Search NASA⌕ Search

SEARCH · Search NASA

Results for “least-squares”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 145 records · Page 8

The radial dependences of the interplanetary magnetic field between 1 and 5 AU Pioneer 10

Pioneer 10 vector helium magnetometer data acquired in 1972-1973 during Bartels solar rotations 1896-1918 are used to investigate the radial dependences of the distant interplanetary magnetic field (IMF) between 1 and 5 AU. Least-square fits were determined for the radial dependences of the averages of the magnitudes of IMF components and total field and plane projections, and radial fits were prepared for the standard deviations of these variables over the solar rotation, one day, and three-hour intervals. The variation of the weighted averages of the radial component of the field with respect to the heliocentric distance, the variation of the tangential component of the field, and the characteristics of a subset corresponding to a relatively low average solar wind velocity are reported.

Rosenberg, R. L.↗

Detailed gravity anomalies from GEOS-3 satellite altimetry data

A technique for deriving mean gravity anomalies from dense altimetry data was developed. A combination of both deterministic and statistical techniques was used. The basic mathematical model was based on the Stokes' equation which describes the analytical relationship between mean gravity anomalies and geoid undulations at a point; this undulation is a linear function of the altimetry data at that point. The overdetermined problem resulting from the excessive altimetry data available was solved using Least-Squares principles. These principles enable the simultaneous estimation of the associated standard deviations reflecting the internal consistency based on the accuracy estimates provided for the altimetry data as well as for the terrestrial anomaly data. Several test computations were made of the anomalies and their accuracy estimates using GOES-3 data.

Gopalapillai, G. S.↗

On the determination and investigation of the terrestrial ionospheric refractive indices using GEOS-3/ATS-6 satellite-to-satellite tracking data

When the radio link between two satellites (GEOS-3/ATS-6) is intercepted by the earth's ionosphere and neutral atmosphere, a change in the Doppler frequency results. Travel through the atmosphere causes the Doppler phase to be advanced in the ionosphere's portion and retarded in the neutral portion of the atmosphere. Analysis of the shortening and lengthening of the phase of the Satellite-to-Satellite Tracking (SST) data that passed within 40-700 km above the earth's surface during its ATS-6 to GEOS-3 to ATS-6 path, caused by the atmosphere, results in refractivity versus height profiles. The SST Doppler data were used directly to adjust the GEOS-3 orbit. Perturbation from the Moon, Sun and a 15th order/degree earth gravity field were included in the orbit solution. This orbit was continued through the occultation period and a model ionosphere was estimated by a least-square adjustment of the Chapman ionosphere parameters from the SST data residuals. The refractivity profile obtained by this model ionosphere was compared to a refractivity profile obtained by a direct integral inversion of the SST data residuals. Systematic differences between the 2 methods were caused by orbital errors, which propagated into the solution. The SST data yielded refractive index profiles in a novel economical manner because no additional or special on-board equipment were required.

Liu, A. S.↗

X-ray reflectometer for optical efficiency and scatter measurements

An instrument has been developed to determine the reflection efficiency and scatter characteristics of optical samples at X-ray wavelengths from 1.5 to 113 A. The reflectometer operates in an oil-free vacuum chamber and measures the reflection efficiency and scatter characteristics as a function of the angle of incidence. The reflection efficiency is given for 8.34-A radiation incident on a fused silica sample finished to a flatness of one-tenth of a wavelength. The experimental reflection efficiency is compared with the theoretical data. The scatter curves are given for the direct X-ray beam and for the beam reflected from the fused silica sample at an angle of incidence of 50 arcmin. The full-width-at-half-maximum (FWHM) resolution of the instrument is approximately 13 arcsec, as determined by a least-squares smoothing of the experimental data.

Reynolds, J. M.↗

Optimal estimation of large structure model errors

In-flight estimation of large structure model errors is usually required as a means of detecting inevitable deficiencies in large structure controller/estimator models. The present paper deals with a least-squares formulation which seeks to minimize a quadratic functional of the model errors. The properties of these error estimates are analyzed. It is shown that an arbitrary model error can be decomposed as the sum of two components that are orthogonal in a suitably defined function space. Relations between true and estimated errors are defined. The estimates are found to be approximations that retain many of the significant dynamics of the true model errors. Current efforts are directed toward application of the analytical results to a reference large structure model.

Rodriguez, G.↗

Determination of the ground albedo and the index of absorption of atmospheric particulates by remote sensing. I - Theory

A statistical technique is developed for inferring the optimum values of the ground albedo and the effective imaginary term of the complex refractive index of atmospheric particulates. The procedure compares measurements of the ratio of the hemispheric diffuse to directly transmitted solar flux density at the earth's surface with radiative transfer computations of the same as suggested by Herman et al. (1975). A detailed study is presented which shows the extent to which the ratio of diffuse to direct solar radiation is sensitive to many of the radiative transfer parameters. Results indicate that the optical depth and size distribution of atmospheric aerosol particles are the two parameters which uniquely specify the radiation field to the point where ground albedo and index of absorption can be inferred. Varying the real part of the complex refractive index of atmospheric particulates as well as their vertical distribution is found to have a negligible effect on the diffuse-direct ratio. The statistical procedure utilizes a semi-analytic gradient search method from least-squares theory and includes a detailed error analysis.

King, M. D.↗

A sunspot periodicity and its possible relation to solar rotation

A least-squares power-spectrum analysis of 122 years of Zurich daily sunspot numbers yields a statistically significant peak at a 12.0715 + or - 0.002 day period. This feature of the sunspot spectrum may be associated with the peak at 12.22 days (sidereal) which Dicke (1976) found in his oblateness data, and may be attributable to the sun's core if it rotates at either a 12.0715-day or a 24.1430-day period (synodic).

Knight, J. W.↗

Astrometric observations of the satellites of the outer planets. I - The Galilean satellites in 1977

Astrometric observations of the Galilean satellites of Jupiter performed around the opposition of 1977 with a 67-cm photovisual refractor are reported. The measurements are reduced to absolute and intersatellite positions by two different methods: a linear least-squares plate-constant solution to the AGK3 reference-star frame and the trail-scale method of Pascu (1977). Results of a plate-constant reduction are also presented for two observations of JV (Amalthea). Comparison of the data with Liske's (1978) theoretical predictions for the intersatellite positions indicates no systematic bias in the data; a probable scatter of about 15 arcsec in both right ascension and declination is estimated.

Ianna, P. A.↗

Estimating GATE rainfall with geosynchronous satellite images

A method of estimating GATE rainfall from either visible or infrared images of geosynchronous satellites is described. Rain is estimated from cumulonimbus cloud area by the equation R = a sub 0 A + a sub 1 dA/dt, where R is volumetric rainfall, A cloud area, t time, and a sub 0 and a sub 1 are constants. Rainfall, calculated from 5.3 cm ship radar, and cloud area are measured from clouds in the tropical North Atlantic. The constants a sub 0 and a sub 1 are fit to these measurements by the least-squares method. Hourly estimates by the infrared version of this technique correlate well (correlation coefficient of 0.84) with rain totals derived from composited radar for an area of 100,000 sq km. The accuracy of this method is described and compared to that of another technique using geosynchronous satellite images. It is concluded that this technique provides useful estimates of tropical oceanic rainfall on a convective scale.

Stout, J. E.↗

Satellite interferometer as an advanced navigation/communication system

An orthogonal system of interferometry baselines aboard a geostationary satellite is proposed to be used for navigation, surveillance, and traffic control. Position determination is based on the relationship between the measured phase differences, the known and unknown transmitter locations, and other systematic error model parameters using a generalized least-squares estimation procedure. It is shown that position accuracy is critically dependent on the baseline length and on the magnitude of the random component of the measuring errors. Several trade-offs with respect to the system accuracies, the number of users, data rates, hardware costs, etc., are examined. Simultaneous use of the same channels for navigation and data transfer is found feasible and five candidate or 'strawman' interferometer system proposals are presented. It is concluded that the system's performance is excellent in comparison with present or planned systems, and that it is viable in meeting potential user's requirements.

Gopalapillai, G. S.↗

Velocity structure of the shallow lunar crust

Data from the thumper shots of the Apollo 14 and Apollo 16 active seismic experiments, testing whether the velocity variation in the shallow lunar crust (depths less than or equal to 10 m) can be represented by a self-compacting-power-layer or by a constant-velocity-layer model, are analyzed. Although filtering and stacking improved the S/N ratios, it was found that measuring the arrival times or amplitudes of arrivals beyond 32 m was not possible. The data quality precluded a definitive distinction between the power-law velocity variation and the layered-velocity model. Furthermore, it was found that the shallow lunar regolith is made up of fine particles, which supports the idea of a 1/6 power-velocity model. Analysis of the amplitudes of first arrivals revealed large errors in the data due to variations in the geophone sensitivities and shot strengths; a least-squares method, that uses data redundancy was employed to eliminate them.

Gangi, A. F.↗

Photographic stellar photometry with the PDS microdensitometer

A technique for photographic stellar photometry with the PDS microdensitometer is described. It employs a least-squares fit to a model density profile to derive an instrumental magnitude index, an image-abnormality index, and the local value of the background density for each image. The instrumental magnitude index is calibrated in terms of true magnitude by the same methods as for iris photometry. A preliminary test of the method using plates of the open cluster NGC 188 indicates that a precision comparable to or slightly better than that of conventional iris photometry or other methods of PDS reduction may easily be attained. Possibilities for the future elaboration of the technique are mentioned.

Stetson, P. B.↗

Orbit/attitude estimation with Landsat-1 and -2 landmark data

The accuracy of spacecraft orbit and attitude determination is investigated using Landsat-1 and -2 picture data. The data consists of ground control points, of known geodetic coordinates, which are identified on a series of Landsat pictures. Both sequential (extended Kalman filter) and batch (nonlinear Bayesian weighted least-squares) estimation techniques have been implemented in two software systems. Discussion of these systems includes a system overview, mathematical formulation, and sample numerical results. Particular emphasis is given to the application of a spectral analysis technique to derive spacecraft attitude models.

Hall, D. L.↗

A subroutine package for discrete estimation problems

In this paper we describe a well documented, compactly coded, storage efficient, thoroughly tested, and easy to use set of FORTRAN IV subroutines for use in Kalman filter or least-squares applications. The package contains both the UDU covariance factorization and the square root information filter algorithms developed at the Jet Propulsion Laboratory. Numerical reliability of the algorithms is a key feature of the package.

Bierman, G. J.↗

Microcomputer-based doppler systems for weather monitoring

Ground-based microcomputer determines geographical positions of beacons using Doppler data from weather satellites. System requires onnly 7 W and incorporates least-squares iteration to compute positions. Results are printed out in alphanumerics either on CRT or on teletype. 6502 CPU was used, although equivalent processor could be substituted (with appropriate modifications to hardware).

Schmid, P. E.↗

Detailed gravity anomalies from Geos 3 satellite altimetry data

Detailed gravity anomalies are computed from a combination of Geos 3 satellite altimeter and terrestrial gravity data using least-squares principles. The mathematical model used is based on the Stokes' equation modified for a nonglobal solution. Using Geos 3 data in the calibration area, the effects of several anomaly parameter configurations and data densities/distributions on the anomalies and their accuracy estimates are studied. The accuracy estimates for 1 deg x 1 deg mean anomalies from low density altimetry data are of the order of 4 mgal. Comparison of these anomalies with the terrestrial data and also with Rapp's data derived using collocation techniques show rms differences of 7.2 and 4.9 mgal, respectively. Indications are that the anomaly accuracies can be improved to about 2 mgal with high density data. Estimation of 30 in. x 30 in. mean anomalies indicates accuracies of the order of 5 mgal. Proper verification of these results will be possible only when accurate ground truth data become available.

Gopalapillai, G. S.↗

A model of the Venus atmosphere from radio, radar, and occultation observations

A model is presented of the atmosphere and surface of Venus which best fits in the least-squares sense the available radio-brightness, radar cross-section, radio interferometric, and Mariner 5 and 10 radio occultation observations. The determinations of the radius of the planet obtained by others from radar time-delay measurements are included in the data set. The values of the adjusted parameters are: molar fraction of CO2 = 95 plus or minus 3%; fraction of combined nitrogen and argon = 5 plus or minus 3%; total atmospheric opacity at a wavelength of 1 cm = 19.4 plus or minus 1.3; mean radius of the surface = 6050.7 plus or minus 0.8 km; mean dielectric constant of the surface = 4.1 plus or minus 0.2, and percentage of total opacity due to chemical species other than CO2 = 45 plus or minus 12. The model temperature and pressure at the mean surface are 755 K and 91.4 atm, respectively.

Muhleman, D. O.↗

The magnetic field of Mercury

The paper examines the magnetic field observations and their analyses relating to the determination of the Mercury magnetic field. Methods of analyzing data included: (1) comparison of bow shock and magnetopause relative positions at Mercury to the earth, (2) direct spherical harmonic analysis, (3) magnetosphere modeling by an image dipole, and (4) scaling of a mathematical model for the terrestrial magnetosphere. Dipole moments were determined using partial quadrupole and octupole terms to improve the least-square fit of models to observations; analyses by method (2) yield a convergent series of dipole moments values considered to best represent the intrinsic planetary field. Finally, it is suggested that the origin of the magnetic field of Mercury cannot be uniquely determined, but the sources of convective energy may be radiogenic decay and heat release, gravitational settling, and differentiation of processional torques.

Ness, N. F.↗