A dynamic equation for stochastic magnetic field lines in the galaxy
Galactic stochastic magnetic field lines, deriving dynamic equation for probability density function
Jones, F. C.↗
SEARCH · Engineering Papers
Results for “probability density function”
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.
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Recognition of crops and soils by spot density measurements of imagery
Computerized techniques and methods were used to conduct preliminary soil and crop identification experiments. The soil identification experiment was conducted by making densitometer measurements on Ektachrome infrared film exposed at 14,000 feet. The density measurements were analyzed by plotting sample probability density functions, two-dimensional scatter plots, and the use of K-class I to determine the complete set of classification results for one, two, three and four features. Due to the presence of nineteen classes, crop identification experiments were more difficult to formulate. Classes of corn, fallow, harvested wheat, roadways, trees and water were classified 75 percent correct.
Nelson, G. D.↗
Simulation of flight maneuver-load distributions by utilizing stationary, non-Gaussian random load histories
Random numbers were generated with the aid of a digital computer and transformed such that the probability density function of a discrete random load history composed of these random numbers had one of the following non-Gaussian distributions: Poisson, binomial, log-normal, Weibull, and exponential. The resulting random load histories were analyzed to determine their peak statistics and were compared with cumulative peak maneuver-load distributions for fighter and transport aircraft in flight.
Leybold, H. A.↗
Distribution of error in least-squares solution of an overdetermined system of linear simultaneous equations
Probability density functions were derived for errors in the evaluation of unknowns by the least squares method in system of nonhomogeneous linear equations. Coefficients of the unknowns were assumed correct and computational precision were also assumed. A vector space was used, with number of dimensions equal to the number of equations. An error vector was defined and assumed to have uniform distribution of orientation throughout the vector space. The density functions are shown to be insensitive to the biasing effects of the source of the system of equations.
Miller, C. D.↗
Two-way coherent tracking systems.
Review of some results pertinent to the development of nonlinear theory on two-way coherent tracking systems. In particular, the model of cascaded systems is presented, and approximations to steady state probability density functions of the two-way system phase and Doppler error are developed. From these, certain numerical results required in the design and planning of these systems are derived.
Lindsey, W. C.↗
On the probability of cycle-slipping in first-order phase-locked loops.
The first-passage time boundary value problem for first-order phase-locked loops (PLL) is analyzed, and spectral representations are developed for the probability density function (pdf), the distribution function, and the moments of the first time to passage (or cycle-slip). For the sinusoidal PLL, an asymptotic formula, that is surprisingly accurate even at low loop SNR's and large frequency offsets, is obtained for the pdf of the time to cycle-slip, in terms of the mean time to slip.
La Frieda, J. R.↗
Effects of atmospheric irregularities on sonic-boom propagation.
A review is given of information obtained in recent years concerning the effects on sonic-boom signatures of departures of the atmosphere from a perfectly stratified time invariant model. These effects include the observed random variations in boom overpressures from those expected for a stratified atmosphere, the anomalously large and variable rise times, and the occurrence of spiked or rounded waveforms rather than the characteristic N waves. The extent of the variability in data recorded during actual flight tests is summarized in the form of histograms, representing experimentally obtained probability density functions. The physical mechanisms believed to be responsible for the variations and the anomalous features in the signatures are described. These include refraction and subsequent wavefront rippling by turbulence, the possible focusing or defocusing of rays, the formation of caustics, and the phenomenon of wavefront folding, diffraction, and scattering. Recent statistical theories of shock propagation through a turbulent atmosphere proposed by Crow, George and Plotkin, Pierce, Horning, and others are reviewed.
Pierce, A. D.↗
A stochastic model for eye movements during fixation on a stationary target.
A stochastic model describing small eye movements occurring during steady fixation on a stationary target is presented. Based on eye movement data for steady gaze, the model has a hierarchical structure; the principal level represents the random motion of the image point within a local area of fixation, while the higher level mimics the jump processes involved in transitions from one local area to another. Target image motion within a local area is described by a Langevin-like stochastic differential equation taking into consideration the microsaccadic jumps pictured as being due to point processes and the high frequency muscle tremor, represented as a white noise. The transform of the probability density function for local area motion is obtained, leading to explicit expressions for their means and moments. Evaluation of these moments based on the model is comparable with experimental results.
Vasudevan, R.↗
A double-loop tracking system.
A nonlinear analysis which can be used to assess certain statistical characteristics of double-loop tracking systems is presented. It takes into account the mutual coupling effects of the loops in the system. Two approaches are taken to obtain steady-state probability density functions (pdf's) of the system phase errors. From these pdf's, important system performance statistics, e.g., the phase-error variances, can be calculated, thus illustrating the application and usefulness of the analysis. The analysis is applied to a satellite transponder as an example.
Yuen, J. H.↗
RFI in hybrid loops - Simulation and experimental results.
A digital simulation of an imperfect second-order hybrid phase-locked loop (HPLL) operating in radio frequency interference (RFI) is described. Its performance is characterized in terms of phase error variance and phase error probability density function (PDF). Monte-Carlo simulation is used to show that the HPLL can be superior to the conventional phase-locked loops in RFI backgrounds when minimum phase error variance is the goodness criterion. Similar experimentally obtained data are given in support of the simulation data.
Ziemer, R. E.↗
Transient analysis of phase-locked tracking systems in the presence of noise.
This paper is concerned with the problem of obtaining time-dependent solutions to a class of Fokker-Planck equations that arise in the analysis and synthesis of a variety of first-order synchronization systems employing the phase-lock principle. These include the classical sinusoidal phase-locked loop, squaring and Costas loops, data-aided loops, hybrid loops, various symbol synchronizer mechanizations, and tunnel-diode oscillators. By analyzing the spectral properties of the associated time-dependent Fokker-Planck boundary value problem, eigenfunction expansions of the reduced modulo-2-pi phase-error-transition probability-density function are developed for a class of first-order synchronization systems.
La Frieda, J. R.↗
Statistical properties of two sine waves in Gaussian noise.
A detailed study is presented of some statistical properties of a stochastic process that consists of the sum of two sine waves of unknown relative phase and a normal process. Since none of the statistics investigated seem to yield a closed-form expression, all the derivations are cast in a form that is particularly suitable for machine computation. Specifically, results are presented for the probability density function (pdf) of the envelope and the instantaneous value, the moments of these distributions, and the relative cumulative density function (cdf).
Esposito, R.↗
A solution to the problem of optimizing the fuel bias for a liquid propellant rocket by an application of the central limit theorem
A method of determining the fuel bias for a bipropellant liquid rocket that minimizes outage associated penalties on payload potential is presented. A fuel bias so derived is normally called the optimum fuel bias. The subjects discussed are: (1) probability density function of outage, (2) computer program listing, and (3) choosing the optimum fuel bias.
Viera, W. J.↗
The problem of the structure of the surface of the lunar maria
The results are described of geological and morphological interpretation of large-scale photographs of the surface of lunar maria. A morphological classification is proposed for small craters. It is shown that the classification of a crater in a given morphological category, reflecting the degree of its morphological maturity, is determined by the age of the given crater. A check on the nature of distribution of small craters, as done on the basis of the nearest neighbor method, show that the distribution is governed by a near-random law. It is found that variations of the probability density function for the craters conform to a normal distribution law. An empirical relation is found for the coefficient of variation as a function of crater diameter and the dimensions of the area on which the counts are made. The rockfalls near craters of various morphological classes are described.
Florenskiy, K. P.↗
Statistical parameters of reverberating fields, calculated by computer
A method, developed for making measurements in reverberation chambers in the steady state mode, is reported. Spatial distribution patterns of the square of the sound pressure vs type of exciting signal were produced theoretically and checked experimentally in a reverberation chamber. Results of measurements of spatial irregularities of the field with pure tones and with noise bands in the 200 to 2,000 Hz frequency range were used for calculating statistical parameters of the reverbation fields by computer. The calculation program included determination of density probability function, integral distribution pattern, mathematical expectation, normalized dispersion of the mean square of the pressure.
Lebedeva, I. V.↗
Experimental probability density distributions for optical and infrared cross-beam units
A series of cross beam experiments for measuring meteorological parameters was conducted. Both optical and infrared sensors were tested for comparison. The test configuration and experiment identification are provided. A data report is presented for an approximate analysis of the probability density distributions of the signals from both the optical and the infared units. Two runs representing each of the two types of cross-beam units were selected for analysis. Probability density functions are also presented for the instantaneous product of the signals for each of the runs.
Huff, L. L.↗
Information preserving coding for multispectral data
A general formulation of the data compression system is presented. A method of instantaneous expansion of quantization levels by reserving two codewords in the codebook to perform a folding over in quantization is implemented for error free coding of data with incomplete knowledge of the probability density function. Results for simple DPCM with folding and an adaptive transform coding technique followed by a DPCM technique are compared using ERTS-1 data.
Duan, J. R.↗
Offset quadrature communications with decision-feedback carrier synchronization
In order to accommodate a quadrature amplitude-shift-keyed (QASK) signal, Simon and Smith (1974) have modified the decision-feedback loop which tracks a quadrature phase-shift-keyed (QPSK). In the investigation reported approaches are considered to modify the loops in such a way that offset QASK signals can be tracked, giving attention to the special case of an offset QPSK. The development of the stochastic integro-differential equation of operation for a decision-feedback offset QASK loop is discussed along with the probability density function of the phase error process.
Simon, M. K.↗