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Results for “least squares solution”

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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At least 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
NASA NTRS1977

Improved ground truth geoid for the GEOS-3 calibration area

The purpose of this investigation is to develop methods and procedures are reported for computing a detailed geoid to be used as geodetic ground truth for the calibration and verification of GEOS-3 altimeter data. The technique developed is based on rectifying the best available detailed geoid so that the rectified geoid will have correct scale, orientation, shape and position with respect to the geocenter. The approach involved the development of a mathematical model based on a second degree polynomial, in rectangular Cartesian coordinates, describing the geoid undulations at the control stations. A generalized least squares solution was obtained for the polynomial which describes the variation of the undulation differences between the control stations geoid and the gravimetric geoid. Three rectified geoid were determined. These geoids correspond to three sets of tracking station data: (1) WFC/C-band data; (2) GSFC/C-band data; and (3) OSU-275 data. The absolute accuracy of these rectified geoids is linearly correlated with the uncertainties of the tracking station coordinates and, to a certain extent, with those of the detailed geoid being rectified.

Mourad, A. G.↗
NASA NTRS1980

A clear-sky spectral solar radiation model for snow-covered mountainous terrain

A clear-sky spectral solar radiation model for direct and diffuse fluxes, combined with topographic calculations from digital terrain data, computes either incident, net, or reflected solar radiation at any point on a snow surface in mountainous terrain. The radiation may be integrated over any wavelength range from 250 to 5000 nm, or over any time step. Atmospheric attenuation parameters are ozone, water vapor, the Angstrom turbidity coefficient and exponent, and the absorptance to reflectance ratio of the atmospheric aerosols. The model derives these, from measurements which may contain both systematic and random errors, by finding the least squares solution to an overdetermined set of nonlinear equations. For calculations over a specified area, it employs table look-up procedures, so that computation speed for the spectral model approaches that for a lumped model. Thus it may be useful as part of a snow surface energy budget calculation over a drainage basin.

Dozier, J.↗
NASA NTRS1980

Lightcurves and phase relation of asteroid 324 Bamberga

Results of a worldwide photometric investigation of the asteroid 324 Bamberga conducted from September to November 1978 are presented. The full-cycle light curve obtained from observations at Torino, Graz, Catania and Table Mountain observatories shows two maxima and two minima with a maximum amplitude of 0.075 magnitudes from which rotation period of 29.42 plus or minus 0.01 hours is derived. Linear least squares solution of the phase relation results in a phase coefficient of 0.034 plus or minus 0.001 mag/deg, a mean V magnitude of 7.20 and a zero-phase absolute V magnitude of 7.17 plus or minus 0.01. The color indices obtained (0.69 for B-V and 0.36 for U-B) are in agreement with the C taxonomic type assigned to the asteroid. The unusual length of the period of 324 Bamberga relative to that of other asteroids of diameter greater than 200 km is pointed out.

Scaltriti, F.↗
NASA NTRS1980

Seasat orbit refinement for altimetry application

This paper describes the use of stochastic differential correction models in refining the Seasat orbit based on post-flight analysis of tracking data. The objective is to obtain orbital-height precision that is commensurate with the inherent Seasat altimetry data precision level of 10 cms. Local corrections to a mean ballistic arc, perturbed principally by atmospheric drag variations and local gravitational anomalies, are obtained by the introduction of stochastic dynamical models in conjunction with optimal estimation/smoothing techniques. Assessment of the resulting orbit with 'ground truth' provided by Seasat altimetry data shows that the orbital height precision is improved by 32% when compared to a conventional least-squares solution using the same data set. The orbital height precision realized by employing stochastic differential correction models is in the range of 73 cms to 208 cms rms.

Mohan, S. N.↗
NASA NTRS1982

Spatial irregularities in Jupiter's upper ionosphere observed by Voyager radio occultations

Radio scintillations (at 3.6 and 13 cm) produced by scattering from ionospheric irregularities during the Voyager occultations are interpreted using a weak-scattering theory. Least squares solutions for ionospheric parameters derived from the observed fluctuation spectra yield estimates of (1) the axial ratio, (2) angular orientation of the anisotropic irregularities, (3) the power law exponent of the spatial spectrum of irregularities, and (4) the magnitude of the spatial variations in electron density. It is shown that the measured angular orientation of the anisotropic irregularities indicates magnetic field direction and may provide a basis for refining Jovian magnetic field models.

Hinson, D. P.↗
NASA NTRS1985

The apsidal motion of the eccentric eclipsing binary DI Herculis - An apparent discrepancy with general relativity

The apsidal motion of the eccentric eclipsing binary DI Herculis (HD 175227) is determined from an analysis of the available observations and eclipse timings from 1959 to 1984. Least squares solutions to the primary and secondary minima extending over an 84-yr interval yielded a small advance of periastron omega dot of 0.65 deg/100 yr + or - 0.18/100 yr. The observed advance of the periastron is about one seventh of the theoretical value of 4.27 deg/100 yr that is expected from the combined relativistic and classical effects. The discrepancy is about -3.62 deg/100 yr, or a magnitude of about 20 sigma. Classical mechanisms which explain the discrepancy are discussed, together with the possibility that there may be problems with general relativity itself.

Guinan, E. F.↗
NASA NTRS1986

On the analytical determination of relaxation modulus of viscoelastic materials by Prony's interpolation method

A computer implementation to Prony's curve fitting by exponential functions is presented. The method, although more than one hundred years old, has not been utilized to its fullest capabilities due to the restriction that the time range must be given in equal increments in order to obtain the best curve fit for a given set of data. The procedure used in this paper utilizes the 3-dimensional capabilities of the Interactive Graphics Design System (I.G.D.S.) in order to obtain the equal time increments. The resultant information is then input into a computer program that solves directly for the exponential constants yielding the best curve fit. Once the exponential constants are known, a simple least squares solution can be applied to obtain the final form of the equation.

Rodriguez, Pedro I.↗
NASA NTRS1987

A new art code for tomographic interferometry

A new algebraic reconstruction technique (ART) code based on the iterative refinement method of least squares solution for tomographic reconstruction is presented. Accuracy and the convergence of the technique is evaluated through the application of numerically generated interferometric data. It was found that, in general, the accuracy of the results was superior to other reported techniques. The iterative method unconditionally converged to a solution for which the residual was minimum. The effects of increased data were studied. The inversion error was found to be a function of the input data error only. The convergence rate, on the other hand, was affected by all three parameters. Finally, the technique was applied to experimental data, and the results are reported.

Tan, H.↗
NASA NTRS1986

Creation of a global geodetic network using Mark III VLBI

The positions of 15 permanent VLBI stations have been determined using Mark III with one-sigma uncertainties of less than 5 cm except for three stations in the Pacific. 46070 delay/delay rate observations acquired by the Crustal Dynamics Project and Polaris/IRIS from 1980-84 were included in a least squares solution to estimate the station positions, 44 radio source positions, and earth orientation parameters.

Ma, Chopo↗
NASA NTRS1987

Estimation of geopotential from satellite-to-satellite range rate data: Numerical results

A technique for high-resolution geopotential field estimation by recovering the harmonic coefficients from satellite-to-satellite range rate data is presented and tested against both a controlled analytical simulation of a one-day satellite mission (maximum degree and order 8) and then against a Cowell method simulation of a 32-day mission (maximum degree and order 180). Innovations include: (1) a new frequency-domain observation equation based on kinetic energy perturbations which avoids much of the complication of the usual Keplerian element perturbation approaches; (2) a new method for computing the normalized inclination functions which unlike previous methods is both efficient and numerically stable even for large harmonic degrees and orders; (3) the application of a mass storage FFT to the entire mission range rate history; (4) the exploitation of newly discovered symmetries in the block diagonal observation matrix which reduce each block to the product of (a) a real diagonal matrix factor, (b) a real trapezoidal factor with half the number of rows as before, and (c) a complex diagonal factor; (5) a block-by-block least-squares solution of the observation equation by means of a custom-designed Givens orthogonal rotation method which is both numerically stable and tailored to the trapezoidal matrix structure for fast execution.

Thobe, Glenn E.↗
NASA NTRS1989

Optimized resolved rate control of seven-degree-of-freedom Laboratory Telerobotic Manipulator (LTM) with application to three-dimensional graphics simulation

The Laboratory Telerobotic Manipulator (LTM) is a seven-degree-of-freedom robot arm. Two of the arms were delivered to Langley Research Center for ground-based research to assess the use of redundant degree-of-freedom robot arms in space operations. Resolved-rate control equations for the LTM are derived. The equations are based on a scheme developed at the Oak Ridge National Laboratory for computing optimized joint angle rates in real time. The optimized joint angle rates actually represent a trade-off, as the hand moves, between small rates (least-squares solution) and those rates which work toward satisfying a specified performance criterion of joint angles. In singularities where the optimization scheme cannot be applied, alternate control equations are devised. The equations developed were evaluated using a real-time computer simulation to control a 3-D graphics model of the LTM.

Barker, L. Keith↗
NASA NTRS1989

Optimum data weighting and error calibration for estimation of gravitational parameters

A new technique was developed for the weighting of data from satellite tracking systems in order to obtain an optimum least squares solution and an error calibration for the solution parameters. Data sets from optical, electronic, and laser systems on 17 satellites in GEM-T1 (Goddard Earth Model, 36x36 spherical harmonic field) were employed toward application of this technique for gravity field parameters. Also, GEM-T2 (31 satellites) was recently computed as a direct application of the method and is summarized here. The method employs subset solutions of the data associated with the complete solution and uses an algorithm to adjust the data weights by requiring the differences of parameters between solutions to agree with their error estimates. With the adjusted weights the process provides for an automatic calibration of the error estimates for the solution parameters. The data weights derived are generally much smaller than corresponding weights obtained from nominal values of observation accuracy or residuals. Independent tests show significant improvement for solutions with optimal weighting as compared to the nominal weighting. The technique is general and may be applied to orbit parameters, station coordinates, or other parameters than the gravity model.

Lerch, F. J.↗
NASA NTRS1989

Optimum data weighting and error calibration for estimation of gravitational parameters

A new technique was developed for the weighting of data from satellite tracking systems in order to obtain an optimum least-squares solution and an error calibration for the solution parameters. Data sets from optical, electronic, and laser systems on 17 satellites in GEM-T1 Goddard Earth Model-T1 (GEM-T1) were employed toward application of this technique for gravity field parameters. Also GEM-T2 (31 satellites) was recently computed as a direct application of the method and is summarized. The method employs subset solutions of the data associated with the complete solution to agree with their error estimates. With the adjusted weights the process provides for an automatic calibration of the error estimates for the solution parameters. The data weights derived are generally much smaller than corresponding weights obtained from nominal values of observation accuracy or residuals. Independent tests show significant improvement for solutions with optimal weighting. The technique is general and may be applied to orbit parameters, station coordinates, or other parameters than the gravity model.

Lerch, Francis J.↗
NASA NTRS1989

Eclipsing binary stars as tests of gravity theories - The apsidal motion of AS Camelopardalis

AS Camelopardalis is an 8th-magnitude eclipsing binary that consists of two main-sequence (B8 V and a B9.5 V) components in an eccentric orbit (e = 0.17) with an orbital period of 3.43 days. Like the eccentric eclipsing system DI Herculis, and a few other systems, AS Cam is an important test case for studying relativistic apsidal motion. In these systems, the theoretical general relativistic apsidal motion is comparable to that expected from classical effects arising from tidal and rotational deformation of the stellar components. Accurate determinations of the orbital and stellar properties of AS Cam have been made by Hilditch (1972) and Khalliulin and Kozyreva (1983) that permit the theoretical relativistic and classical contributions to the apsidal motion to be determined reasonably well. All the published timings of primary and secondary minima have been gathered and supplemented with eclipse timings from 1899 to 1920 obtained from the Harvard plate collection. Least-squares solutions of the eclipse timings extending over an 80 yr interval yield a smaller than expected apsidal motion, in agreement with that found by Khalliulin and Kozyreva from a smaller set of data. The observed apsidal motion for AS Cam is about one-third that expected from the combined relativistic and classical effects. Thus, AS Cam joins DI Her in having an observed apsidal motion significantly less than that predicted from theory.

Maloney, Frank P.↗
NASA NTRS1989

Automated generation of influence functions for planar crack problems

A numerical procedure for the generation of influence functions for Mode I planar problems is described. The resulting influence functions are in a form for convenient evaluation of stress-intensity factors for complex stress distributions. Crack surface displacements are obtained by a least-squares solution of the Williams eigenfunction expansion for displacements in a cracked body. Discrete values of the influence function, evaluated using the crack surface displacements, are curve fit using an assumed functional form. The assumed functional form includes appropriate limit-behavior terms for very deep and very shallow cracks. Continuous representation of the influence function provides a convenient means for evaluating stress-intensity factors for arbitrary stress distributions by numerical integration. The procedure is demonstrated for an edge-cracked strip and a radially cracked disk. Comparisons with available published results demonstrate the accuracy of the procedure.

Sire, Robert A.↗
NASA NTRS1991

Demonstration of precise estimation of polar motion parameters with the global positioning system: Initial results

Data from the Global Positioning System (GPS) were used to determine precise polar motion estimates. Conservatively calculated formal errors of the GPS least squares solution are approx. 10 cm. The GPS estimates agree with independently determined polar motion values from very long baseline interferometry (VLBI) at the 5 cm level. The data were obtained from a partial constellation of GPS satellites and from a sparse worldwide distribution of ground stations. The accuracy of the GPS estimates should continue to improve as more satellites and ground receivers become operational, and eventually a near real time GPS capability should be available. Because the GPS data are obtained and processed independently from the large radio antennas at the Deep Space Network (DSN), GPS estimation could provide very precise measurements of Earth orientation for calibration of deep space tracking data and could significantly relieve the ever growing burden on the DSN radio telescopes to provide Earth platform calibrations.

Lichten, S. M.↗
NASA NTRS1991

A new activity index for comets

An activity index (AI) is derived from observational data to measure the increase of activity in magnitudes for comets when brightest near perihelion as compared to their inactive reflective brightnesses at great solar distances. In all, AI determinations are made for 32 long-period (L-P) comets and for 14 short-period (S-P). The range of values of AI is the order of 3 to 10 magnitudes with a median about 6. An expected strong correlation with perihelion distance, q, was found to vary as approx. q(-2.3). Residuals from a least-square solution, delta AI, were used for comparing comets of different orbital classes, the standard deviation of a single value of delta AI was only plus or minus 1(m).1 for L-P comets and plus or minus 1(m)2 for S-P comets. Among the L-P comets, 19 of Period, P greater than 10(exp 4) yr yielded delta AI greater than or equal to -0(m).27 compared to +0(m).39 for 13 of 10(exp 4) greater than P greater than 10(exp 2) yr. This denies any effect of aging among the L-P comets. The 14 S-P comets yielded (delta AI) less 0(m).3 plus or minus 0(m).3 than the 32 L-P comets. The results suggest a common actively level, nature and probably origin for comets of all orbits, sizes and ages.

Whipple, Fred L.↗
NASA NTRS1991

The control network of Mars: April 1991

The modern geodetic control network of Mars was first established based on Mariner 9 images with 1-2 km/pixel resolutions and covered almost the entire Martian surface. The introduction of higher resolution (10-200 meter/pixel) Viking Orbiter images greatly improved the accuracy and density of points in the control network. Analysis of the Viking Lander radio tracking data led to more accurate measurements of Mars' rotation period, spin axis direction, and the lander coordinates relative to the inertial reference frame. The prime meridian on Mars was defined by the Geodesy/Cartography Group of the Mariner 9 Television Team as the crater Airy-0, located about 5 degrees south of the equator. The Viking 1 Lander site was identified on a high resolution Viking frame. The control point measurements form the basis of a least squares solution determined by analytical triangulation after the pixel measurements are corrected for geometric distortions and converted to millimeter coordinates in the camera focal plane. Photogrammetric strips encircling Mars at the equator and at 60 degree north south were used to strengthen the overall net and improve the accuracy of the coordinates of points. In addition, photogrammetric strips along 0, 90, 180, and 270 degrees longitude to the Viking 1 Lander site have all significantly strengthened the control network. Most recently, photogrammetric strips were added to the net along 30 degrees north latitude between 0 and 180 degrees, and along 30 degrees between 180 and 360 degrees. The Viking 1 Lander site and Airy-0 are linked through photogrammetric strips occurring along the 0 degree meridian from Airy-0 to 65 degrees north, from that point through the Viking 1 Lander site to the equator, and along the equator to 180 degrees longitude. The Viking 1 lander site is thus a well calibrated area with coordinates of points accurate to approximately 200 meters relative to the J2000 inertial coordinate system. This will be a useful calibration region for upcoming missions. The current status of the control network calculations is presented.

Davies, Merton E.↗