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NASA NTRS2010

Guidance and Control System for a Satellite Constellation

A distributed guidance and control algorithm was developed for a constellation of satellites. The system repositions satellites as required, regulates satellites to desired orbits, and prevents collisions. 1. Optimal methods are used to compute nominal transfers from orbit to orbit. 2. Satellites are regulated to maintain the desired orbits once the transfers are complete. 3. A simulator is used to predict potential collisions or near-misses. 4. Each satellite computes perturbations to its controls so as to increase any unacceptable distances of nearest approach to other objects. a. The avoidance problem is recast in a distributed and locally-linear form to arrive at a tractable solution. b. Plant matrix values are approximated via simulation at each time step. c. The Linear Quadratic Gaussian (LQG) method is used to compute perturbations to the controls that will result in increased miss distances. 5. Once all danger is passed, the satellites return to their original orbits, all the while avoiding each other as above. 6. The delta-Vs are reasonable. The controller begins maneuvers as soon as practical to minimize delta-V. 7. Despite the inclusion of trajectory simulations within the control loop, the algorithm is sufficiently fast for available satellite computer hardware. 8. The required measurement accuracies are within the capabilities of modern inertial measurement devices and modern positioning devices.

Bryson, Jonathan Lamar↗

NASA NTRS1980

Narrow-band nonlinear sea waves

Probabilistic description of nonlinear waves with a narrow-band spectrum is simplified to a form in which each realization of the surface displacement becomes an amplitude-modulated Stokes wave with a mean frequency and random phase. Under appropriate conditions this simplification provides a convenient yet rigorous means of describing nonlinear effects on sea surface properties in a semiclosed or closed form. In particular, it is shown that surface displacements are non-Gaussian and skewed, as was previously predicted by the Gram-Charlier approximation; that wave heights are Rayleigh distributed, just as in the linear case; and that crests are non-Rayleigh.

Tayfun, M. A.↗

NASA NTRS1989

Modal, ray, and beam techniques for analyzing the EM scattering by open-ended waveguide cavities

The problem of high-frequency electromagnetic (EM) scattering by open-ended waveguide cavities with an interior termination is analyzed via three different approaches. When cavities can be adequately modeled by joining together piecewise separable waveguide sections, a hybrid combination of asymptotic high-frequency and modal techniques is employed. In the case of more arbitrarily shaped waveguide cavities for which modes cannot even be defined in the conventional sense, the geometrical optics ray approach proves to be highly useful. However, at sufficiently high frequencies, both of these approaches tend to become inefficient. Hence, a paraxial Gaussian batch technique, which retains much of the simplicity of the ray approximation but is potentially more efficient, is investigated. Typical numerical results based on the different approaches are discussed.

Pathak, Prabhakar H.↗

NASA NTRS2009

Recent Results on "Approximations to Optimal Alarm Systems for Anomaly Detection"

An optimal alarm system and its approximations may use Kalman filtering for univariate linear dynamic systems driven by Gaussian noise to provide a layer of predictive capability. Predicted Kalman filter future process values and a fixed critical threshold can be used to construct a candidate level-crossing event over a predetermined prediction window. An optimal alarm system can be designed to elicit the fewest false alarms for a fixed detection probability in this particular scenario.

Martin, Rodney Alexander↗

NASA NTRS2008

Adaptive Key Component Control of Nonlinear Evolving Flexible Structures

Balas, Mark↗

NASA NTRS1988

Focal region fields of distorted reflectors

The problem of the focal region fields scattered by an arbitrary surface reflector under uniform plane wave illumination is solved. The physical optics (PO) approximation is used to calculate the current induced on the reflector. The surface of the reflector is described by a number of triangular domain-wise 5th degree bivariate polynomials. A 2-dimensional Gaussian quadrature is employed to numerically evaluate the integral expressions of the scattered fields. No Freshnel or Fraunhofer zone approximations are made. The relation of the focal fields problem to surface compensation techniques and other applications are mentioned. Several examples of distorted parabolic reflectors are presented. The computer code developed is included, together with instructions on its usage.

Buris, N. E.↗

NASA NTRS1993

A function approximation approach to anomaly detection in propulsion system test data

Ground test data from propulsion systems such as the Space Shuttle Main Engine (SSME) can be automatically screened for anomalies by a neural network. The neural network screens data after being trained with nominal data only. Given the values of 14 measurements reflecting external influences on the SSME at a given time, the neural network predicts the expected nominal value of a desired engine parameter at that time. We compared the ability of three different function-approximation techniques to perform this nominal value prediction: a novel neural network architecture based on Gaussian bar basis functions, a conventional back propagation neural network, and linear regression. These three techniques were tested with real data from six SSME ground tests containing two anomalies. The basis function network trained more rapidly than back propagation. It yielded nominal predictions with, a tight enough confidence interval to distinguish anomalous deviations from the nominal fluctuations in an engine parameter. Since the function-approximation approach requires nominal training data only, it is capable of detecting unknown classes of anomalies for which training data is not available.

Whitehead, Bruce A.↗

NASA NTRS2006

Small-Scale Gravity Waves in ER-2 MMS/MTP Wind and Temperature Measurements during CRYSTAL-FACE

Lower stratospheric wind and temperature measurements made from NASA's high-altitude ER-2 research aircraft during the CRYSTAL-FACE campaign in July 2002 were analyzed to retrieve information on small scale gravity waves (GWs) at the aircraft's flight level (typically approximately 20 km altitude). For a given flight segment, the S-transform (a Gaussian wavelet transform) was used to search for and identify small horizontal scale GW events, and to estimate their apparent horizontal wavelengths. The horizontal propagation directions of the events were determined using the Stokes parameter method combined with the cross S-transform analysis. The vertical temperature gradient was used to determine the vertical wavelengths of the events. GW momentum fluxes were calculated from the cross S-transform. Other wave parameters such as intrinsic frequencies were calculated using the GW dispersion relation. More than 100GW events were identified. They were generally high frequency waves with vertical wavelength of approximately 5 km and horizontal wavelength generally shorter than 20 km. Their intrinsic propagation directions were predominantly toward the east, whereas their ground-based propagation directions were primarily toward the west. Among the events, approximately 20% of them had very short horizontal wavelength, very high intrinsic frequency, and relatively small momentum fluxes, and thus they were likely trapped in the lower stratosphere. Using the estimated GW parameters and the background winds and stabilities from the NCAR/NCEP reanalysis data, we were able to trace the sources of the events using a simple reverse ray-tracing. More than 70% of the events were traced back to convective sources in the troposphere, and the sources were generally located upstream of the locations of the events observed at the aircraft level. Finally, a probability density function of the reversible cooling rate due to GWs was obtained in this study, which may be useful for cirrus cloud models.

Wang, L.↗

NASA NTRS1976

Development and application of an atmospheric turbulence model for use in flight simulators in flight simulators

The influence of simulated turbulence on aircraft handling qualities was investigated. Pilot opinion of the handling qualities of a light general aviation aircraft were evaluated in a motion-base simulator using a simulated turbulence environment. A realistic representation of turbulence disturbances is described in terms of rms intensity and scale length and their random variations with time. The time histories generated by the proposed turbulence models showed characteristics which appear to be more similar to real turbulence than the frequently-used Gaussian turbulence model. In addition, the proposed turbulence models can flexibly accommodate changes in atmospheric conditions and be easily implemented in flight simulator studies. Six turbulence time histories, including the conventional Gaussian model, were used in an IFR-tracking task. The realism of each of the turbulence models and the handling qualities of the simulated airplane were evaluated. Analysis of pilot opinions shows that at approximately the same rms intensities of turbulence, the handling quality ratings transit from the satisfactory level, for the simple Gaussian model, to an unacceptable level for more realistic and compositely structured turbulence models.

Jacobson, I. D.↗

NASA NTRS2011

Deep UV Luminosity Functions at the Infall Region of the Coma Cluster

We have used deep GALEX observations at the infall region of the Coma cluster to measure the faintest UV luminosity functions (LFs) presented for a rich galaxy cluster thus far. The Coma UV LFs are measured to M(sub uv) = -10.5 in the GALEX FUV and NUV bands, or 3.5 mag fainter than previous studies, and reach the dwarf early-type galaxy population in Coma for the first time. The Schechter faint-end slopes (alpha approximately equal to -1.39 in both GALEX bands) are shallower than reported in previous Coma UV LF studies owing to a flatter LF at faint magnitudes. A Gaussian-plus-Schechter model provides a slightly better parametrization of the UV LFs resulting in a faint-end slope of alpha approximately equal to -1.15 in both GALEX bands. The two-component model gives faint-end slopes shallower than alpha = -1 (a turnover) for the LFs constructed separately for passive and star forming galaxies. The UV LFs for star forming galaxies show a turnover at M(sub UV) approximately equal to -14 owing to a deficit of dwarf star forming galaxies in Coma with stellar masses below M(sub *) = 10(sup 8) solar mass. A similar turnover is identified in recent UV LFs measured for the Virgo cluster suggesting this may be a common feature of local galaxy clusters, whereas the field UV LFs continue to rise at faint magnitudes. We did not identify an excess of passive galaxies as would be expected if the missing dwarf star forming galaxies were quenched inside the cluster. In fact, the LFs for both dwarf passive and star forming galaxies show the same turnover at faint magnitudes. We discuss the possible origin of the missing dwarf star forming galaxies in Coma and their expected properties based on comparisons to local field galaxies.

Hammer, D. M.↗

NASA NTRS1992

Topology of large-scale structure in seeded hot dark matter models

The topology of the isodensity surfaces in seeded hot dark matter models, in which static seed masses provide the density perturbations in a universe dominated by massive neutrinos is examined. When smoothed with a Gaussian window, the linear initial conditions in these models show no trace of non-Gaussian behavior for r0 equal to or greater than 5 Mpc (h = 1/2), except for very low seed densities, which show a shift toward isolated peaks. An approximate analytic expression is given for the genus curve expected in linear density fields from randomly distributed seed masses. The evolved models have a Gaussian topology for r0 = 10 Mpc, but show a shift toward a cellular topology with r0 = 5 Mpc; Gaussian models with an identical power spectrum show the same behavior.

Beaky, Matthew M.↗

NASA NTRS1994

New description of charged particle propagation in random magnetic fields

When charged particles spiral along a large constant magnetic field, their trajectories are scattered by random components that are superposed on the guiding field. In the simplest analysis of this situation, scattering causes the particles to diffuse parallel to the guiding field. At the next level of approximation, moving pulses that correspond to a coherent mode of propagation are present, but they are represented by delta-functions whose infinitely narrow width makes no sense physically and is inconsistent with the finite duration of coherent pulses observed in solar energetic particle events. To derive a more realistic description, the transport problem is formulated in terms of 4 x 4 matrices, which derive from a representation of the particle distribution function in terms of eigenfunctions of the scattering operator, and which lead to useful approximations that give explicit predictions of the detailed evolution not only of the coherent pulses, but also of the diffusive wake. More specifically, the new description embodies a simple convolution of a narrow Gaussian with the solutions above that involve delta-functions, but with a slightly reduced coherent velocity. The validity of these approximations, which can easily be calculated on a desktop computer, has been exhaustively confirmed by comparison with results of Monte Carlo simulations which kept track of 50 million particles and which were carried out on the Maspar computer at Goddard Space Flight Center.

Earl, James A.↗

NASA NTRS2020

Electromagnetic scattering by discrete random media illuminated by a Gaussian beam I: Derivation of the radiative transfer equation

In this paper we present the vector radiative transfer theory for a discrete random medium illuminated by a Gaussian beam. The analysis is based on a plane wave spectrum representation for a Gaussian beam and uses an approach developed previously for a discrete random medium illuminated by a plane electromagnetic wave. Specifically, we establish an integral representation for the coherent field, define an approximate coherent field that satisfies the differential equation fulfilled by the coherent field corresponding to a plane electromagnetic wave and matches the Gaussian beam at the interface of the particulate medium, and finally, derive the vector radiative transfer equation. For weakly focused Gaussian beams, the resulting equation is the traditional radiative transfer equation

Gaussian beam↗

NASA NTRS1980

An experimental study of the surface elevation probability distribution and statistics of wind-generated waves

Laboratory experiments were performed to measure the surface elevation probability density function and associated statistical properties for a wind-generated wave field. The laboratory data along with some limited field data were compared. The statistical properties of the surface elevation were processed for comparison with the results derived from the Longuet-Higgins (1963) theory. It is found that, even for the highly non-Gaussian cases, the distribution function proposed by Longuet-Higgins still gives good approximations.

Huang, N. E.↗

NASA NTRS1988

Range data description based on multiple characteristics

An algorithm for describing range images based on Mean curvature (H) and Gaussian curvature (K) is presented. Range images are unique in that they directly approximate the physical surfaces of a real world 3-D scene. The curvature parameters are derived from the fundamental theorems of differential geometry and provides visible invariant pixel labels that can be used to characterize the scene. The sign of H and K can be used to classify each pixel into one of eight possible surface types. Due to the sensitivity of these parameters to noise the resulting HK-sing map does not directly identify surfaces in the range images and must be further processed. A region growing algorithm based on modeling the scene points with a Markov Random Field (MRF) of variable neighborhood size and edge models is suggested. This approach allows the integration of information from multiple characteristics in an efficient way. The performance of the proposed algorithm on a number of synthetic and real range images is discussed.

Al-Hujazi, Ezzet↗

NASA NTRS1985

Gaussian beams for surface waves in laterally slowly-varying media

Asymptotic ray theory is applied to surface waves in a medium where the lateral variations of structure are very smooth. The elastodynamic equations of motion in ray-centered coordinates are derived, and a laterally slowly-varying approximation for elastodynamic equations is obtained. Parabolic equations for Love and Rayleigh waves are studied and solved, and the properties of Gaussian beams of seismic surface waves are examined.

Yomogida, K.↗

NASA NTRS1984

Computing approximate random Delta v magnitude probability densities

This paper describes the development and use of an algorithm to compute approximate statistics of the magnitude of a single random trajectory correction maneuver (TCM) Delta v vector. The TCM Delta v vector is modeled as a three component Cartesian vector each of whose components is a random variable having a normal (Gaussian) distribution with zero mean and possibly unequal standard deviations. The algorithm uses these standard deviations as input to produce approximations to (1) the mean and standard deviation of the magnitude of Delta v, (2) points of the probability density function of the magnitude of Delta v, and (3) points of the cumulative and inverse cumulative distribution functions of Delta v. The approximates are based on Monte Carlo techniques developed in a previous paper by the author and extended here. The algorithm described is expected to be useful in both pre-flight planning and in-flight analysis of maneuver propellant requirements for space missions.

Chadwick, C.↗

NASA NTRS1992

Accretion rates of protoplanets. II - Gaussian distributions of planetesimal velocities

In the present growth-rate calculations for a protoplanet that is embedded in a disk of planetesimals with triaxial Gaussian velocity dispersion and uniform surface density, the protoplanet is on a circular orbit. The accretion rate in the two-body approximation is found to be enhanced by a factor of about 3 relative to the case where all planetesimals' eccentricities and inclinations are equal to the rms values of those disk variables having locally Gaussian velocity dispersion. This accretion-rate enhancement should be incorporated by all models that assume a single random velocity for all planetesimals in lieu of a Gaussian distribution.

Greenzweig, Yuval↗