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NASA NTRS2002

Statistical Properties of Maximum Likelihood Estimators of Power Law Spectra Information

A simple power law model consisting of a single spectral index, a is believed to be an adequate description of the galactic cosmic-ray (GCR) proton flux at energies below 10(exp 13) eV, with a transition at the knee energy, E(sub k), to a steeper spectral index alpha(sub 2) greater than alpha(sub 1) above E(sub k). The Maximum likelihood (ML) procedure was developed for estimating the single parameter alpha(sub 1) of a simple power law energy spectrum and generalized to estimate the three spectral parameters of the broken power law energy spectrum from simulated detector responses and real cosmic-ray data. The statistical properties of the ML estimator were investigated and shown to have the three desirable properties: (P1) consistency (asymptotically unbiased). (P2) efficiency asymptotically attains the Cramer-Rao minimum variance bound), and (P3) asymptotically normally distributed, under a wide range of potential detector response functions. Attainment of these properties necessarily implies that the ML estimation procedure provides the best unbiased estimator possible. While simulation studies can easily determine if a given estimation procedure provides an unbiased estimate of the spectra information, and whether or not the estimator is approximately normally distributed, attainment of the Cramer-Rao bound (CRB) can only he ascertained by calculating the CRB for an assumed energy spectrum-detector response function combination, which can be quite formidable in practice. However. the effort in calculating the CRB is very worthwhile because it provides the necessary means to compare the efficiency of competing estimation techniques and, furthermore, provides a stopping rule in the search for the best unbiased estimator. Consequently, the CRB for both the simple and broken power law energy spectra are derived herein and the conditions under which they are attained in practice are investigated. The ML technique is then extended to estimate spectra information from an arbitrary number of astrophysics data sets produced by vastly different science instruments. This theory and its successful implementation will facilitate the interpretation of spectral information from multiple astrophysics missions and thereby permit the derivation of superior spectral parameter estimates based on the combination of data sets.

Howell, L. W.↗

NASA NTRS1985

Statistical methods for efficient design of community surveys of response to noise: Random coefficients regression models

Research studies of residents' responses to noise consist of interviews with samples of individuals who are drawn from a number of different compact study areas. The statistical techniques developed provide a basis for those sample design decisions. These techniques are suitable for a wide range of sample survey applications. A sample may consist of a random sample of residents selected from a sample of compact study areas, or in a more complex design, of a sample of residents selected from a sample of larger areas (e.g., cities). The techniques may be applied to estimates of the effects on annoyance of noise level, numbers of noise events, the time-of-day of the events, ambient noise levels, or other factors. Methods are provided for determining, in advance, how accurately these effects can be estimated for different sample sizes and study designs. Using a simple cost function, they also provide for optimum allocation of the sample across the stages of the design for estimating these effects. These techniques are developed via a regression model in which the regression coefficients are assumed to be random, with components of variance associated with the various stages of a multi-stage sample design.

Tomberlin, T. J.↗

NASA NTRSDate not supplied

CFD-Based Frequency Domain Method for Dynamic Stability Derivative Estimation with Application to Transonic Truss-Braced Wing

This paper presents a dynamic stability estimation technique obtained from high-fidelity CFD simulations of the Mach 0.8 Transonic Truss-Braced Wing (TTBW). A series of unsteady RANS CFD simulations in FUN3D is performed on the TTBW in pitch and plunge oscillations at various reduced frequencies. The time-domain data are transformed into the frequency-domain data by Fourier series. Transfer functions of the dynamic stability derivatives are then estimated by a frequency-domain regression. The dynamic stability derivatives with respect to the angle of attack are determined by the regression of the unsteady aerodynamic coefficients for the plunge motion. The dynamic stability derivatives with respect to the pitch rate are deter-mined by the regression of the differential unsteady aerodynamic coefficients for the pitch motion upon the removal of the angle of attack contribution by the plunge motion. The steady-state stability derivatives are then compared to the results obtained from a stability analysis code VSPAERO as well as steady-state FUN3D simulations. The comparison of the steady-state stability derivatives shows excellent agreement.

Dynamic Stability Derivatives↗

NASA NTRS1994

Phytoplankton production in the Sargasso Sea as determined using optical mooring data

Optical measurements from an untended mooring provide high-frequency observations of in-water optical properties and permit the estimation of important biological parameters continuously as a function of time. A 9-month time series, composed of three separate deployments, of optical data from the BIOWATT 1987 deep-sea mooring located in the oligotrophic waters of the Sargasso Sea at 34 deg N, 70 deg W are presented. These data have been tested using several bio-optical models for the purpose of providing a continuous estimate of phytoplankton productivity. The data are discussed in the context of contemporaneous shipboard observations and for future ocean color satellite observations. We present a continuous estimation of phytoplankton productivity for the 9-month time series. Results from the first 70-day deployment are emphasized to demonstrate the utility of optical observations as proxy measures of biological parameters, to present preliminary analysis, and to compare our bio-optical observations with concurrent physical observations. The bio-optical features show variation in response to physical forcings including diel variations of incident solar irradiance, episodic changes corresponding to wind forcing, variability caused by advective mesoscale eddy events in the vicinity of the mooring, and seasonal variability corresponding to changes in solar radiation, shoaling of the mixed layer depth, and succession of phytoplankton populations.

Waters, K. J.↗

NASA NTRS2016

Oxygen, Neon, and Iron X-Ray Absorption in the Local Interstellar Medium

We present a detailed study of X-ray absorption in the local interstellar medium by analyzing the X-ray spectra of 24 galactic sources obtained with the Chandra High Energy Transmission Grating Spectrometer and the XMM-Newton Reflection Grating Spectrometer. Methods. By modeling the continuum with a simple broken power-law and by implementing the new ISMabs X-ray absorption model, we have estimated the total H, O, Ne, and Fe column densities towards the observed sources. Results. We have determined the absorbing material distribution as a function of source distance and galactic latitude longitude. Conclusions. Direct estimates of the fractions of neutrally, singly, and doubly ionized species of O, Ne, and Fe reveal the dominance of the cold component, thus indicating an overall low degree of ionization. Our results are expected to be sensitive to the model used to describe the continuum in all sources.

SM: general / ISM: atoms / ISM: abundances / ISM: ↗

NASA NTRS1980

The luminosity functions of the 1969 Perseid and Orionid meteor showers

Observations of the 1969 Perseid and Orionid meteor showers are presented and used to derive luminosity functions for the 288 Perseids and 56 Orionids detected. Visual counts were performed under very good to excellent seeing conditions at the times of peak activities, and the brightnesses of the meteors were estimated to the nearest magnitude by comparison with the magnitudes of known objects. Maximum likelihood estimates of the power law index of the luminosity function of 1.56 + or - 0.06 for the Perseids and of 1.85 + or - 0.1 for the Orionids are obtained which are lower than the values found by other investigators. Under the assumption that the luminosity of visual meteors is proportional to their mass, the luminosity function power law may also be used to characterize the mass function.

Krisciunas, K.↗

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 NTRS2006

Spatial Correlation Function of the Chandra Selected Active Galactic Nuclei

We present the spatial correlation function analysis of non-stellar X-ray point sources in the Chandra Large Area Synoptic X-ray Survey of Lockman Hole Northwest (CLASXS). Our 9 ACIS-I fields cover a contiguous solid angle of 0.4 deg(exp 2) and reach a depth of 3 x 10(exp -15) erg/square cm/s in the 2-8 keV band. We supplement our analysis with data from the Chandra Deep Field North (CDFN). The addition of this field allows better probe of the correlation function at small scales. A total of 233 and 252 sources with spectroscopic information are used in the study of the CLASXS and CDFN fields respectively. We calculate both redshift-space and projected correlation functions in co-moving coordinates, averaged over the redshift range of 0.1 < z < 3.0, for both CLASXS and CDFN fields for a standard cosmology with Omega(sub Lambda) = 0.73,Omega(sub M) = 0.27, and h = 0.71 (H(sub 0) = 100h km/s Mpc(exp -1). The correlation function for the CLASXS field over scales of 3 Mpc< s < 200 Mpc can be modeled as a power-law of the form xi(s) = (S/SO)(exp - gamma), with gamma = 1.6(sup +0.4 sub -0.3) and S(sub o) = 8.0(sup +.14 sub -1.5) Mpc. The redshift-space correlation function for CDFN on scales of 1 Mpc< s < 100 Mpc is found to have a similar correlation length so = 8.55(sup +0.74 sub -0.74) Mpc, but a shallower slope (gamma = 1.3 +/- 0.1). The real-space correlation functions derived from the projected correlation functions, are found to be tau(sub 0 = 8.1(sup +1.2 sub -2.2) Mpc, and gamma = 2.1 +/- 0.5 for the CLASXS field, and tau(sub 0) = 5.8(sup +.1.0 sub -1.5) Mpc, gamma = 1.38(sup +0.12 sub -0.14 for the CDFN field. By comparing the real- and redshift-space correlation functions in the combined CLASXS and CDFN samples, we are able to estimate the redshift distortion parameter Beta = 0.4 +/- 0.2 at an effective redshift z = 0.94. We compare the correlation functions for hard and soft spectra sources in the CLASXS field and find no significant difference between the two groups. We have also found that the correlation between X-ray luminosity and clustering amplitude is weak, which, however, is fully consistent with the expectation using the simplest relations between X-ray luminosity, black hole mass, and dark halo mass. We study the evolution of the AGN clustering by dividing the samples into 4 redshift bins over 0.1 Mpc< z <3.0 Mpc. We find a very mild evolution in the clustering amplitude, which show the same evolution trend found in optically selected quasars in the 2dF survey. We estimate the evolution of the bias, and find that the bias increases rapidly with redshift (b(z = 0.45) = 0.95 +/- 0.15 and b(z = 2.07) = 3.03 +/- 0.83): The typical mass of the dark matter halo derived from the bias estimates show little change with redshift. The average halo mass is found to be log (M(sub halo)/M(sun))approximates 12.1. Subject headings: cosmology: observations - large-scale structure of the universe - x-rays: diffuse background - galaxies: nuclei

Yang, Y.↗

NASA NTRSDate not supplied

Nonlinear Dynamic Control Derivative Analysis for Aircraft with Application to Transonic Truss-Braced Wing

This paper presents the development of a nonlinear dynamic control derivative estimation method. A nonlinear aerodynamic model is developed to account for the effects of large control surface deflections on aircraft aerodynamic forces and moments. A series of unsteady RANS CFD simulations is performed to simulate the control surface oscillations at various reduced frequencies. The time-domain data are transformed into the frequency-domain data by a Fourier series analysis. Transfer functions of the dynamic control derivatives are then estimated by a frequency-domain regression. The method is applied to the Transonic Truss-Braced Wing (TTBW) to estimate the dynamic control derivatives for the elevator, aileron, and rudder.

Aircraft Control Derivatives↗

NASA NTRS1991

A frequency-domain estimator for use in adaptive control systems

This paper presents a frequency-domain estimator that can identify both a parametrized nominal model of a plant as well as a frequency-domain bounding function on the modeling error associated with this nominal model. This estimator, which we call a robust estimator, can be used in conjunction with a robust control-law redesign algorithm to form a robust adaptive controller.

Lamaire, Richard O.↗

NASA NTRS1984

Observations of solar-flare ionization in the mesosphere using coherent-scatter radar

Observations of solar-flare ionization in the mesosphere can be made using coherent-scatter radar systems. The scattered power profiles they measure in the 60-90 km altitude region is a function of the ion concentration gradient and the intensity of turbulent mixing at each altitude. By comparing the power profiles before, during and after a solar flare, it is possible to estimate the ion production rate during the flare as a function of altitude and time. This analysis is used to compare the ion production rates with generally accepted ion-chemical models. Comparisons are made with ion production rates estimated from the solar X-ray flux for the same flare made by geostationary satellites.

Parker, J. W.↗

NASA NTRS1983

The X-ray luminosity function of very rich clusters and the luminosity-richness relation

For a sample of galactic clusters that includes richness class three, four, and five clusters, the significance of the luminosity-richness relation is estimated using nonparametric methods which are valid for any luminosity function. The Kolmogorov-Smirnov test is used to determine the significance at which the X-ray luminosities of clusters in one richness class are statistically equal to those in another. The a priori expectation that the high richness clusters are more luminous on average than lower richness objects is confirmed, but it is found that the luminosity function for clusters of richness class three or higher turns over for luminosities less than about 3 x 10 to the 44th ergs/s, while that for lower richness classes extends to at least an order of magnitude lower luminosity.

Soltan, A.↗

NASA NTRS1989

X-ray constraints on large scale clustering

HEAO-1 A2 all-sky survey data are analyzed to investigate the autocorrelation function of the surface brightness fluctuations of the extra-galactic 2-10-keV X-ray background on angular scales ranging from 3 to 27 deg. No significant signal has been detected on any scale. The derived upper limits set important bounds on correlated emission on scales of 10 Mpc or greater. X-ray data are found to be compatible with optical estimates of the two-point spatial correlation function of rich clusters of galaxies and with recent predictions for their cosmological evolution. Constraints on clustering of active galactic nuclei and on its dependence on cosmic time are analyzed in the light of results of recent optical studies.

De Zotti, G.↗

NASA NTRS1995

The Relative Contribution of Interaural Time and Magnitude Cues to Dynamic Sound Localization

This paper presents preliminary data from a study examining the relative contribution of interaural time differences (ITDs) and interaural level differences (ILDs) to the localization of virtual sound sources both with and without head motion. The listeners' task was to estimate the apparent direction and distance of virtual sources (broadband noise) presented over headphones. Stimuli were synthesized from minimum phase representations of nonindividualized directional transfer functions; binaural magnitude spectra were derived from the minimum phase estimates and ITDs were represented as a pure delay. During dynamic conditions, listeners were encouraged to move their heads; the position of the listener's head was tracked and the stimuli were synthesized in real time using a Convolvotron to simulate a stationary external sound source. ILDs and ITDs were either correctly or incorrectly correlated with head motion: (1) both ILDs and ITDs correctly correlated, (2) ILDs correct, ITD fixed at 0 deg azimuth and 0 deg elevation, (3) ITDs correct, ILDs fixed at 0 deg, 0 deg. Similar conditions were run for static conditions except that none of the cues changed with head motion. The data indicated that, compared to static conditions, head movements helped listeners to resolve confusions primarily when ILDs were correctly correlated, although a smaller effect was also seen for correct ITDs. Together with the results for static conditions, the data suggest that localization tends to be dominated by the cue that is most reliable or consistent, when reliability is defined by consistency over time as well as across frequency bands.

Wenzel, Elizabeth M.↗

NASA NTRS1992

Enhanced orbital gyrocompassing by the optical flow sensed by an Earth-pointing camera

A new method for improving the orbital gyrocompassing process involving the attitude angle estimation of an earth-pointing satellite in low-Earth orbit uses an electro-optical sensor for direct measurement of the satellite azimuth angle. Simulations have shown that this additional measurement drastically reduces the estimator convergence time, especially when the sun sensor is rendered ineffective, e.g., by high solar elevations. The azimuth-sensing method is based on estimation of the image shift between successive picture frames of an on-board, Earth-pointing, charge-coupled device (CCD) full-matrix camera. The shift-estimation algorithm is based on minimizing a cost function which expresses mean-squared differences in brightness patterns of selected areas of the two frames. An extensive evaluation program with a computer-controlled 2-axis light table and actual satellite images has demonstrated high robustness for a wide range of variation of parameters including image texture content; camera focal length; sampling rate; and number of pixels processed. It was shown to be possible to estimate the azimuth angle within 0.1-0.2 degrees, for a suitably chosen parameter set.

Topaz, Leora↗

NASA NTRS1991

A system identification model for adaptive nonlinear control

A system identification model that combines generalized-spline function approximation with a nonlinear control system is described. The complete control system contains three main elements: a nonlinear-inverse-dynamic control law that depends on a comprehensive model of the plant, a state estimator whose outputs drive the control law, and a function approximation scheme that models the system dynamics. The system-identification task, which combines an extended Kalman filter with a function approximator modeled as an artificial neural network, is considered. The results of an application of the identification techniques to a nonlinear transport aircraft model are presented.

Linse, Dennis J.↗

NASA NTRS2002

Optical properties of intact leaves for estimating chlorophyll concentration

Changes in leaf chlorophyll content can serve as relative indicators of plant vigor and environmental quality. This study identified reflectance, transmittance, and absorptance wavebands and band ratios within the 400- to 850-nm range for intact leaves that could be used to estimate extracted leaf chlorophyll per unit leaf area (areal concentration) with minimal error. Leaf optical properties along with chlorophyll a, b, and a + b concentrations were measured for the planar-leaved sweetgum (Liquidambar styraciflua L.), red maple (Acer rubrum L.), wild grape (Vitis rotundifolia Michx.), and switchcane [Arundinaria gigantea (Walter) Muhl.], and for needles of longleaf pine (Pinus palustris Miller). Generally, reflectance, transmittance, and absorptance corresponded most precisely with chlorophyll concentrations at wavelengths near 700 nm, although regressions were also strong in the 550- to 625-nm range. A power function was superior to a simple linear function in yielding low standard deviations of the estimate (s). When data were combined among the planar-leaved species, s values were low at approximately 50 mumol/m2 out of a 940 mumol/m2 range in chlorophyll a + b at best-fit wavelengths of 707 to 709 nm. Minimal s values for chlorophyll a + b ranged from 32 to 62 mumol/m2 across species when band ratios having numerator wavelengths of 693 to 720 nm were used with the application of a power function. Optimal denominator wavelengths for the band ratios were 850 nm for reflectance and transmittance and 400 nm for absorptance. This information can be applied in designing field portable chlorophyll meters and in the landscape-scale remote sensing of plant responses to the environment.

Chlorophyll/analysis↗

NASA NTRS1991

New method for estimating low-earth-orbit collision probabilities

An unconventional but general method is described for estimating the probability of collision between an earth-orbiting spacecraft and orbital debris. This method uses a Monte Caralo simulation of the orbital motion of the target spacecraft and each discrete debris object to generate an empirical set of distances, each distance representing the separation between the spacecraft and the nearest debris object at random times. Using concepts from the asymptotic theory of extreme order statistics, an analytical density function is fitted to this set of minimum distances. From this function, it is possible to generate realistic collision estimates for the spacecraft.

Vedder, John D.↗