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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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NASA NTRS1975

On the alleged collisional origin of the Kirkwood Gaps

This paper examines two proposed mechanisms whereby asteroidal collisions and close approaches may have given rise to the Kirkwood Gaps. The first hypothesis is that asteroids in near-resonant orbits have markedly increased collision probabilities and so are preferentially destroyed, or suffer decay in population density, within the resonance zones. A simple order-of-magnitude analysis shows that this hypothesis is untenable since it leads to conclusions which are either unrealistic or not in accord with present understanding of asteroidal physics. The second hypothesis is the Brouwer-Jefferys theory that collisions would smooth an asteroidal distribution function, as a function of Jacobi constant, thus forming resonance gaps. This hypothesis is examined by direct numerical integration of 50 asteroid orbits near the 2:1 resonance, with collisions simulated by random variables. No tendency to form a gap was observed.

Heppenheimer, T. A.↗

NASA NTRS1975

Design and simulation of stratified probability digital receiver with application to the multipath communication

One approach to the problem of simplifying complex nonlinear filtering algorithms is through using stratified probability approximations where the continuous probability density functions of certain random variables are represented by discrete mass approximations. This technique is developed in this paper and used to simplify the filtering algorithms developed for the optimum receiver for signals corrupted by both additive and multiplicative noise.

Deal, J. H.↗

NASA NTRS1976

Determination of statistics for any rotation of axes of a bivariate normal elliptical distribution

Transformation of statistics from a dimensional set to another dimensional set involves linear functions of the original set of statistics. Similarly, linear functions will transform statistics within a dimensional set such that the new statistics are relevant to a new set of coordinate axes. A restricted case of the latter is the rotation of axes in a coordinate system involving any two correlated random variables. A special case is the transformation for horizontal wind distributions. Wind statistics are usually provided in terms of wind speed and direction (measured clockwise from north) or in east-west and north-south components. A direct application of this technique allows the determination of appropriate wind statistics parallel and normal to any preselected flight path of a space vehicle. Among the constraints for launching space vehicles are critical values selected from the distribution of the expected winds parallel to and normal to the flight path. These procedures are applied to space vehicle launches at Cape Kennedy, Florida.

Falls, L. W.↗

NASA NTRS1975

A note on the consistency of maximum likelihood estimates for finite families of stochastic processes

The note considers families of stochastic processes indexed by a finite number of alternative parameter values. For general classes of stochastic processes, it is shown that maximum-likelihood estimates converge almost surely to the correct parameter value. This is established by use of a submartingale property of the sequence of maximized-likelihood ratios together with a technique first employed by Wald (1949) in the case of independent identically distributed random variables.

Caines, P. E.↗

NASA NTRS1975

Onboard navigation of the Space Shuttle

This paper discusses the Kalman filter used in the navigation software of the Space Shuttle. The form of the filter will be discussed: the standard Kalman filter versus the square-root version of this filter. Both of these filters have severe nonlinearity problems. Two successful solutions of the nonlinearity problem are presented. A real-time program must have a good method of editing bad data. The data editing scheme is discussed. Those elements of the Kalman filter state vector which are random variables will be discussed.

Lear, W. M.↗

NASA NTRS1975

Parameter adaptive estimation of random processes

This paper is concerned with the parameter adaptive least squares estimation of random processes. The main result is a general representation theorem for the conditional expectation of a random variable on a product probability space. Using this theorem along with the general likelihood ratio expression, the least squares estimate of the process is found in terms of the parameter conditioned estimates. The stochastic differential for the a posteriori probability and the stochastic differential equation for the a posteriori density are found by using simple stochastic calculus on the representations obtained. The results are specialized to the case when the parameter has a discrete distribution. The results can be used to construct an implementable recursive estimator for certain types of nonlinear filtering problems. This is illustrated by some simple examples.

Caglayan, A. K.↗

NASA NTRS1976

Behavior of queues at signalized intersections in heavy traffic

This paper derives the asymptotic behavior of traffic queues at signalized intersections when the excess of departure capacity over arrivals approaches zero from above. The most interesting result is that the distribution of queue length approaches a negative exponential, with fewer restrictive assumptions than hitherto known. The main improvement results from more precise use of a combinatorial lemma of Spitzer, giving the maximum of the partial sums of a sequence of independent identically distributed random variables, plus some specific constructive probability calculations, many of them involving the Fourier transform. New results are presented on the probability that the queue be below a fixed bound and/or on the probability that the queue be empty. Applications to on-line estimators for real-time traffic control are suggested.

Posner, E. C.↗

NASA NTRS1978

The role of drop velocity in statistical spray description

The justification for describing a spray by treating drop velocity as a random variable on an equal statistical basis with drop size was studied experimentally. A double exposure technique using fluorescent drop photography was used to make size and velocity measurements at selected locations in a steady ethanol spray formed by a swirl atomizer. The size velocity data were categorized to construct bivariate spray density functions to describe the spray immediately after formation and during downstream propagation. Bimodal density functions were formed by environmental interaction during downstream propagation. Large differences were also found between spatial mass density and mass flux size distribution at the same location.

Groeneweg, J. F.↗

NASA NTRS1978

Design of a compensation for an ARMA model of a discrete time system

The design of an optimal dynamic compensator for a multivariable discrete time system is studied. Also the design of compensators to achieve minimum variance control strategies for single input single output systems is analyzed. In the first problem the initial conditions of the plant are random variables with known first and second order moments, and the cost is the expected value of the standard cost, quadratic in the states and controls. The compensator is based on the minimum order Luenberger observer and it is found optimally by minimizing a performance index. Necessary and sufficient conditions for optimality of the compensator are derived. The second problem is solved in three different ways; two of them working directly in the frequency domain and one working in the time domain. The first and second order moments of the initial conditions are irrelevant to the solution. Necessary and sufficient conditions are derived for the compensator to minimize the variance of the output.

Mainemer, C. I.↗

NASA NTRS1978

The role of drop velocity in statistical spray description

The justification for describing a spray by treating drop velocity as a random variable on an equal statistical basis with drop size was studied experimentally. A double-exposure technique using fluorescent drop photography was used to make size and velocity measurements at selected locations in a steady ethanol spray formed by a swirl atomizer. The size-velocity data were categorized to construct bivariate spray density functions to describe the spray immediately after formation and during downstream propagation. It was found that a statistical treatment of drop velocity was supported by the data. Spray density function shapes and modal characteristics depended strongly on position and the amount of droplet-gas interaction that had occurred. Bimodal density functions were formed by environmental interaction during downstream propagation. Large differences were also found between spatial mass density and mass flux size distributions at the same location.

Groeneweg, J. F.↗

NASA NTRS1979

Performability evaluation of the SIFT computer

Performability modeling and evaluation techniques are applied to the SIFT computer as it might operate in the computational evironment of an air transport mission. User-visible performance of the total system (SIFT plus its environment) is modeled as a random variable taking values in a set of levels of accomplishment. These levels are defined in terms of four attributes of total system behavior: safety, no change in mission profile, no operational penalties, and no economic process whose states describe the internal structure of SIFT as well as relavant conditions of the environment. Base model state trajectories are related to accomplishment levels via a capability function which is formulated in terms of a 3-level model hierarchy. Performability evaluation algorithms are then applied to determine the performability of the total system for various choices of computer and environment parameter values. Numerical results of those evaluations are presented and, in conclusion, some implications of this effort are discussed.

Meyer, J. F.↗

NASA NTRS1979

On the distribution of computation for sequential decoding using the stack algorithm

A method is developed for estimating the computational distribution for the stack algorithm for sequential decoding, that is, the probability that the computation required to decode the first branch of the tree is greater than or equal to N, for small N. The analysis relies heavily on the theory of multitype branching processes. A step in the analysis is the determination of the distribution of the minimum of the cumulative metrics along the transmitted path in the code tree. This is used to obtain the distribution of the number of computations made by the decoder in order to decode the first branch in the tree, and this random variable serves as an approximation of the average number of computations per decoded branch. At information rates below the cutoff rate, the calculated computational performance is virtually identical to that obtained by time-consuming simulations.

Johannesson, R.↗

NASA NTRS1979

Simulation of the pressure field near a jet by randomly distributed vortex rings

Fluctuations of the pressure field in the vicinity of a jet are simulated numerically by a flow model consisting of axially symmetric vortex rings with viscous cores submerged in a uniform stream. The time interval between the shedding of successive vortices is taken to be a random variable with a probability distribution chosen to match that from experiments. It is found that up to 5 diameters downstream of the jet exit, statistics of the computed pressure field are in good agreement with experimental results. Statistical comparisons are provided for the overall sound pressure level, the peak amplitude, and the Strouhal number based on the peak frequency of the pressure signals.

Fung, Y. T.↗

NASA NTRS1980

Rate statistics for radio noise from lightning

Radio frequency noise from lightning was measured at several frequencies in the HF - VHF range at the Kennedy Space Center, Florida. The data were examined to determine flashing rate statistics during periods of strong activity from nearby storms. It was found that the time between flashes is modeled reasonably well by a random variable with a lognormal distribution.

Levine, D. M.↗

NASA NTRS1980

Satellite communication performance evaluation: Computational techniques based on moments

Computational techniques that efficiently compute bit error probabilities when only moments of the various interference random variables are available are presented. The approach taken is a generalization of the well known Gauss-Quadrature rules used for numerically evaluating single or multiple integrals. In what follows, basic algorithms are developed. Some of its properties and generalizations are shown and its many potential applications are described. Some typical interference scenarios for which the results are particularly applicable include: intentional jamming, adjacent and cochannel interferences; radar pulses (RFI); multipath; and intersymbol interference. While the examples presented stress evaluation of bit error probilities in uncoded digital communication systems, the moment techniques can also be applied to the evaluation of other parameters, such as computational cutoff rate under both normal and mismatched receiver cases in coded systems. Another important application is the determination of the probability distributions of the output of a discrete time dynamical system. This type of model occurs widely in control systems, queueing systems, and synchronization systems (e.g., discrete phase locked loops).

Omura, J. K.↗

NASA NTRS1980

Performability evaluation of the SIFT computer

The paper deals with the models, techniques, and evaluation methods that were successfully used to test the performance of the SIFT degradable computing system. The performance of the computer plus its air transport mission environment is modeled as a random variable, taking values in a set of 'accomplishment level'. The levels are defined in terms of four attributes of total system (computer plus environment) behavior, namely safety, no change in mission profile, no operational penalties, and no economic penalties. The base model of the total system is a stochastic process, whose states describe the internal structure of SIFT and the relevant conditions of its computational environment. Base model state trajectories are related to accomplishment levels via a special function, and solution methods are then used to determine the performability of the total system for various parameters of the computer and environment.

Meyer, J. F.↗

NASA NTRS1981

Analysis of coherent satellite communication systems in the presence of interference and noise

The general analysis presented can be used to evaluate the performance of M-ary phase shift keying (MPSK) used over a nonlinear satellite channel in the presence of interference (CW tone and ISI) and channel noise. The numerical evaluation is based on the classical moment technique for approximating the probability distribution from moments of a random variable. The mathematical formulation of error probabilities of MPSK signals transmitted over nonlinear satellite repeaters is presented to include the effect of CW tone interference as well as the intersymbol interference. The approach is general and can be extended to include the effect of the synchronization.

Huang, T.-C.↗

NASA NTRS1981

Parameter estimation for slit-type scanning sensors

The Infrared Astronomical Satellite, scheduled for launch into a 900 km near-polar orbit in August 1982, will perform an infrared point source survey by scanning the sky with slit-type sensors. The description of position information is shown to require the use of a non-Gaussian random variable. Methods are described for deciding whether separate detections stem from a single common source, and a formulism is developed for the scan-to-scan problems of identifying multiple sightings of inertially fixed point sources for combining their individual measurements into a refined estimate. Several cases are given where the general theory yields results which are quite different from the corresponding Gaussian applications, showing that argument by Gaussian analogy would lead to error.

Fowler, J. W.↗