properties of Charge-Coupled Device (CCD) arrays and to speckle effects associated with the coherent illumination of aerosols from pulsed lasers. The signal noise estimates were incorporated into the PDT signal analysis process and combined with computed scattering signals using a Mae scattering theory for a distributed range of aerosol particle sizes. The results are used to define the necessary instrument configuration, to show that the expected signal levels from a practical PDT system are sufficiently large to allow its useful application in large facilities, and to show that the expected velocity measurement uncertainties are small compared to the mean velocities of interest for most subsonic, large-scale wind tunnel testing, Experimental studies using several bench-top setups are then described that validate the physics of the PDT model and demonstrate the ability to obtain accurate PDT measurements using procedures that are compatible with large-scale wind tunnel operations. The PDT measurement capabilities found in this study lead to the conclusion that PDT offers significant advantages compared to other means of measuring velocity fields in large-scale wind tunnels, including those operating at low speeds.

McKenzie, Robert L.↗
DOE OSTI2026

Efficient Simulation of Logical Magic State Preparation Protocols

Developing space- and time-efficient logical magic state preparation (MSP) protocols will likely be an essential step toward building a large-scale fault-tolerant quantum computer. Motivated by this need, we introduce a scalable method for simulating logical MSP protocols under the standard circuit-level noise model. When applied to protocols based on code-switching, magic state cultivation, and magic state distillation, our method yields a complexity polynomial in (i) the number of qubits and (ii) the nonstabilizerness, e.g., stabilizer rank or Pauli rank, of the target encoded magic state. The efficiency of our simulation method is rooted in a curious fact: every circuit-level Pauli error in these protocols propagates to a Clifford error at the end. This property is satisfied by a large family of protocols, including those that repeatedly measure a transversal Clifford that squares to a Pauli. We provide a proof-of-principle numerical simulation that prepares a magic state using such logical Clifford measurements. Our work enables practical simulation of logical MSP protocols without resorting to approximations or resource-intensive state-vector simulations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2026

Representativity error scaling of models of the high temperature test facility

Error scaling is a critical step toward the validation of modeling capabilities for high-temperature gas-cooled reactors (HTGRs). Extensive effort is being made to bring HTGRs into the validation basis of numerous thermal-hydraulics codes. Here, this paper demonstrates how systems-level codes can be leveraged to perform error scaling analyses between an experimental facility and a plant-to-be facility. Specifically, we focus on two conduction cooldown experiments from the High Temperature Test Facility (HTTF) and the General Atomics 350 MW th modular high-temperature gas-cooled reactor (MHTGR-350). The error scaling methodology employed in this study is representativity, which in the context of this work was used to quantify how well experiments captured the physics of the plant facility by comparing sensitivity vectors between the two facilities. In addition, two different RELAP5–3D models of the HTTF were included in the comparison to determine if modeling methodologies notably impact the representativity results. The key figures of merit are the maximum block temperature and the coolant outlet temperature. The time-dependent maximum block temperature had a low representativity of below 0.1 for both models across both transients. The coolant outlet temperature had a higher representativity of around 0.6 for both models during the pressurized conduction cooldown, but it was below 0.2 for the depressurized conduction cooldown. Overall, the HTTF experiments were not representative of the transients in the MHTGR-350. However, these results can play a significant role in informing future potential experiments for HTGR systems that iterate on what the HTTF accomplished.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗
NASA NTRS1985

The International Cometary Explorer mission to comet Giacobini-Zinner

The International Cometary Explorer (ICE), scheduled to pass the tail of Comet Giacobini-Zinner on September 11, 1985, was expected to address first-order questions bout the interaction between solar wind and comets. Since ICE was not initially intended for comet studies, it did not have sun-sensitive imaging instruments designed to image the comet nucleus. In effect, ICE was free to pass through the tail of the comet. The ICE spacecraft, a 16-faceted cylindrical drum just over five ft high with a spin axis normal to the ecliptic plane, was designed to encounter the comet at a distance of 0.47 AU from the earth. Scientific instruments on board the spacecraft include: (1) the electron plasma experiment, (2) the vector helium magnetometer, (3) the plasma wave experiment, (4) the radio waves experiment, (5) the plasma ion experiment, (6) the low-energy cosmic ray experiment, and (7) the energetic protons experiment. Targeting error was expected as a result of solar-wind induced plasma tail wagging. Comet interception was planned to be at a distance of 10,000 km from the nucleus.

Von Rosenvinge, T. T.↗
NASA NTRS1988

Recent advances in electronic structure theory and their influence on the accuracy of ab initio potential energy surfaces

Recent advances in electronic structure theory and the availability of high speed vector processors have substantially increased the accuracy of ab initio potential energy surfaces. The recently developed atomic natural orbital approach for basis set contraction has reduced both the basis set incompleteness and superposition errors in molecular calculations. Furthermore, full CI calculations can often be used to calibrate a CASSCF/MRCI approach that quantitatively accounts for the valence correlation energy. These computational advances also provide a vehicle for systematically improving the calculations and for estimating the residual error in the calculations. Calculations on selected diatomic and triatomic systems will be used to illustrate the accuracy that currently can be achieved for molecular systems. In particular, the F+H2 yields HF+H potential energy hypersurface is used to illustrate the impact of these computational advances on the calculation of potential energy surfaces.

Bauschlicher, Charles W., Jr.↗
NASA NTRS1989

Recent advances in electronic structure theory and their influence on the accuracy of ab initio potential energy surfaces

Recent advances in electronic structure theory and the availability of high speed vector processors have substantially increased the accuracy of ab initio potential energy surfaces. The recently developed atomic natural orbital approach for basis set contraction has reduced both the basis set incompleteness and superposition errors in molecular calculations. Furthermore, full CI calculations can often be used to calibrate a CASSCF/MRCI approach that quantitatively accounts for the valence correlation energy. These computational advances also provide a vehicle for systematically improving the calculations and for estimating the residual error in the calculations. Calculations on selected diatomic and triatomic systems will be used to illustrate the accuracy that currently can be achieved for molecular systems. In particular, the F + H2 yields HF + H potential energy hypersurface is used to illustrate the impact of these computational advances on the calculation of potential energy surfaces.

Bauschlicher, Charles W., Jr.↗
NASA NTRS2015

An Upper Bound on Orbital Debris Collision Probability When Only One Object has Position Uncertainty Information

Upper bounds on high speed satellite collision probability, P (sub c), have been investigated. Previous methods assume an individual position error covariance matrix is available for each object. The two matrices being combined into a single, relative position error covariance matrix. Components of the combined error covariance are then varied to obtain a maximum P (sub c). If error covariance information for only one of the two objects was available, either some default shape has been used or nothing could be done. An alternative is presented that uses the known covariance information along with a critical value of the missing covariance to obtain an approximate but useful P (sub c) upper bound. There are various avenues along which an upper bound on the high speed satellite collision probability has been pursued. Typically, for the collision plane representation of the high speed collision probability problem, the predicted miss position in the collision plane is assumed fixed. Then the shape (aspect ratio of ellipse), the size (scaling of standard deviations) or the orientation (rotation of ellipse principal axes) of the combined position error ellipse is varied to obtain a maximum P (sub c). Regardless as to the exact details of the approach, previously presented methods all assume that an individual position error covariance matrix is available for each object and the two are combined into a single, relative position error covariance matrix. This combined position error covariance matrix is then modified according to the chosen scheme to arrive at a maximum P (sub c). But what if error covariance information for one of the two objects is not available? When error covariance information for one of the objects is not available the analyst has commonly defaulted to the situation in which only the relative miss position and velocity are known without any corresponding state error covariance information. The various usual methods of finding a maximum P (sub c) do no good because the analyst defaults to no knowledge of the combined, relative position error covariance matrix. It is reasonable to think, given an assumption of no covariance information, an analyst might still attempt to determine the error covariance matrix that results in an upper bound on the P (sub c). Without some guidance on limits to the shape, size and orientation of the unknown covariance matrix, the limiting case is a degenerate ellipse lying along the relative miss vector in the collision plane. Unless the miss position is exceptionally large or the at-risk object is exceptionally small, this method results in a maximum P (sub c) too large to be of practical use. For example, assuming that the miss distance is equal to the current ISS alert volume along-track (+ or -) distance of 25 kilometers and that the at-risk area has a 70 meter radius. The maximum (degenerate ellipse) P (sub c) is about 0.00136. At 40 kilometers, the maximum P (sub c) would be 0.00085 which is still almost an order of magnitude larger than the ISS maneuver threshold of 0.0001. In fact, a miss distance of almost 340 kilometers is necessary to reduce the maximum P (sub c) associated with this degenerate ellipse to the ISS maneuver threshold value. Such a result is frequently of no practical value to the analyst. Some improvement may be made with respect to this problem by realizing that while the position error covariance matrix of one of the objects (usually the debris object) may not be known the position error covariance matrix of the other object (usually the asset) is almost always available. Making use of the position error covariance information for the one object provides an improvement in finding a maximum P (sub c) which, in some cases, may offer real utility. The equations to be used are presented and their use discussed.

Frisbee, Joseph H., Jr.↗
NASA NTRS1981

Comparison of PASCAL and FORTRAN for solving problems in the physical sciences

The paper compares PASCAL and FORTRAN for problem solving in the physical sciences, due to requests NASA has received to make PASCAL available on the Numerical Aerodynamic Simulator (scheduled to be operational in 1986). PASCAL disadvantages include the lack of scientific utility procedures equivalent to the IBM scientific subroutine package or the IMSL package which are available in FORTRAN. Advantages include a well-organized, easy to read and maintain writing code, range checking to prevent errors, and a broad selection of data types. It is concluded that FORTRAN may be the better language, although ADA (patterned after PASCAL) may surpass FORTRAN due to its ability to add complex and vector math, and the specify the precision and range of variables.

Watson, V. R.↗
NASA NTRS1993

Determination of the stability and control derivatives of the NASA F/A-18 HARV using flight data

This report documents the research conducted for the NASA-Ames Cooperative Agreement No. NCC 2-759 with West Virginia University. A complete set of the stability and control derivatives for varying angles of attack from 10 deg to 60 deg were estimated from flight data of the NASA F/A-18 HARV. The data were analyzed with the use of the pEst software which implements the output-error method of parameter estimation. Discussions of the aircraft equations of motion, parameter estimation process, design of flight test maneuvers, and formulation of the mathematical model are presented. The added effects of the thrust vectoring and single surface excitation systems are also addressed. The results of the longitudinal and lateral directional derivative estimates at varying angles of attack are presented and compared to results from previous analyses. The results indicate a significant improvement due to the independent control surface deflections induced by the single surface excitation system, and at the same time, a need for additional flight data especially at higher angles of attack.

Napolitano, Marcello R.↗