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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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All sourcesNASA NTRSDOE OSTI
NASA NTRS1980

Tables of stark level transition probabilities and branching ratios in hydrogen-like atoms

The transition probabilities which are given in terms of n prime k prime and n k are tabulated. No additional summing or averaging is necessary. The electric quantum number k plays the role of the angular momentum quantum number l in the presence of an electric field. The branching ratios between stark levels are also tabulated. Necessary formulas for the transition probabilities and branching ratios are given. Symmetries are discussed and selection rules are given. Some disagreements for some branching ratios are found between the present calculation and the measurement of Mark and Wierl. The transition probability multiplied by the statistical weight of the initial state is called the static intensity J sub S, while the branching ratios are called the dynamic intensity J sub D.

Omidvar, K.↗
NASA NTRS1980

The dwarf spheroidal galaxy in Draco. III - Proper motion membership probabilities

PDS astrometry from photographic plates of the Draco dwarf galaxy is used to derive proper motion membership probabilities for stars measured in earlier photometric studies. It is found that removing probable foreground stars from the color-magnitude diagram of Draco tends to strengthen earlier conclusions about the structure of the giant and subgiant branches. The possible existence of an upper horizontal branch containing core helium-burning stars of more than one solar mass is still questionable. A reduced proper motion diagram for probable foreground stars is presented and discussed briefly.

Stetson, P. B.↗
NASA NTRS1980

Maximum likelihood estimation of label imperfection probabilities and its use in the identification of mislabeled patterns

Estimating label imperfections and the use of estimations in the identification of mislabeled patterns are discussed. Expressions are presented for the asymptotic variances of the probability of correct classification and proportion, and for the maximum likelihood estimates of classification errors and a priori probabilities. Models are developed for imperfections in the labels and classification errors, and expressions are derived for the probability of imperfect label identification schemes resulting in wrong decisions. The expressions are used in computing thresholds and the techniques are given practical applications. The imperfect label identification scheme in the multiclass case is found to amount to establishing a region around each decision surface, and decisions of the label correction scheme are found in close agreement with the analyst-interpreter interpretations of the imagery films. As an example, the application of the maximum likelihood estimation to the processing of Landsat MSS data is discussed.

Chittineni, C. B.↗
NASA NTRS1982

Development of STS/Centaur failure probabilities liftoff to Centaur separation

The results of an analysis to determine STS/Centaur catastrophic vehicle response probabilities for the phases of vehicle flight from STS liftoff to Centaur separation from the Orbiter are presented. The analysis considers only category one component failure modes as contributors to the vehicle response mode probabilities. The relevant component failure modes are grouped into one of fourteen categories of potential vehicle behavior. By assigning failure rates to each component, for each of its failure modes, the STS/Centaur vehicle response probabilities in each phase of flight can be calculated. The results of this study will be used in a DOE analysis to ascertain the hazard from carrying a nuclear payload on the STS.

Hudson, J. M.↗
NASA NTRS1982

A model of subjective probabilities from small groups

Methods for aggregating the opinions of individual forecasters in order to improve the quality of probabilistic forecasts are presented. Experimental results obtained by Seaver in his study of probability judgments by groups of four people are considered. The decision variable partition model of subjective probability and a simple model of the effects of interaction on judgments were used to simulate the group judgment of discrete probabilities investigated by Seaver. The initial results of the simulation are very promising in that (1) they show the principal effects Seaver observed and (2) these effects can, for the most part, be traced to specific characteristics of the models.

Ferrell, W. R.↗
NASA NTRS1980

The use of prior probabilities in maximum likelihood classification of remotely sensed data

Possibilities for the improvement of classification accuracies by the use of prior information about the expected distribution of classes in the maximum likelihood classification of remote sensing data are examined. The modification of the maximum likelihood decision rule to take into account one or several sets of probabilities for the occurrence of classes which probabilities are based on independent knowledge of the area surveyed is demonstrated. It is then shown that the use of prior probabilities is sufficiently versatile so as to allow the prior weighting of output classes based on their anticipated sizes as well as the merging of continuously varying measurements with discrete collateral information data sets and the construction of time-sequential classification systems in which an earlier classification modifies the outcome of a latter one.

Strahler, A. H.↗
NASA NTRS1984

Simulations for Full Unit-memory and Partial Unit-memory Convolutional Codes with Real-time Minimal-byte-error Probability Decoding Algorithm

A program which was written to simulate Real Time Minimal-Byte-Error Probability (RTMBEP) decoding of full unit-memory (FUM) convolutional codes on a 3-bit quantized AWGN channel is described. This program was used to compute the symbol-error probability of FUM codes and to determine the signal to noise (SNR) required to achieve a bit error rate (BER) of 10 to the minus 6th power for corresponding concatenated systems. A (6,6/30) FUM code, 6-bit Reed-Solomon code combination was found to achieve the required BER at a SNR of 1.886 dB. The RTMBEP algorithm was then modified for decoding partial unit-memory (PUM) convolutional codes. A simulation program was also written to simulate the symbol-error probability of these codes.

Vo, Q. D.↗
NASA NTRS1986

A new technique for predicting geosynchronous satellite collision probability

A new technique has been developed to predict the probability of an expired geosynchronous satellite colliding with an active satellite. This new technique employs deterministic methods for modeling the motion of satellites and applies statistical techniques to estimate the collision probability. The collision probability is used to estimate the expected time between collisions based on realistic distributions of expired and active satellites. The primary advantage of this new technique is that realistic distributions can be used in the prediction process instead of uniform distributions as has been used in previous techniques. The expected time between collisions based on a current NORAD database is estimated to be in the hundreds of years.

Mccormick, B.↗
NASA NTRS1987

More on the decoder error probability for Reed-Solomon codes

The decoder error probability for Reed-Solomon codes (more generally, linear maximum distance separable codes) is examined. McEliece and Swanson offered an upper bound on P sub E (u), the decoder error probability given that u symbol errors occurs. This upper bound is slightly greater than Q, the probability that a completely random error pattern will cause decoder error. By using a combinatoric technique, the principle of inclusion and exclusion, an exact formula for P sub E (u) is derived. The P sub e (u) for the (255, 223) Reed-Solomon Code used by NASA, and for the (31,15) Reed-Solomon code (JTIDS code), are calculated using the exact formula, and the P sub E (u)'s are observed to approach the Q's of the codes rapidly as u gets larger. An upper bound for the expression is derived, and is shown to decrease nearly exponentially as u increases. This proves analytically that P sub E (u) indeed approaches Q as u becomes large, and some laws of large numbers come into play.

Cheung, K.-M.↗
NASA NTRS1985

Land mobile satellite transmission measurements at 869 MHz. A comparison of error probabilities for various message block durations and fade margins as a function of vegetation shadowing

In order to give vehicles travelling in rural areas of the U.S. access to the telephone network, a Land Mobile Satellite System is being planned. Previously presented data by the author were analyzed for the probability that the received signal level dropped below a threshold during short time blocks of various signal durations and the conditional probability that such an event would reoccur after a given delay. If it assumed that a fade threshold crossing of even 1 msec would produce an error in the transmission, then the derived quantities can be considered error probabilities. Extensive tables and graphs are presented with the results from the analysis. They can be used to devise communication strategies which will provide improved link availability in the presence of vegetation shadowing.

Vogel, Wolfhard J.↗
NASA NTRS1989

More On The Decoder-Error Probability Of Reed-Solomon Codes

Paper extends theory of decoder-error probability for linear maximum-distance separable (MDS) codes. General class of error-correcting codes includes Reed-Solomon codes, important in communications with distant spacecraft, military communications, and compact-disk recording industry. Advancing beyond previous theoretical developments that placed upper bounds on decoder-error probabilities, author derives an exact formula for probability PE(u) that decoder will make error when u code symbols in error.

Cheung, Kar-Ming↗
NASA NTRS1987

Calculating the CEP (Circular Error Probable)

This report compares the probability contained in the Circular Error Probable associated with an Elliptical Error Probable to that of the EEP at a given confidence level. The levels examined are 50 percent and 95 percent. The CEP is found to be both more conservative and less conservative than the associated EEP, depending on the eccentricity of the ellipse. The formulas used are derived in the appendix.

Source record↗
NASA NTRS1989

Probabilities and statistics for backscatter estimates obtained by a scatterometer with applications to new scatterometer design data

The values of the Normalized Radar Backscattering Cross Section (NRCS), sigma (o), obtained by a scatterometer are random variables whose variance is a known function of the expected value. The probability density function can be obtained from the normal distribution. Models for the expected value obtain it as a function of the properties of the waves on the ocean and the winds that generated the waves. Point estimates of the expected value were found from various statistics given the parameters that define the probability density function for each value. Random intervals were derived with a preassigned probability of containing that value. A statistical test to determine whether or not successive values of sigma (o) are truly independent was derived. The maximum likelihood estimates for wind speed and direction were found, given a model for backscatter as a function of the properties of the waves on the ocean. These estimates are biased as a result of the terms in the equation that involve natural logarithms, and calculations of the point estimates of the maximum likelihood values are used to show that the contributions of the logarithmic terms are negligible and that the terms can be omitted.

Pierson, Willard J., Jr.↗
NASA NTRS1989

Probabilities for gravitational lensing by point masses in a locally inhomogeneous universe

Probability functions for gravitational lensing by point masses that incorporate Poisson statistics and flux conservation are formulated in the Dyer-Roeder construction. Optical depths to lensing for distant sources are calculated using both the method of Press and Gunn (1973) which counts lenses in an otherwise empty cone, and the method of Ehlers and Schneider (1986) which projects lensing cross sections onto the source sphere. These are then used as parameters of the probability density for lensing in the case of a critical (q0 = 1/2) Friedmann universe. A comparison of the probability functions indicates that the effects of angle-averaging can be well approximated by adjusting the average magnification along a random line of sight so as to conserve flux.

Isaacson, Jeffrey A.↗
NASA NTRS1989

More on the decoder error probability for Reed-Solomon codes

The decoder error probability for Reed-Solomon codes (more generally, linear maximum distance separable codes) is examined. McEliece and Swanson offered an upper bound on P sub E (u), the decoder error probability given that u symbol errors occur. This upper bound is slightly greater than Q, the probability that a completely random error pattern will cause decoder error. By using a combinatoric technique, the principle of inclusion and exclusion, an exact formula for P sub E (u) is derived. The P sub E (u) for the (255,223) Reed-Solomon Code used by NASA, and for the (31,15) Reed-Solomon code (JTIDS code), are calculated using the exact formula, and the P sub E (u)'s are observed to approach the Q's of the codes rapidly as u gets larger. An upper bound for the expression is derived, and is shown to decrease nearly exponentially as u increases. This proves analytically that P sub E (u) indeed approaches Q as u becomes large, and some laws of large numbers come into play.

Cheung, Kar-Ming↗
NASA NTRS1991

Maximum-entropy probability distributions under Lp-norm constraints

Continuous probability density functions and discrete probability mass functions are tabulated which maximize the differential entropy or absolute entropy, respectively, among all probability distributions with a given L sub p norm (i.e., a given pth absolute moment when p is a finite integer) and unconstrained or constrained value set. Expressions for the maximum entropy are evaluated as functions of the L sub p norm. The most interesting results are obtained and plotted for unconstrained (real valued) continuous random variables and for integer valued discrete random variables. The maximum entropy expressions are obtained in closed form for unconstrained continuous random variables, and in this case there is a simple straight line relationship between the maximum differential entropy and the logarithm of the L sub p norm. Corresponding expressions for arbitrary discrete and constrained continuous random variables are given parametrically; closed form expressions are available only for special cases. However, simpler alternative bounds on the maximum entropy of integer valued discrete random variables are obtained by applying the differential entropy results to continuous random variables which approximate the integer valued random variables in a natural manner. All the results are presented in an integrated framework that includes continuous and discrete random variables, constraints on the permissible value set, and all possible values of p. Understanding such as this is useful in evaluating the performance of data compression schemes.

Dolinar, S.↗
NASA NTRS1991

An evaluation of probable bedrock exposure in the Sinus Meridiani region of the Martian highlands

Estimates of the amount of probable bedrock exposures visible in the highest-resolution Viking imaging data for a selected region of the Martian surface are presented. The study region includes portions of the classical low-albedo regions of Sinus Meridiani and Sinus Sabaeus and the high-albedo region of Arabia, and is completely within the cratered highlands of Mars. More than 400 images were used to estimate the percentage of the area of each frame having locally steep slopes. It is seen that 42 percent of the high-resolution frames have less than one percent probable bedrock exposure while three percent of the frames have 15 percent probable bedrock exposure.

Zimbelman, J. R.↗
NASA NTRS1992

Generalized probability model for calculation of interference to the Deep Space Network due to circularly Earth-orbiting satellites

The probability of exceeding interference power levels and the duration of interference at the Deep Space Network (DSN) antenna is calculated parametrically when the state vector of an Earth-orbiting satellite over the DSN station view area is not known. A conditional probability distribution function is derived, transformed, and then convolved with the interference signal uncertainties to yield the probability distribution of interference at any given instant during the orbiter's mission period. The analysis is applicable to orbiting satellites having circular orbits with known altitude and inclination angle.

Ruggier, C. J.↗