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All sourcesNASA NTRSDOE OSTI
NASA NTRS2004

Application of a Semiparametric Statistical Method to Spacecraft Sensor and Calibration Data

A semiparametric statistical method is applied to spacecraft sensor data and spacecraft sensor residual data. The method stipulates a reference distribution and deviations from it. The problem is to estimate the reference distribution and the distorted distributions from all available data from all the sources under consideration. The problem can be solved by assuming a distortion form and independent data.

Kedem, Benjamin↗
NASA NTRS2010

Context Modeler for Wavelet Compression of Spectral Hyperspectral Images

A context-modeling sub-algorithm has been developed as part of an algorithm that effects three-dimensional (3D) wavelet-based compression of hyperspectral image data. The context-modeling subalgorithm, hereafter denoted the context modeler, provides estimates of probability distributions of wavelet-transformed data being encoded. These estimates are utilized by an entropy coding subalgorithm that is another major component of the compression algorithm. The estimates make it possible to compress the image data more effectively than would otherwise be possible. The following background discussion is prerequisite to a meaningful summary of the context modeler. This discussion is presented relative to ICER-3D, which is the name attached to a particular compression algorithm and the software that implements it. The ICER-3D software is summarized briefly in the preceding article, ICER-3D Hyperspectral Image Compression Software (NPO-43238). Some aspects of this algorithm were previously described, in a slightly more general context than the ICER-3D software, in "Improving 3D Wavelet-Based Compression of Hyperspectral Images" (NPO-41381), NASA Tech Briefs, Vol. 33, No. 3 (March 2009), page 7a. In turn, ICER-3D is a product of generalization of ICER, another previously reported algorithm and computer program that can perform both lossless and lossy wavelet-based compression and decompression of gray-scale-image data. In ICER-3D, hyperspectral image data are decomposed using a 3D discrete wavelet transform (DWT). Following wavelet decomposition, mean values are subtracted from spatial planes of spatially low-pass subbands prior to encoding. The resulting data are converted to sign-magnitude form and compressed. In ICER-3D, compression is progressive, in that compressed information is ordered so that as more of the compressed data stream is received, successive reconstructions of the hyperspectral image data are of successively higher overall fidelity.

Kiely, Aaron↗
NASA NTRS1948

A simple approximate method for obtaining spanwise lift distributions over swept wings

It is shown how Schrenk's empirical method of estimating the lift distribution over straight wings can be adapted to swept wings by replacing the elliptical distribution by a new "ideal" distribution which varies with sweep.The application of the method is discussed in detail and several comparisons are made to show the agreement of the proposed method with more rigorous ones. It is shown how first-order compressibility corrections applicable to subcritical speeds may be included in this method.

Diederich, Franklin W↗
NASA NTRS1985

A Residuals Approach to Filtering, Smoothing and Identification for Static Distributed Systems

An approach for state estimation and identification of spatially distributed parameters embedded in static distributed (elliptic) system models is advanced. The method of maximum likelihood is used to find parameter values that maximize a likelihood functional for the system model, or equivalently, that minimize the negative logarithm of this functional. To find the minimum, a Newton-Raphson search is conducted that from an initial estimate generates a convergent sequence of parameter estimates. For simplicity, a Gauss-Markov approach is used to approximate the Hessian in terms of products of first derivatives. The gradient and approximate Hessian are computed by first arranging the negative log likelihood functional into a form based on the square root factorization of the predicted covariance of the measurement process. The resulting data processing approach, referred to here by the new term of predicted data covariance square root filtering, makes the gradient and approximate Hessian calculations very simple. A closely related set of state estimates is also produced by the maximum likelihood method: smoothed estimates that are optimal in a conditional mean sense and filtered estimates that emerge from the predicted data covariance square root filter.

Rodriguez, G.↗
NASA NTRS1973

Bayesian estimation of life parameters in the Weibull distribution.

Development of a Bayesian analysis of the scale and shape parameters in the Weibull distribution and the corresponding reliability function with respect to the usual life-testing procedures. For the scale parameter theta, Bayesian estimates of theta and reliability are obtained for the uniform, exponential, and inverted gamma prior probability densities. Bhattacharya's results (1967) for the one-parameter exponential life-testing distribution are reduced to a special case of these results. A fully Bayesian analysis of both the scale and shape parameters is developed by assuming independent prior distributions; since in the latter case, analytical tractability is not possible, Bayesian estimates are obtained through a conjunction of Monte Carlo simulation and numerical-integration techniques. In both cases, a computer simulation is carried out, and a comparison is made between the Bayesian and the corresponding minimum-variance unbiased, or maximum likelihood, estimates. As expected, the Bayesian estimates are superior.

Canavos, G. C.↗
NASA NTRS1978

An iterative procedure for obtaining maximum-likelihood estimates of the parameters for a mixture of normal distributions

This paper addresses the problem of obtaining numerically maximum-likelihood estimates of the parameters for a mixture of normal distributions. In recent literature, a certain successive-approximations procedure, based on the likelihood equations, was shown empirically to be effective in numerically approximating such maximum-likelihood estimates; however, the reliability of this procedure was not established theoretically. Here, we introduce a general iterative procedure, of the generalized steepest-ascent (deflected-gradient) type, which is just the procedure known in the literature when the step-size is taken to be 1. We show that, with probability 1 as the sample size grows large, this procedure converges locally to the strongly consistent maximum-likelihood estimate whenever the step-size lies between 0 and 2. We also show that the step-size which yields optimal local convergence rates for large samples is determined in a sense by the 'separation' of the component normal densities and is bounded below by a number between 1 and 2.

Peters, B. C., Jr.↗
NASA NTRS1972

Electron microprobe analysis program for biological specimens: BIOMAP

BIOMAP is a Univac 1108 compatible program which facilitates the electron probe microanalysis of biological specimens. Input data are X-ray intensity data from biological samples, the X-ray intensity and composition data from a standard sample and the electron probe operating parameters. Outputs are estimates of the weight percentages of the analyzed elements, the distribution of these estimates for sets of red blood cells and the probabilities for correlation between elemental concentrations. An optional feature statistically estimates the X-ray intensity and residual background of a principal standard relative to a series of standards.

Edwards, B. F.↗
NASA NTRS1992

Statistical plant set estimation using Schroeder-phased multisinusoidal input design

A frequency domain method is developed for plant set estimation. The estimation of a plant 'set' rather than a point estimate is required to support many methods of modern robust control design. The approach here is based on using a Schroeder-phased multisinusoid input design which has the special property of placing input energy only at the discrete frequency points used in the computation. A detailed analysis of the statistical properties of the frequency domain estimator is given, leading to exact expressions for the probability distribution of the estimation error, and many important properties. It is shown that, for any nominal parametric plant estimate, one can use these results to construct an overbound on the additive uncertainty to any prescribed statistical confidence. The 'soft' bound thus obtained can be used to replace 'hard' bounds presently used in many robust control analysis and synthesis methods.

Bayard, D. S.↗
NASA NTRS2010

Sub-10-Micron and Respirable Particles in Lunar Soils

Based on published lunar soil grain size distribution data, we estimate that 1-3% of the mass of typical mature lunar soils is comprised of grains less than 2.5 micrometers in diameter. These particles are in the respirable range (small enough to be inhaled). Estimates are used because the early methods of obtaining grain size distributions did not give reliable results below about 10 micrometers. Grain size analyses of Apollo 11 soil 10084 by a laser diffraction technique shows that this soil contains roughly 2% by volume in the respirable grain size, in agreement with our prior estimate.

Cooper, Bonnie L.↗
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 NTRS2001

Distributed Spacecraft Control Architectures

A fundamental issue for estimation and control of distributed systems such as formation flying spacecraft is the information exchange architecture. In centralized schemes, each subordinate need only share its measurement data with a central hub, and the subordinates depend on the center to direct their actions. In decentralized schemes, all nodes participate in the data exchange, so that each has the same in by formation as the center, and may thereby self-direct the same action that the center would have commanded, assuming all share a common goal. This talk compares and contrasts the centralized and decentralized schemes in the context of autonomously maintaining a distributed satellite formation.

Carpenter, James Russell↗
NASA NTRS2007

Derivation and Application of a Global Albedo yielding an Optical Brightness To Physical Size Transformation Free of Systematic Errors

Orbital object data acquired via optical telescopes can play a crucial role in accurately defining the space environment. Radar systems probe the characteristics of small debris by measuring the reflected electromagnetic energy from an object of the same order of size as the wavelength of the radiation. This signal is affected by electrical conductivity of the bulk of the debris object, as well as its shape and orientation. Optical measurements use reflected solar radiation with wavelengths much smaller than the size of the objects. Just as with radar, the shape and orientation of an object are important, but we only need to consider the surface electrical properties of the debris material (i.e., the surface albedo), not the bulk electromagnetic properties. As a result, these two methods are complementary in that they measure somewhat independent physical properties to estimate the same thing, debris size. Short arc optical observations such as are typical of NASA's Liquid Mirror Telescope (LMT) give enough information to estimate an Assumed Circular Orbit (ACO) and an associated range. This information, combined with the apparent magnitude, can be used to estimate an "absolute" brightness (scaled to a fixed range and phase angle). This absolute magnitude is what is used to estimate debris size. However, the shape and surface albedo effects make the size estimates subject to systematic and random errors, such that it is impossible to ascertain the size of an individual object with any certainty. However, as has been shown with radar debris measurements, that does not preclude the ability to estimate the size distribution of a number of objects statistically. After systematic errors have been eliminated (range errors, phase function assumptions, photometry) there remains a random geometric albedo distribution that relates object size to absolute magnitude. Measurements by the LMT of a subset of tracked debris objects with sizes estimated from their radar cross sections indicate that the random variations in the albedo follow a log-normal distribution quite well. In addition, this distribution appears to be independent of object size over a considerable range in size. Note that this relation appears to hold for debris only, where the shapes and other properties are not primarily the result of human manufacture, but of random processes. With this information in hand, it now becomes possible to estimate the actual size distribution we are sampling from. We have identified two characteristics of the space debris population that make this process tractable and by extension have developed a methodology for performing the transformation.

Mulrooney, Dr. Mark K.↗
NASA NTRS1988

Advanced probabilistic methods for quantifying the effects of various uncertainties in structural response

The effects of actual variations, also called uncertainties, in geometry and material properties on the structural response of a space shuttle main engine turbopump blade are evaluated. A normal distribution was assumed to represent the uncertainties statistically. Uncertainties were assumed to be totally random, partially correlated, and fully correlated. The magnitude of these uncertainties were represented in terms of mean and variance. Blade responses, recorded in terms of displacements, natural frequencies, and maximum stress, was evaluated and plotted in the form of probabilistic distributions under combined uncertainties. These distributions provide an estimate of the range of magnitudes of the response and probability of occurrence of a given response. Most importantly, these distributions provide the information needed to estimate quantitatively the risk in a structural design.

Nagpal, Vinod K.↗
NASA NTRS1975

Bayesian estimation - A sensitivity analysis

The robustness of the assigned prior distribution in a Bayesian estimation problem is examined. A Bayesian analysis for a stochastic intensity parameter of a Poisson distribution is summarized in which the natural conjugate is assigned as the prior distribution of the random parameter. The sensitivity analysis is carried out by assuming the existence of a true prior which is different in form from that of the assigned prior distribution. By using mean-squared error as a measure of performance, the ensuing Bayes decision function is compared to the corresponding minimum variance unbiased estimator. Results indicate that the Bayes estimator is largely robust to deviations from the assigned prior and remains squared-error superior to the MVU type within a broad region.

Canavos, G. C.↗
NASA NTRS1973

Bistatic-radar estimation of surface-slope probability distributions with applications to the moon.

A method for extracting surface-slope frequency distributions from bistatic-radar data has been developed and applied to the lunar surface. Telemetry transmissions from orbiting Apollo spacecraft were received on the earth after reflection from the lunar surface. The echo-frequency spectrum was related analytically to the probability distribution of lunar slopes. Standard regression techniques were used to solve the inverse problem of finding slope distributions from observed echo-frequency spectra. Data taken simultaneously at two wavelengths, 13 and 116 cm, have yielded diverse slope statistics.

Parker, M. N.↗
NASA NTRS1973

Investigations of atmospheric extinction using direct solar radiation measurements made with a multiple wavelength radiometer.

A multiple wavelength solar radiometer designed for the purpose of measuring atmospheric optical depth at discrete wavelengths through the visible region is described. Experimental techniques, including sample observations, are presented for obtaining atmospheric optical depth from radiometer measurements. These techniques apply for conditions where the optical depth is either temporally variant or invariant during the course of a day. The influence of the aerosol size distribution on optical depth is investigated. Theoretical calculations of the wavelength dependency of the aerosol optical depth contribution are presented for several representative aerosol size distributions. Methods are also presented for estimating the aerosol size distribution and aerosol mass loading from multiwavelength optical depth measurements.

Shaw, G. E.↗