Results for “error estimate” — Page 89

NASA NTRS2005

Optimal Estimation of Clock Values and Trends from Finite Data

We show how to solve two problems of optimal linear estimation from a finite set of phase data. Clock noise is modeled as a stochastic process with stationary dth increments. The covariance properties of such a process are contained in the generalized autocovariance function (GACV). We set up two principles for optimal estimation: with the help of the GACV, these principles lead to a set of linear equations for the regression coefficients and some auxiliary parameters. The mean square errors of the estimators are easily calculated. The method can be used to check the results of other methods and to find good suboptimal estimators based on a small subset of the available data.

stationary increments↗

NASA NTRS1989

Aerosol anomalies in Nimbus-7 coastal zone color scanner data obtained in Japan area

About 400 CZCS (coastal zone color scanner) scenes covering the Japan area in November 1978-May 1982 were processed to study the applicability of the Gordon-Clark atmospheric correction scheme which produces water-leaving radiances Lw at 443 nm, 520 nm, and 550 nm as well as phytoplankton pigment maps. Typical spring-fall aerosol radiance in the images was found to be 0.8-1.5 micro-W/sq cm-nm-sr, which is about 50 percent more than reported for the US eastern coastal images. The correction for about half the data resulted in negative Lw (443) values, implying overestimation of the aerosol effect for this channel. Several possible reasons for this are considered, including deviation of the aerosol optical thickness tau(a) at 443 nm from that estimated by Angstrom's exponential law, which the algorithm assumes. The analysis shows that, assuming the use of the Gordon-Clark algorithm, and for a pigment concentration of about 1 microgram/l, -40 percent to +100 percent error in satellite estimates is common. Although this does not fully explain the negative Lw (443) in the satellite data, it seems to contribute to the problem significantly, together with other error sources, including one in the sensor calibration.

Fukushima, Hajime↗

NASA NTRS1988

Error indicators and accuracy improvements of finite element solutions

Practical and reliable estimators of the discretization errors in engineering problems are developed. Error indicators for identifying the regions or elements of the solution domain which are likely to have the largest discretization errors are presented, and a simple computational procedure for improving the accuracy of the finite element solutions for shell problems is given. The similarities between the proposed procedure and a preconditioned conjugate gradient (PCG) technique are identified and exploited to generate pointwise error indicators from the PCG technique. Numerical examples in the linear static analysis of shells are presented.

Noor, Ahmed K.↗

NASA NTRS2005

Hardware in-the-Loop Demonstration of Real-Time Orbit Determination in High Earth Orbits

This paper presents results from a study conducted at Goddard Space Flight Center (GSFC) to assess the real-time orbit determination accuracy of GPS-based navigation in a number of different high Earth orbital regimes. Measurements collected from a GPS receiver (connected to a GPS radio frequency (RF) signal simulator) were processed in a navigation filter in real-time, and resulting errors in the estimated states were assessed. For the most challenging orbit simulated, a 12 hour Molniya orbit with an apogee of approximately 39,000 km, mean total position and velocity errors were approximately 7 meters and 3 mm/s respectively. The study also makes direct comparisons between the results from the above hardware in-the-loop tests and results obtained by processing GPS measurements generated from software simulations. Care was taken to use the same models and assumptions in the generation of both the real-time and software simulated measurements, in order that the real-time data could be used to help validate the assumptions and models used in the software simulations. The study makes use of the unique capabilities of the Formation Flying Test Bed at GSFC, which provides a capability to interface with different GPS receivers and to produce real-time, filtered orbit solutions even when less than four satellites are visible. The result is a powerful tool for assessing onboard navigation performance in a wide range of orbital regimes, and a test-bed for developing software and procedures for use in real spacecraft applications.

Moreau, Michael↗

NASA NTRS1976

Accuracy of satellite derived radiometric data

Plotting of the mean errors of daily mean air temperature estimates suggests that water vapor is a possible factor in the high standard errors of estimate obtained.

Abeele, W. V.↗

NASA NTRS1979

Earth-Moon system: Dynamics and parameter estimation

The following topics are discussed: (1) the Unified Model of Lunar Translation/Rotation (UMLTR); (2) the effect of figure-figure interactions on lunar physical librations; (3) the effect of translational-rotational coupling on the lunar orbit; and(4) an error analysis for estimating lunar inertias from LURE (Lunar Laser Ranging Experiment) data.

Breedlove, W. J., Jr.↗

NASA NTRS1989

Determination of longitudinal aerodynamic derivatives using flight data from an icing research aircraft

A flight test was performed with the NASA Lewis Research Center's DH-6 icing research aircraft. The purpose was to employ a flight test procedure and data analysis method, to determine the accuracy with which the effects of ice on aircraft stability and control could be measured. For simplicity, flight testing was restricted to the short period longitudinal mode. Two flights were flown in a clean (baseline) configuration, and two flights were flown with simulated horizontal tail ice. Forty-five repeat doublet maneuvers were performed in each of four test configurations, at a given trim speed, to determine the ensemble variation of the estimated stability and control derivatives. Additional maneuvers were also performed in each configuration, to determine the variation in the longitudinal derivative estimates over a wide range of trim speeds. Stability and control derivatives were estimated by a Modified Stepwise Regression (MSR) technique. A measure of the confidence in the derivative estimates was obtained by comparing the standard error for the ensemble of repeat maneuvers, to the average of the estimated standard errors predicted by the MSR program. A multiplicative relationship was determined between the ensemble standard error, and the averaged program standard errors. In addition, a 95 percent confidence interval analysis was performed for the elevator effectiveness estimates, C sub m sub delta e. This analysis identified the speed range where changes in C sub m sub delta e could be attributed to icing effects. The magnitude of icing effects on the derivative estimates were strongly dependent on flight speed and aircraft wing flap configuration. With wing flaps up, the estimated derivatives were degraded most at lower speeds corresponding to that configuration. With wing flaps extended to 10 degrees, the estimated derivatives were degraded most at the higher corresponding speeds. The effects of icing on the changes in longitudinal stability and control derivatives were adequately determined by the flight test procedure and the MSR analysis method discussed herein.

Ranaudo, R. J.↗

NASA NTRS1989

Determination of longitudinal aerodynamic derivatives using flight data from an icing research aircraft

A flight test was performed with the NASA Lewis Research Center's DH-6 icing research aircraft. The purpose was to employ a flight test procedure and data analysis method, to determine the accuracy with which the effects of ice on aircraft stability and control could be measured. For simplicity, flight testing was restricted to the short period longitudinal mode. Two flights were flown in a clean (baseline) configuration, and two flights were flown with simulated horizontal tail ice. Forty-five repeat doublet maneuvers were performed in each of four test configurations, at a given trim speed, to determine the ensemble variation of the estimated stability and control derivatives. Additional maneuvers were also performed in each configuration, to determine the variation in the longitudinal derivative estimates over a wide range of trim speeds. Stability and control derivatives were estimated by a Modified Stepwise Regression (MSR) technique. A measure of the confidence in the derivative estimates was obtained by comparing the standard error for the ensemble of repeat maneuvers, to the average of the estimated standard errors predicted by the MSR program. A multiplicative relationship was determined between the ensemble standard error, and the averaged program standard errors. In addition, a 95 percent confidence interval analysis was performed for the elevator effectiveness estimates, C sub m sub delta e. This analysis identified the speed range where changes in C sub m sub delta e could be attributed to icing effects. The magnitude of icing effects on the derivative estimates were strongly dependent on flight speed and aircraft wing flap configuration. With wing flaps up, the estimated derivatives were degraded most at lower speeds corresponding to that configuration. With wing flaps extended to 10 degrees, the estimated derivatives were degraded most at the higher corresponding speeds. The effects of icing on the changes in longitudinal stability and control derivat

Ranaudo, R. J.↗

NASA NTRS2021

Constraining the Neutron Star Mass–Radius Relation and Dense Matter Equation of State with NICER. III. Model Description and Verification of Parameter Estimation Codes

We describe the X-ray pulse profile models we use and how we use them to analyze Neutron Star Interior Composition Explorer(NICER)observations of rotation-powered millisecond pulsars to obtain information about the mass–radius relation of neutron stars and the equation of state of the dense matter in their cores. Here we detail our modeling of the observed profile of PSR J0030+0451 that we analyzed in Miller et al. and Riley et al. and describe a cross-verification of computations of the pulse profiles of a star with R/M 3, in case stars this compact need to be considered in future analyses. We also present our early cross-verification efforts of the parameter estimation procedures used by Miller et al. and Riley et al. by analyzing two distinct synthetic data sets. Both codes yielded credible regions in the mass–radius plane that are statistically consistent with one another, and both gave posterior distributions for model parameter values consistent with the values that were used to generate the data. We also summarize the additional tests of the parameter estimation procedure of Miller et al. that used synthetic pulse profiles and the NICER pulse profile of PSR J0030+0451. We then illustrate how the precision of mass and radius estimates depends on the pulsar’s spin rate and the size of its hot spot by analyzing four different synthetic pulse profiles. Finally, we assess possible sources of systematic error in the estimates made using this technique, some of which may warrant further investigation.

Slavko Bogdanov↗

NASA NTRS1997

The Surface Heat Flux as a Function of Ground Cover for Climate Models

Surface heat fluxes were examined as a function of surface properties and meteorological conditions in a 100 km x 100 km grid square at 1-km spatial resolution centered at the location of the First ISLSCP (International Satellite Land Surface Climatology Project) Field Experiment (FIFE), the Forest Ecosystem Dynamics site in central Maine, and a semiarid rangeland site around Walnut Gulch, Arizona. This investigation treats the surface heat flux variability within a GCM grid box to provide insight into methods for treating that variability in climate models. The heat fluxes were calculated using NOAA AVHRR and available meteorological data. The average heat fluxes that were estimated using the various area ground-cover representations were compared with the ensemble average heat fluxes for the entire area, which were assumed to be the best representation of the heat fluxes for the areas. Average beat fluxes were estimated for the entire 100 km x 100 km area based on a single ground-cover representation, and the mean error for the area sensible heat flux was about 10% and for the area latent heat flux, 21%. The estimation error was reduced, and in some cases significantly reduced, when the area heat fluxes were estimated by partitioning the area according to significant ground cover. The most significant effect of the partitioning was on the latent heat flux estimates.

Vukovich, Fred M.↗

NASA NTRS1975

Sensitivity analysis of short-arc station coordinate determinations from range data

The accurate determination of the geocentric coordinates of a tracking station is essential for most geodetic and geophysical satellite applications. Since most of these satellites are close to the earth, the geopotential model is a dominant source of error which significantly influences station coordinate determinations. Other sources, such as GM error and drag, also influence the accuracy of the station coordinate determination. One technique for reducing the effect of these errors is to use short-arcs consisting of a few passes of the satellite over the tracking station. This paper analyzes the sensitivity of short-arc station coordinate estimates to various errors in the physical model, to the number of observations, and to the station-satellite geometry using simulated as well as real data.

Schutz, B. E.↗

NASA NTRS1976

Sensitivity analysis of short-arc station coordinate determinations from range data

The accurate determination of the geocentric coordinates of a tracking station is essential for most geodetic and geophysical satellite applications. Since most of these satellites are close to the earth, the geopotential model is a dominant source of error which significantly influences station coordinate determinations. Other sources, such as GM error and drag, also influence the accuracy of the station coordinate determination. One technique for reducing the effect of these errors is to use short-arcs consisting of a few passes of the satellite over the tracking station. This paper analyzes the sensitivity of short-arc station coordinate estimates to various errors in the physical model, to the number of observations, and to the station-satellite geometry using simulated as well as real data.

Schutz, B. E.↗

NASA NTRS1985

Testing an Energy Balance Model for Estimating Actual Evapotranspiration Using Remotely Sensed Data

An energy-balance model is used to estimate daily evapotranspiration for 3 days for a barley field and a wheat field near Hannover, Federal Republic of Germany. The model was calibrated using once-daily estimates of surface temperatures, which may be remotely sensed. The evaporation estimates were within the 95% error bounds of independent eddy correlation estimates for the daytime periods for all three days for both sites, but the energy-balance estimates are generally higher; it is unclear which estimate is biassed. Soil moisture in the top 2 cm of soil, which may be remotely sensed, may be used to improve these evaporation estimates under partial ground cover. Sensitivity studies indicate the amount of ground data required is not excessive.

Gurney, R. J.↗

NASA NTRS1991

Signal-to-noise considerations for sky-subtracted CCD data

The standard equation for calculating the uncertainty of photometry obtained from CCDs does not correctly consider the random errors, or 'noise', introduced into observations by procedures used in reducing the data. This paper presents a thorough derivation of the theoretical error equation that considers the contributions from all internal noise sources in the signal-to-noise ratio (S/N) of a sky-subtracted image. A simplified version used for estimating the internal errors from empirical data is also derived. The propagation of noise through the data-reduction process is illustrated through a series of equations for the change in S/N that results from a variety of different operations performed on a CCD frame. Comparing these effects with the results expected for an observation made with an ideal detector suggests a number of ways to improve the precision of photometry through the practices employed in obtaining and reducing the observations.

Newberry, Michael V.↗

NASA NTRS1992

Precision of the calibration of the AXAF engineering test article (VETA) mirrors

Measurements of the VETA encircled energies have been performed at 5 energies within 16 radii ranging from 0.05 to 200 arcseconds. We report here on the analysis of the accuracy of those measurements. A common 'error tree' structure applies, and we present representative numbers for the larger terms. At 0.277, 1.5, and 2.07 keV, and for radii of 3 arcsec and larger, our measurements have estimated 1 sigma errors of 0.6 to 1.5 percent. Effects of measurement statistics and of the VETA test mount limit the accuracy at smaller angles, and modulation by the counter window support structure together with the imperfect position repeatability limit the accuracy for the 0.93 and 2.3 keV energies. We expect to mitigate these limitations when calibrating the complete AXAF flight mirror assembly.

Schwartz, D. A.↗

NASA NTRS1993

Precision of the calibration of the AXAF Engineering Test Article (VETA) mirrors

Measurements of the VETA encircled energies have been performed at 5 energies within 16 radii ranging from 0.05 to 200 arcseconds. We report here on the analysis of the accuracy of those measurements. A common 'error tree' structure applies, and we present representative numbers for the larger terms. At 0.277, 1.5, and 2.07 keV, and for radii of 3 arcsec and larger, our measurements have estimated 1 sigma errors of 0.6 to 1.5 percent. Effects of measurement statistics and of the VETA test mount limit the accuracy at smaller angles, and modulation by the counter window support structure together with the imperfect position repeatability limit the accuracy for the 0.93 and 2.3 keV energies. We expect to mitigate these limitations when calibrating the complete AXAF flight mirror assembly.

Schwartz, D. A.↗

NASA NTRS1979

Identification evaluation methods

Methods for airplane parameter estimation, the equation error method, output error method, and two advanced methods are presented and their basic properties described. The advanced methods include the maximum likelihood and extended Kalman filter method. For a better understanding of the estimation techniques a first-order scalar differential equation is used as a model of the system under test. Application of the methods to a general multivariable linear system is briefly outlined. A note on the parameter estimation in the frequency domain is also presented. Numerical examples along with the comparison of results from various methods are given.

Klein, V.↗

NASA NTRS1986

Radio-source positions from VLBI

Positions of 85 compact extragalactic radio sources and the Galactic object Beta Persei (Algol) have been determined in the J2000.0 coordinate system for analysis of VLBI observations made with the bandwidth-synthesis technique. Twenty-four of these sources were observed with the Mark I VLBI system in 37 sessions distributed between April 1972 and May 1978, and 82 of the sources were observed with the Mark III system in 85 sessions distributed between August 1979 and December 1982. Each session spanned at least 24 hr. Standard errors for the estimated positions on the sky of the about 10 sources frequently observed with the Mark I system are about 1 mas, except for the declinations of nearly equatorial sources, where these errors approach 5 mas. Corresponding uncertainties for the about 20 sources frequently observed with the Mark III system are 0.3 and 2 mas, respectively.

Ma, C.↗