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NASA NTRS1992

Initial weather regimes as predictors of numerical 30-day mean forecast accuracy

Thirty 30-day mean 500-mb-height anomaly forecasts generated by the NCAR Community Climate Model (CCM) for the year 1978 are examined in order to determine if the forecast accuracy can be estimated with the initial conditions. The initial weather regimes were defined in such a way that the regimes could discriminate between the best and the worst 30-day mean forecasts run from the initial fields in this data set. On the basis of the CCM experiments, it is suggested that the accuracy of numerical 30-day mean forecasts may depend upon the accuracy with which the cyclones and their interactions with the planetary scale are predicted early in the forecast cycle, and that this accuracy may depend upon the initial conditions.

Colucci, Stephen J.↗

NASA NTRS1993

A critical analysis of the accuracy of several numerical techniques for combustion kinetic rate equations

A detailed analysis of the accuracy of several techniques recently developed for integrating stiff ordinary differential equations is presented. The techniques include two general-purpose codes EPISODE and LSODE developed for an arbitrary system of ordinary differential equations, and three specialized codes CHEMEQ, CREK1D, and GCKP4 developed specifically to solve chemical kinetic rate equations. The accuracy study is made by application of these codes to two practical combustion kinetics problems. Both problems describe adiabatic, homogeneous, gas-phase chemical reactions at constant pressure, and include all three combustion regimes: induction, heat release, and equilibration. To illustrate the error variation in the different combustion regimes the species are divided into three types (reactants, intermediates, and products), and error versus time plots are presented for each species type and the temperature. These plots show that CHEMEQ is the most accurate code during induction and early heat release. During late heat release and equilibration, however, the other codes are more accurate. A single global quantity, a mean integrated root-mean-square error, that measures the average error incurred in solving the complete problem is used to compare the accuracy of the codes. Among the codes examined, LSODE is the most accurate for solving chemical kinetics problems. It is also the most efficient code, in the sense that it requires the least computational work to attain a specified accuracy level. An important finding is that use of the algebraic enthalpy conservation equation to compute the temperature can be more accurate and efficient than integrating the temperature differential equation.

Radhadrishnan, Krishnan↗

NASA NTRS1992

Spacecraft-spacecraft very long baseline interferometry. Part 1: Error modeling and observable accuracy

In Part 1 of this two-part article, an error budget is presented for Earth-based delta differential one-way range (delta DOR) measurements between two spacecraft. Such observations, made between a planetary orbiter (or lander) and another spacecraft approaching that planet, would provide a powerful target-relative angular tracking data type for approach navigation. Accuracies of better than 5 nrad should be possible for a pair of spacecraft with 8.4-GHz downlinks, incorporating 40-MHz DOR tone spacings, while accuracies approaching 1 nrad will be possible if the spacecraft incorporate 32-GHz downlinks with DOR tone spacing on the order of 250 MHz; these accuracies will be available for the last few weeks or months of planetary approach for typical Earth-Mars trajectories. Operational advantages of this data type are discussed, and ground system requirements needed to enable spacecraft-spacecraft delta DOR observations are outlined. This tracking technique could be demonstrated during the final approach phase of the Mars '94 mission, using Mars Observer as the in-orbit reference spacecraft, if the Russian spacecraft includes an 8.4-GHz downlink incorporating DOR tones. Part 2 of this article will present an analysis of predicted targeting accuracy for this scenario.

Edwards, C. D., Jr.↗

NASA NTRS1993

Techniques for improving the accuracy of cyrogenic temperature measurement in ground test programs

The performance of a sensor is often evaluated by determining to what degree of accuracy a measurement can be made using this sensor. The absolute accuracy of a sensor is an important parameter considered when choosing the type of sensor to use in research experiments. Tests were performed to improve the accuracy of cryogenic temperature measurements by calibration of the temperature sensors when installed in their experimental operating environment. The calibration information was then used to correct for temperature sensor measurement errors by adjusting the data acquisition system software. This paper describes a method to improve the accuracy of cryogenic temperature measurements using corrections in the data acquisition system software such that the uncertainty of an individual temperature sensor is improved from plus or minus 0.90 deg R to plus or minus 0.20 deg R over a specified range.

Dempsey, Paula J.↗

NASA NTRS1993

Techniques for improving the accuracy of cryogenic temperature measurement in ground test programs

Dempsey, Paula J.↗

NASA NTRS1993

Accuracy of Tilt Rotor Hover Performance Predictions

The accuracy of various methods used to predict tilt rotor hover performance was established by comparing predictions with large-scale experimental data. A wide range of analytical approaches were examined. Blade lift was predicted with a lifting line analysis, two lifting surface analyses, and by a finite-difference solution of the full potential equation. Blade profile drag was predicted with two different types of airfoil tables and an integral boundary layer analysis. The inflow at the rotor was predicted using momentum theory, two types of prescribed wakes, and two free wake analyses. All of the analyses were accurate at moderate thrust coefficients. The accuracy of the analyses at high thrust coefficients was dependent upon their treatment of high sectional angles of attack on the inboard sections of the rotor blade. The analyses which allowed sectional lift coefficients on the inboard stations of the blade to exceed the maximum observed in two-dimensional wind tunnel tests provided better accuracy at high thrust coefficients than those which limited lift to the maximum two-dimensional value. These results provide tilt rotor aircraft designers guidance on which analytical approaches provide the best results, and the level of accuracy which can be expected from the best analyses.

Felker, Fort F.↗

NASA NTRS1993

New perspectives for high accuracy SLR with second generation geodesic satellites

This paper reports on the accuracy limitations imposed by geodesic satellite signatures, and on the potential for achieving millimetric performances by means of alternative satellite concepts and an optimized 2-color system tradeoff. Long distance laser ranging, when performed between a ground (emitter/receiver) station and a distant geodesic satellite, is now reputed to enable short arc trajectory determinations to be achieved with an accuracy of 1 to 2 centimeters. This state-of-the-art accuracy is limited principally by the uncertainties inherent to single-color atmospheric path length correction. Motivated by the study of phenomena such as postglacial rebound, and the detailed analysis of small-scale volcanic and strain deformations, the drive towards millimetric accuracies will inevitably be felt. With the advent of short pulse (less than 50 ps) dual wavelength ranging, combined with adequate detection equipment (such as a fast-scanning streak camera or ultra-fast solid-state detectors) the atmospheric uncertainty could potentially be reduced to the level of a few millimeters, thus, exposing other less significant error contributions, of which by far the most significant will then be the morphology of the retroreflector satellites themselves. Existing geodesic satellites are simply dense spheres, several 10's of cm in diameter, encrusted with a large number (426 in the case of LAGEOS) of small cube-corner reflectors. A single incident pulse, thus, results in a significant number of randomly phased, quasi-simultaneous return pulses. These combine coherently at the receiver to produce a convolved interference waveform which cannot, on a shot to shot basis, be accurately and unambiguously correlated to the satellite center of mass. This paper proposes alternative geodesic satellite concepts, based on the use of a very small number of cube-corner retroreflectors, in which the above difficulties are eliminated while ensuring, for a given emitted pulse, the return of a single clean pulse with an adequate cross-section.

Lund, Glenn↗

NASA NTRS1993

On the accuracy of ERS-1 orbit predictions

Since the launch of ERS-1, the D-PAF (German Processing and Archiving Facility) provides regularly orbit predictions for the worldwide SLR (Satellite Laser Ranging) tracking network. The weekly distributed orbital elements are so called tuned IRV's and tuned SAO-elements. The tuning procedure, designed to improve the accuracy of the recovery of the orbit at the stations, is discussed based on numerical results. This shows that tuning of elements is essential for ERS-1 with the currently applied tracking procedures. The orbital elements are updated by daily distributed time bias functions. The generation of the time bias function is explained. Problems and numerical results are presented. The time bias function increases the prediction accuracy considerably. Finally, the quality assessment of ERS-1 orbit predictions is described. The accuracy is compiled for about 250 days since launch. The average accuracy lies in the range of 50-100 ms and has considerably improved.

Koenig, Rolf↗

NASA NTRS1994

A note on the accuracy of spectral method applied to nonlinear conservation laws

Fourier spectral method can achieve exponential accuracy both on the approximation level and for solving partial differential equations if the solutions are analytic. For a linear partial differential equation with a discontinuous solution, Fourier spectral method produces poor point-wise accuracy without post-processing, but still maintains exponential accuracy for all moments against analytic functions. In this note we assess the accuracy of Fourier spectral method applied to nonlinear conservation laws through a numerical case study. We find that the moments with respect to analytic functions are no longer very accurate. However the numerical solution does contain accurate information which can be extracted by a post-processing based on Gegenbauer polynomials.

Shu, Chi-Wang↗

NASA NTRS1994

Determining the accuracy of maximum likelihood parameter estimates with colored residuals

An important part of building high fidelity mathematical models based on measured data is calculating the accuracy associated with statistical estimates of the model parameters. Indeed, without some idea of the accuracy of parameter estimates, the estimates themselves have limited value. In this work, an expression based on theoretical analysis was developed to properly compute parameter accuracy measures for maximum likelihood estimates with colored residuals. This result is important because experience from the analysis of measured data reveals that the residuals from maximum likelihood estimation are almost always colored. The calculations involved can be appended to conventional maximum likelihood estimation algorithms. Simulated data runs were used to show that the parameter accuracy measures computed with this technique accurately reflect the quality of the parameter estimates from maximum likelihood estimation without the need for analysis of the output residuals in the frequency domain or heuristically determined multiplication factors. The result is general, although the application studied here is maximum likelihood estimation of aerodynamic model parameters from flight test data.

Morelli, Eugene A.↗

NASA NTRS1994

The Accuracy of Parameter Estimation in System Identification of Noisy Aircraft Load Measurement

This thesis focuses on the subject of the accuracy of parameter estimation and system identification techniques. Motivated by a complicated load measurement from NASA Dryden Flight Research Center, advanced system identification techniques are needed. The objective of this problem is to accurately predict the load experienced by the aircraft wing structure during flight determined from a set of calibrated load and gage response relationship. We can then model the problem as a black box input-output system identification from which the system parameter has to be estimated. Traditional LS (Least Square) techniques and the issues of noisy data and model accuracy are addressed. A statistical bound reflecting the change in residual is derived in order to understand the effects of the perturbations on the data. Due to the intrinsic nature of the LS problem, LS solution faces the dilemma of the trade off between model accuracy and noise sensitivity. A method of conflicting performance indices is presented, thus allowing us to improve the noise sensitivity while at the same time configuring the degredation of the model accuracy. SVD techniques for data reduction are studied and the equivalence of the Correspondence Analysis (CA) and Total Least Squares Criteria are proved. We also looked at nonlinear LS problems with NASA F-111 data set as an example. Conventional methods are neither easily applicable nor suitable for the specific load problem since the exact model of the system is unknown. Neural Network (NN) does not require prior information on the model of the system. This robustness motivated us to apply the NN techniques on our load problem. Simulation results for the NN methods used in both the single load and the 'warning signal' problems are both useful and encouraging. The performance of the NN (for single load estimate) is better than the LS approach, whereas no conventional approach was tried for the 'warning signals' problems. The NN design methodology is also presented. The use of SVD, CA and Collinearity Index methods are used to reduce the number of neurons in a layer.

Kong, Jeffrey↗

NASA NTRS1995

The construction of high-accuracy schemes for acoustic equations

An accuracy analysis of various high order schemes is performed from an interpolation point of view. The analysis indicates that classical high order finite difference schemes, which use polynomial interpolation, hold high accuracy only at nodes and are therefore not suitable for time-dependent problems. Thus, some schemes improve their numerical accuracy within grid cells by the near-minimax approximation method, but their practical significance is degraded by maintaining the same stencil as classical schemes. One-step methods in space discretization, which use piecewise polynomial interpolation and involve data at only two points, can generate a uniform accuracy over the whole grid cell and avoid spurious roots. As a result, they are more accurate and efficient than multistep methods. In particular, the Cubic-Interpolated Psuedoparticle (CIP) scheme is recommended for computational acoustics.

Tang, Lei↗

NASA NTRS1995

High Accuracy In-Flight Wavelength Calibration of Imaging Spectrometry Data

Accurate wavelength calibration of imaging spectrometer data is essential if proper atmospheric transmission corrections are to be made to obtain apparent surface reflectance. Accuracies of 0.1 nm are necessary for a 10 nm-sampling instrument in order to match the slopes of the deep atmospheric water vapor features that dominate the 0.7-2.3 micrometer regions. The Airborne Visible/Infrared Imaging Spectrometer (AVIRIS) is calibrated in the laboratory to determine the wavelength position and full-width-half-maximum (FWHM) response for each of the 224 channels. The accuracies are limited by the quality of the monochromator used as a source. The accuracies vary from plus or minus to plus or minus 1.5 nm depending on the wavelength region, in general decreasing with increasing wavelength. Green et al. make corrections to the wavelength calibrations by using the known positions of 14 atmospheric absorption features throughout the 0.4-2.5 micrometer wavelength region. These features, having varying width and intensity, were matched to the MODTRAN model with a non-linear least squares fitting algorithm. A complete calibration was developed for all 224 channels by interpolation. Instrument calibration cannot be assumed to be stable to 0.1 nm over a flight season given the rigors of thermal cycling and launch and landing loads. The upcoming sensor HYDICE will require a means for in-flight spectral calibration of each scene because the calibration is both temperature and pressure sensitive. In addition, any sensor using a two-dimensional array has the potential for systematic wavelength shifts as a function of cross-track position, commonly called 'smile'. Therefore, a rapid means for calibrating complete images will be required. The following describes a method for determining instrument wavelength calibration using atmospheric absorption features that is efficient enough to be used for entire images on workstations. This study shows the effect of the surface reflectance on the calibration accuracy and the calibration history for the AVIRIS B spectrometer over the 1992 flight season.

Goetz, Alexander F. H.↗

NASA NTRS1996

Some Considerations in the Determination of the Accuracy of a Measurement in Space of the Newtonian Gravitational Constant (G)

A commonly suggested method for determining the Newtonian constant of universal gravitation (G) is to observe the motion of two bodies of known mass moving about each other in an orbiting laboratory. In low Earth orbit (LEO), bodies constructed of even the densest material available experience a gravitational attraction that is several times smaller than the 'tidal' forces (due to their proximity to the Earth), which tend to pull them apart. While the tidal forces do not preclude stable orbits of the two objects about each other, they and the Coriolis force (in the rotating laboratory) dominate the motion, and the gravitational attraction of the two bodies may be considered a weak (but significant) contribution to the motion. As a result, compared to an experiment that would be performed in a laboratory far from the Earth, greater accuracy of measuring the motion of the two bodies may be required for a given accuracy in the determination of G. We find that the accuracy with which positions must be determined is not much different in an experiment in LEO than in one performed far from the Earth, but that rotational periods must be determined more accurately. Using a curvature matrix analysis, we also find that a value of G may be extracted (with some loss in accuracy, but probably some practical gain) from an analysis of the time dependence of the distance between the bodies rather than of a full specification (distance and direction) of their relative positions. A measurement of the gravitational constant to one part in 10(exp 4) continues to be thinkable, but one part in 10(exp 5) will be very difficult.

Baker, Stephen D.↗

NASA NTRS1997

Accuracy Study of a 2-Component Point Doppler Velocimeter (PDV)

A two-component Point Doppler Velocimeter (PDV) which has recently been developed is described, and a series of velocity measurements which have been obtained to quantify the accuracy of the PDV system are summarized. This PDV system uses molecular iodine vapor cells as frequency discriminating filters to determine the Doppler shift of laser light which is scattered off of seed particles in a flow. The majority of results which have been obtained to date are for the mean velocity of a rotating wheel, although preliminary data are described for fully-developed turbulent pipe flow. Accuracy of the present wheel velocity data is approximately +/- 1 % of full scale, while linearity of a single channel is on the order of +/- 0.5 % (i.e., +/- 0.6 m/sec and +/- 0.3 m/sec, out of 57 m/sec, respectively). The observed linearity of these results is on the order of the accuracy to which the speed of the rotating wheel has been set for individual data readings. The absolute accuracy of the rotating wheel data is shown to be consistent with the level of repeatability of the cell calibrations. The preliminary turbulent pipe flow data show consistent turbulence intensity values, and mean axial velocity profiles generally agree with pitot probe data. However, there is at present an offset error in the radial velocity which is on the order of 5-10 % of the mean axial velocity.

Kuhlman, John↗

NASA NTRS1998

Effects of magnetometer calibration and maneuvers on accuracies of magnetometer-only attitude-and-rate determination

Two different algorithms - a deterministic magnetic-field-only algorithm and a Kalman filter for gyroless spacecraft - are used to estimate the attitude and rates of the Rossi X-Ray Timing Explorer (RXTE) using only measurements from a three-axis magnetometer. The performance of these algorithms is examined using in-flight data from various scenarios. In particular, significant enhancements in accuracies are observed when' the telemetered magnetometer data are accurately calibrated using a recently developed calibration algorithm. Interesting features observed in these studies of the inertial-pointing RXTE include a remarkable sensitivity of the filter to the numerical values of the noise parameters and relatively long convergence time spans. By analogy, the accuracy of the deterministic scheme is noticeably lower as a result of reduced rates of change of the body-fixed geomagnetic field. Preliminary results show the filter-per-axis attitude accuracies ranging between 0.1 and 0.5 deg and rate accuracies between 0.001 deg/sec and 0.005 deg./sec, whereas the deterministic method needs a more sophisticated techniques for smoothing time derivatives of the measured geomagnetic field to clearly distinguish both attitude and rate solutions from the numerical noise. Also included is a new theoretical development in the deterministic algorithm: the transformation of a transcendental equation in the original theory into an 8th-order polynomial equation. It is shown that this 8th-order polynomial reduces to quadratic equations in the two limiting cases-infinitely high wheel momentum, and constant rates-discussed in previous publications.

Challa, M.↗

NASA NTRS1999

Improving the Accuracy of Quadrature Method Solutions of Fredholm Integral Equations That Arise from Nonlinear Two-Point Boundary Value Problems

In this paper we are concerned with high-accuracy quadrature method solutions of nonlinear Fredholm integral equations of the form y(x) = r(x) + definite integral of g(x, t)F(t,y(t))dt with limits between 0 and 1,0 less than or equal to x les than or equal to 1, where the kernel function g(x,t) is continuous, but its partial derivatives have finite jump discontinuities across x = t. Such integral equations arise, e.g., when one applied Green's function techniques to nonlinear two-point boundary value problems of the form y "(x) =f(x,y(x)), 0 less than or equal to x less than or equal to 1, with y(0) = y(sub 0) and y(l) = y(sub l), or other linear boundary conditions. A quadrature method that is especially suitable and that has been employed for such equations is one based on the trepezoidal rule that has a low accuracy. By analyzing the corresponding Euler-Maclaurin expansion, we derive suitable correction terms that we add to the trapezoidal rule, thus obtaining new numerical quadrature formulas of arbitrarily high accuracy that we also use in defining quadrature methods for the integral equations above. We prove an existence and uniqueness theorem for the quadrature method solutions, and show that their accuracy is the same as that of the underlying quadrature formula. The solution of the nonlinear systems resulting from the quadrature methods is achieved through successive approximations whose convergence is also proved. The results are demonstrated with numerical examples.

Sidi, Avram↗

NASA NTRS1999

Improving the Accuracy of Quadrature Method Solutions of Fredholm Integral Equations that Arise from Nonlinear Two-Point Boundary Value Problems

In this paper we are concerned with high-accuracy quadrature method solutions of nonlinear Fredholm integral equations of the form y(x) = r(x) + integral(0 to 1) g(x,t) F(t, y(t)) dt, 0 less than or equal to x less than or equal to 1, where the kernel function g(x,t) is continuous, but its partial derivatives have finite jump discontinuities across x = t. Such integrals equations arise, e.g., when one applies Green's function techniques to nonlinear two-point boundary value problems of the form U''(x) = f(x,y(x)), 0 less than or equal to x less than or equal to 1, with y(0) = y(sub 0) and g(l) = y(sub 1), or other linear boundary conditions. A quadrature method that is especially suitable and that has been employed for such equations is one based on the trapezoidal rule that has a low accuracy. By analyzing the corresponding Euler-Maclaurin expansion, we derive suitable correction terms that we add to the trapezoidal thus obtaining new numerical quadrature formulas of arbitrarily high accuracy that we also use in defining quadrature methods for the integral equations above. We prove an existence and uniqueness theorem for the quadrature method solutions, and show that their accuracy is the same as that of the underlying quadrature formula. The solution of the nonlinear systems resulting from the quadrature methods is achieved through successive approximations whose convergence is also proved. The results are demonstrated with numerical examples.

Sidi, Avram↗