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NASA NTRS1984

Estimation of parameters in linear structural relationships Sensitivity to the choice of the ratio of error variances

Maximum likelihood estimation of parameters in linear structural relationships under normality assumptions requires knowledge of one or more of the model parameters if no replication is available. The most common assumption added to the model definition is that the ratio of the error variances of the response and predictor variates is known. This paper investigates the use of asymptotic formulae for variances and mean squared errors as a function of sample size and the assumed value for the error variance ratio.

Lakshminarayanan, M. Y.↗

NASA NTRS1983

High dynamic, low volume GPS receiver

A new GPS receiver concept and design are presented to meet the high dynamic and low volume requirements for range applications in missiles and drones. The receiver has the potential to satisfy all range requirements with one basic receiver, which has significant potential economic benefit over the alternate approach of using a family of receivers, each tailored for specific applications. The main new concept is to use approximate maximum likelihood estimates of pseudo range and range-rate, rather than tracking with carrier phase locked loops and code delay locked loops. Preliminary analysis indicates that receivers accelerating at 50 g or more can track with position errors due to acceleration of approximately 0.2 m/g, or 10 m at 50 g. Implementation is almost entirely digital to meet the low volume requirements.

Hurd, W. J.↗

NASA NTRS1985

Time-resolved speckle effects on the estimation of laser-pulse arrival times

A maximum-likelihood (ML) estimator of the pulse arrival in laser ranging and altimetry is derived for the case of a pulse distorted by shot noise and time-resolved speckle. The performance of the estimator is evaluated for pulse reflections from flat diffuse targets and compared with the performance of a suboptimal centroid estimator and a suboptimal Bar-David ML estimator derived under the assumption of no speckle. In the large-signal limit the accuracy of the estimator was found to improve as the width of the receiver observational interval increases. The timing performance of the estimator is expected to be highly sensitive to background noise when the received pulse energy is high and the receiver observational interval is large. Finally, in the speckle-limited regime the ML estimator performs considerably better than the suboptimal estimators.

Tsai, B.-M.↗

NASA NTRS1985

Einstein X-ray survey of the Pleiades - The dependence of X-ray emission on stellar age

The data obtained with two pointed observations of 1 deg by 1 deg fields of the Pleiades region have been analyzed, and the results are presented. The maximum-likelihood X-ray luminosity functions for the Pleiades G and K stars in the cluster are derived, and it is shown that, for the G stars, the Pleiades X-ray luminosity function is significantly brighter than the corresponding function for Hyades G dwarf stars. This finding indicates a dependence of X-ray luminosity on stellar age, which is confirmed by comparison of the same data with median X-ray luminosities of pre-main sequence and local disk population dwarf G stars. It is suggested that the significantly larger number of bright X-ray sources associated with G stars than with K stars, the lack of detection of M stars, and the relatively rapid rotation of the Pleiades K stars can be explained in terms of the onset of internal differential rotation near the convective envelope-radidative core interface after the spin-up phase during evolution to the main sequence.

Micela, G.↗

NASA NTRS1984

Determination of hot-spot susceptibility of multistring photovoltaic modules in a central-station application

Part of the effort of the Jet Propulsion Laboratory (JPL) Flat-Plate Solar Array Project (FSA) includes a program to improve module and array reliability. A collaborative activity with industry dealing with the problem of hot-spot heating due to the shadowing of photovoltaic cells in modules and arrays containing several paralleled cell strings is described. The use of multiparallel strings in large central-station arrays introduces the likelihood of unequal current sharing and increased heating levels. Test results that relate power dissipated, current imbalance, cross-strapping frequency, and shadow configuration to hot-spot heating levels are presented. Recommendations for circuit design configurations appropriate to central-station applications that reduce the risk of hot-spot problems are offered. Guidelines are provided for developing hot-spot tests for arrays when current imbalance is a threat.

Gonzalez, C. C.↗

NASA NTRS1985

On the identification of a highly augmented airplane

The results of applying linear least squares and maximum likelihood estimation procedures to flight data from the AFTI/F-16 airplane are presented. Data from two flight control system modes are analyzed. It is shown that though a simple aerodynamic model structure is adequate for the simple mode, a more complicated model is necessary to adequately describe the highly augmented mode. The effect of augmentation of roll control is shown to be visible in the control parameters.

Batterson, J. G.↗

NASA NTRS1985

Statistical analysis of astronomical data containing upper bounds - General methods and examples drawn from X-ray astronomy

Statistical procedures taken from the field of survival analysis have been adapted to astronomical usage and have been applied to a sample of stars in the B-V color range between 0.1 and 0.5 with measured soft X-ray luminosities and projected equatorial velocities. The two-sample problem and linear regression problem with arbitrarily censored data were studied. A new method for determining the linear regression between two random variables in the presence of arbitrary censoring has been developed which can also be used for a likelihood-ratio test for the independence of two random variables and for principal-component analysis in the presence of arbitrary censoring. The required numerical computations can be carried out straightforwardly and rapidly.

Schmitt, J. H. M. M.↗

NASA NTRS1985

Statistical methods for astronomical data with upper limits. I - Univariate distributions

The statistical treatment of univariate censored data is discussed. A heuristic derivation of the Kaplan-Meier maximum-likelihood estimator from first principles is presented which results in an expression amenable to analytic error analysis. Methods for comparing two or more censored samples are given along with simple computational examples, stressing the fact that most astronomical problems involve upper limits while the standard mathematical methods require lower limits. The application of univariate survival analysis to six data sets in the recent astrophysical literature is described, and various aspects of the use of survival analysis in astronomy, such as the limitations of various two-sample tests and the role of parametric modelling, are discussed.

Feigelson, E. D.↗

NASA NTRS1985

Identification of integro-differential systems for application to unsteady aerodynamics and aeroelasticity

Integrodifferential equations for unsteady aerodynamic and aeroelastic phenomena are identified by means of several approaches. When the product of the frequency of motion and maximum time delay is much smaller than unity, the integral term can be approximated by a constant; when greater than unity, however, approximation of the integral is not possible. Approximations of integrodifferential models are needed to obtain identifiability. While the least-squares method may be used for model determination, the maximum likelihood technique is needed for accurate parameter estimation. High angle of attack and post stall/spin regions appear to have characteristics that can be satisfied by indicial models.

Gupta, N. K.↗

NASA NTRS1985

Performance comparisons between information extraction techniques using variable spatial resolution data

The decreased instantaneous field of view (IFOV) is one of the principal advances noted for the Thematic Mapper (TM) sensor. The 42.5 microradian IFOV of TM and the 710 km nominal orbit altitude result in a 30 m nominal spatial resolution at the earth surface. This is a considerable decrease in the projected pixel area when compared to the 79 m nominal spatial resolution of the Landsat Multispectral Scanner (MSS). An experiment was conducted which allowed a rigorous test of the influence of classifier design, with data spatial resolution of TM (30 m) and approximately that of the Landsat MSS (90 m), on classification performance for a particular TM scene. The experiment involved evaluation of the results for the per-point Gaussian maximum likelihood (GML) classifier and the supervised ECHO (Extraction and Classification of Homogeneous Objects) classifier.

Latty, R. S.↗

NASA NTRS1986

Attaching Metal Fasteners to Silica Tiles

Stress distributed so high load borne. Fastener bonded in densified hole or captured in plug of similar refractory material, which in turn bonded in hole in parent tile. Plug or bonding distributes mechanical load from fastener to broad region surrounding fastener, reducing local stress concentration and likelihood of breakage. Bonded-plug method has been successful in attaching mechanical fasteners to porous silica refractory tiles used on outer surface of Space Shuttle orbiter.

Holt, J. W.↗

NASA NTRS1985

Decoding convolutionally encoded images

Maximum Likelihood Convolutional Decoding, which is used by the Deep Space Network for short constraint-length convolutional codes, assumes that all strings of information bits are equally likely. In some cases, like image data, this is not the case. The use of information about an adjacent pixel in decoding convolutionally encoded Voyager images is examined. It is discovered that, in a region of interest, as much as 2 dB may be gained.

Pitt, G. H., III↗

NASA NTRS1985

Fracture analysis of radial scientific instrument module registration fittings of the space telescope

The space telescope contains various scientific instrument (SI) modules which are mounted to the Focal Plane Structure (FPS) in a statically determinate manner. This is accomplished by using three registration fittings per SI module, one resisting three translations, another resisting two and the third resisting only one. Due to thermal insulating requirements these fittings are complex devices composed of numerous pieces. The structural integrity of these fittings is of great importance to the safety of the orbiter transporting the telescope, so in addition to the stress analyses performed during the design of these components, fracture susceptibility also needs to be considered. The pieces of the registration fittings for the Radial SI Module containing the Wide Field Planetary Camera are examined to determine which would endanger the orbiter if they fractured and what is the likelihood of their fracture. The latter is stated in terms of maximum allowable initial flaw sizes in these pieces.

Springfield, C. W., Jr.↗

NASA NTRS1986

Effects of wing modification on an aircraft's aerodynamic parameters as determined from flight data

A study of the effects of four wing-leading-edge modifications on a general aviation aircraft's stability and control parameters is presented. Flight data from the basic aircraft configuration and configurations with wing modifications are analyzed to determine each wing geometry's stability and control parameters. The parameter estimates and aerodynamic model forms are obtained using the stepwise regression and maximum likelihood techniques. The resulting parameter estimates and aerodynamic models are verified using vortex-lattice theory and by analysis of each model's ability to predict aircraft behavior. Comparisons of the stability and control derivative estimates from the basic wing and the four leading-edge modifications are accomplished so that the effects of each modification on aircraft stability and control derivatives can be determined.

Hess, R. A.↗

NASA NTRS1986

A methodology for airplane parameter estimation and confidence interval determination in nonlinear estimation problems

An algorithm for maximum likelihood (ML) estimation is developed with an efficient method for approximating the sensitivities. The ML algorithm relies on a new optimization method referred to as a modified Newton-Raphson with estimated sensitivities (MNRES). MNRES determines sensitivities by using slope information from local surface approximations of each output variable in parameter space. With the fitted surface, sensitivity information can be updated at each iteration with less computational effort than that required by either a finite-difference method or integration of the analytically determined sensitivity equations. MNRES eliminates the need to derive sensitivity equations for each new model, and thus provides flexibility to use model equations in any convenient format. A random search technique for determining the confidence limits of ML parameter estimates is applied to nonlinear estimation problems for airplanes. The confidence intervals obtained by the search are compared with Cramer-Rao (CR) bounds at the same confidence level. The degree of nonlinearity in the estimation problem is an important factor in the relationship between CR bounds and the error bounds determined by the search technique. Beale's measure of nonlinearity is developed in this study for airplane identification problems; it is used to empirically correct confidence levels and to predict the degree of agreement between CR bounds and search estimates.

Murphy, P. C.↗

NASA NTRS1986

The measurement of aircraft performance and stability and control after flight through natural icing conditions

The effects of airframe icing on the performance and stability and control of a twin-engine commuter-class aircraft were measured by the NASA Lewis Research Center. This work consisted of clear air tests with artificial ice shapes attached to the horizontal tail, and natural icing flight tests in measured icing clouds. The clear air tests employed static longitudinal flight test methods to determine degradation in stability margins for four simulated ice shapes. The natural icing flight tests employed a data acquisition system, which was provided under contract to NASA by Kohlman Systems Research Incorporated. This system used a performance modeling method and modified maximum likelihood estimation (MMLE) technique to determine aircraft performance degradation and stability and control. Flight test results with artificial ice shapes showed that longitudinal, stick-fixed, static margins are reduced on the order of 5 percent with flaps up. Natural icing tests with the KSR system corroborated these results and showed degradation in the elevator control derivatives on the order of 8 to 16 percent depending on wing flap configuration. Performance analyses showed the individual contributions of major airframe components to the overall degration in lift and drag.

Ranaudo, R. J.↗

NASA NTRS1986

A Monte Carlo study of Weibull reliability analysis for space shuttle main engine components

The incorporation of a number of additional capabilities into an existing Weibull analysis computer program and the results of Monte Carlo computer simulation study to evaluate the usefulness of the Weibull methods using samples with a very small number of failures and extensive censoring are discussed. Since the censoring mechanism inherent in the Space Shuttle Main Engine (SSME) data is hard to analyze, it was decided to use a random censoring model, generating censoring times from a uniform probability distribution. Some of the statistical techniques and computer programs that are used in the SSME Weibull analysis are described. The methods documented in were supplemented by adding computer calculations of approximate (using iteractive methods) confidence intervals for several parameters of interest. These calculations are based on a likelihood ratio statistic which is asymptotically a chisquared statistic with one degree of freedom. The assumptions built into the computer simulations are described. The simulation program and the techniques used in it are described there also. Simulation results are tabulated for various combinations of Weibull shape parameters and the numbers of failures in the samples.

Abernethy, K.↗

NASA NTRS1986

Simulation and study of small numbers of random events

Random events were simulated by computer and subjected to various statistical methods to extract important parameters. Various forms of curve fitting were explored, such as least squares, least distance from a line, maximum likelihood. Problems considered were dead time, exponential decay, and spectrum extraction from cosmic ray data using binned data and data from individual events. Computer programs, mostly of an iterative nature, were developed to do these simulations and extractions and are partially listed as appendices. The mathematical basis for the compuer programs is given.

Shelton, R. D.↗