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Results for “least-squares method”

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 NTRS1954

Application of several methods for determining transfer functions and frequency response of aircraft from flight data

In the process of analyzing the longitudinal frequency-response characteristics of aircraft, information on some of the methods of analysis has been obtained by the Langley Aeronautical Laboratory of the National Advisory Committee for Aeronautics. In the investigation of these methods, the practical applications and limitations were stressed. In general, the methods considered may be classed as: (1) analysis of sinusoidal response, (2) analysis of transient response as to harmonic content through determination of the Fourier integral by manual or machine methods, and (3) analysis of the transient through the use of least-squares solutions of the coefficients of an assumed equation for either the transient time response or frequency response (sometimes referred to as curve-fitting methods). (author)

Eggleston, John M↗
NASA NTRS1972

Numerical method for the solution of large systems of differential equations of the boundary layer type

A numerical method for the solution of large systems of nonlinear differential equations of the boundary-layer type is described. The method is a modification of the technique for satisfying asymptotic boundary conditions. The present method employs inverse interpolation instead of the Newton method to adjust the initial conditions of the related initial-value problem. This eliminates the so-called perturbation equations. The elimination of the perturbation equations not only reduces the user's preliminary work in the application of the method, but also reduces the number of time-consuming initial-value problems to be numerically solved at each iteration. For further ease of application, the solution of the overdetermined system for the unknown initial conditions is obtained automatically by applying Golub's linear least-squares algorithm. The relative ease of application of the proposed numerical method increases directly as the order of the differential-equation system increases. Hence, the method is especially attractive for the solution of large-order systems. After the method is described, it is applied to a fifth-order problem from boundary-layer theory.

Green, M. J.↗
NASA NTRS1974

Triangulation of multistation camera data to locate a curved line in space

A method is described for finding the location of a curved line in space from local azimuth as a function of elevation data obtained at several observation sites. A least-squares criterion is used to insure the best fit to the data. The method is applicable to the triangulation of an object having no identifiable structural features, provided its width is very small compared with its length so as to approximate a line in space. The method was implemented with a digital computer program and was successfully applied to data obtained from photographs of a barium ion cloud which traced out the earth's magnetic field line at very high altitudes.

Fricke, C. L.↗
NASA NTRS1971

A program for identification of linear systems

A program has been written for the identification of parameters in certain linear systems. These systems appear in biomedical problems, particularly in compartmental models of pharmacokinetics. The method presented here assumes that some of the state variables are regularly modified by jump conditions. This simulates administration of drugs following some prescribed drug regime. Parameters are identified by a least-square fit of the linear differential system to a set of experimental observations. The method is especially suited when the interval of observation of the system is very long.

Buell, J.↗
NASA NTRS1973

Mars gravity derived from the long-period motion of Mariner 9

The spherical harmonic coefficients in the Mars gravity field are determined using a two-stage filtering process. In the first stage, a weighted least-squares orbit determination processor is applied to Mariner 9 radio data to estimate the mean Kepler elements of each orbit. A finite difference method is then used to generate orbital element rates. In the second stage, the gravity coefficients are determined using another weighted least-squares processor which fits the long period Lagrange perturbation equations to the estimated rates. The resulting gravity potential and associated equipotential surface is presented and error sources discussed. Gravity field results are applied to various physical properties of Mars, such as moments of inertia.-

Ferrari, A. J.↗
NASA NTRS1974

The contamination of lunar highland rocks by KREEP - Interpretation by mixing models

A mixing model method was used to determine the component abundance in the Apollo 16 and 17 soils. This method uses the chemical composition of the soils for up to 30 elements and a weighted least-squares mixing model technique. Elements included in the calculations are: Si, Ti, Al, Ca, Fe, Mg, P, Cr, Mn, Na, K, Rb, Ba, U, Th, La, Ce, Sm, Eu, Sr, Yb, Y, Sc, V, Zr, Nb, Co, Ni, Li, Au, and Ir. The method was used to examine the possibility that some of the highland rocks such as VHA and low-K Fra Mauro basalt are mixtures. The results of the mixing model calculations show that it is possible that these rocks are mixtures of KREEP, troctolite, 'anorthosites', and a meteoritic component. The Rb-Sr systematics are consistent with such a model for the genesis of the highland rocks. KREEP has high relative concentrations of Rb, U, and radiogenic Sr and Pb and its model age of about 4.4 AE dominates the model age of all the 'contaminated' highland rocks.

Schonfeld, E.↗
NASA NTRS1961

A Method of Estimating Residuals in Orbital Theory

The degree of approximation used in determining the orbits of earth satellites is reflected in the residuals (differences between calculated and observed positions). The least-squares procedure generally used to fit theory to observation tends to obscure the significance of theoretical parameters, so that the physical sources of residuals cease to be apparent. A method is outlined herein for estimating the magnitude of the residuals to be expected from an approximate theory presumed to have one missing or incorrect term.

Lecar, Myron↗
NASA NTRS1973

Thermal conductivity of particulate materials: A summary of measurements taken at the Marshall Space Flight Center

Thermal conductivity measurements of particulate materials in vacuum are presented in summary. Particulate basalt and soda lime glass beads of various size ranges were used as samples. The differentiated line heat source method was used for the measurements. A comprehensive table is shown giving all pertinent experimental conditions. Least-squares curve fits to the data are presented.

Fountain, J. A.↗
NASA NTRS1971

An Empirical Method for Determining the Lunar Gravity Field

A method has been devised to determine the spherical harmonic coefficients of the lunar gravity field. This method consists of a two-step data reduction and estimation process. In the first step, a weighted least-squares empirical orbit determination scheme is applied to Doppler tracking data from lunar orbits to estimate long-period Kepler elements and rates. Each of the Kepler elements is represented by an independent function of time. The long-period perturbing effects of the earth, sun, and solar radiation are explicitly modeled in this scheme. Kepler element variations estimated by this empirical processor are ascribed to the non-central lunar gravitation features. Doppler data are reduced in this manner for as many orbits as are available. In the second step, the Kepler element rates are used as input to a second least-squares processor that estimates lunar gravity coefficients using the long-period Lagrange perturbation equations.

Ferrari, A. J.↗
NASA NTRS1973

Lunar gravity derived from long-period satellite motion - A proposed method.

A new method has been devised to determine the spherical harmonic coefficients of the lunar gravity field. This method consists of a two-step data reduction and estimation process. In the first step, a weighted least-squares empirical orbit determination scheme is applied to Doppler tracking data from lunar orbits to estimate long-period Kepler elements and rates. Each of the Kepler elements is represented by an independent function of time. The long-period perturbing effects of the earth, sun, and solar radiation are explicitly modeled in this scheme. Kepler element variations estimated by this empirical processor are then ascribed to the non-central lunar gravitation features. Doppler data are reduced in this manner for as many orbits as are available. In the second step, the Kepler element rates are used as input to a second least-squares processor that estimates lunar gravity coefficients using the long-period Lagrange perturbation equations.

Ferrari, A. J.↗
NASA NTRS1972

On the mass-luminosity relation.

The results of a least-squares study of the mass-luminosity relation for eclipsing and visual binary stars consisting of main sequence components are presented. Two methods are discussed. First, the values of the coefficients A and B in the relation log M = A + BM sub BOL are determined. Then a technique which permits the determination of alpha and beta in the relation M = alpha L beta, when only the sum of the masses, and not the individual masses of each component, is known. The results and a comparison of the two methods are discussed. It is found that the following mass-luminosity relation represents the observational data satisfactorily: log M = 0.504 - 0.103 M sub BOL, -8 less than or equal to M sub BOL less than or equal to +10.5. A discussion of the data and of the possibility that separate mass-luminosity relations may exist for visual and eclipsing binaries is given. The possibility that more than one mass-luminosity relation is required in the range -8 less than or equal to M sub BOL less than or equal to +13 is also discussed.

Mccluskey, G. E., Jr.↗
NASA NTRS1972

A two-spacecraft test of a single spacecraft method of estimating shock normals

By assuming the validity of a subset of the Rankine-Hugoniot conservation relations for interplanetary (IP) shocks in an isotropic medium it has been demonstrated, in principle, that improved shock normals can be calculated by using a least-squares technique on combined magnetic field and plasma data from a single spacecraft. The scheme uses those six conservation relations not involving pressure and temperature. This paper deals with a test of the scheme by examining in detail a shock across which the magnetic field changed direction by a small amount (approximately 10 deg). On January 26, 1968 at about 1430 UT this shock was observed by the plasma and magnetic field instruments in Explorers 33 and 35. The spacecraft were 76.6 and 56.9 R sub E sunward of the earth, respectively (and 43.5 R sub E from each other), and therefore well outside the earth's bow shock region, a necessary condition for a valid test.

Lepping, R. P.↗
NASA NTRS1974

The two-dimensional tunnel structures of K3Sb5O14 and K2Sb4O11

The structures of K3Sb5O14 and K2Sb4O11 have been solved by the single-crystal X-ray direct method and the heavy-atom method, respectively. The structure of K3Sb5O14 is orthorhombic, with space group Pbam and cell parameters a = 24.247 (4), b = 7.157 (2), c = 7.334 (2) A, Z = 4. The structure of K2Sb4O11 is monoclinic, with space group C2/m and cell parameters a = 19.473 (4), b = 7.542 (1), c = 7.198 (1) A, beta = 94.82 (2) deg, Z = 4. A full-matrix least-squares refinement gave R = 0.072 and R = 0.067, respectively. In both structures, oxygen atoms form an octahedron around each Sb atom and an irregular polyhedron around each K atom. By sharing corners and edges, the octahedra form a skeleton network having intersecting b-axis and c-axis tunnels. The K(+) ions, which have more than ten oxygen near neighbors, are located in these tunnels. Evidence for K(+)-ion transport within and between tunnels comes from ion exchange of the alkali ions in molten salts and anisotropic temperature factors that are anomalously large in the direction of the tunnels.

Hong, H. Y.-P.↗
NASA NTRS1971

Development of techniques for measuring pilot workload

An objective method of assessing information workload based on physiological measurements was developed. Information workload, or reserve capacity, was measured using a visual discrimination secondary task and subjective rating of task difficulty. The primary task was two axis (pitch and roll) tracking, and the independent variables in this study were aircraft pitch dynamics and wind gust disturbances. The study was structured to provide: (1) a sensitive, nonloading measure of reserve capacity, and (2) an unencumbering reliable measurement of the psychophysiological state. From these, a measured workload index (MWI) and physiological workload index (PWI) were extracted. An important measure of the success of this study was the degree to which the MWI and PWI agreed across the 243 randomly-presented, four-minute trials (9 subjects X 9 tasks X 3 replications). The electrophysiological data collected included vectorcardiogaram, respiration, electromyogram, skin impedance, and electroencephalogram. Special computer programs were created for the analysis of each physiological variable. The digital data base then consisted of 82 physiological features for each of the 243 trials. A prediction of workload based on physiological observations was formulated as a simultaneous least-squares prediction problem. A best subset of 10 features was chosen to predict the three measures of reserve capacity. The cannonical correlation coefficient was .754 with a chi squared value of 91.3 which allows rejection of the null hypothesis with p of .995.

Spyker, D. A.↗