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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 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1976

On estimating gravity anomalies: A comparison of least squares collocation with least squares techniques

The least squares collocation algorithm for estimating gravity anomalies from geodetic data is shown to be an application of the well known regression equations which provide the mean and covariance of a random vector (gravity anomalies) given a realization of a correlated random vector (geodetic data). It is also shown that the collocation solution for gravity anomalies is equivalent to the conventional least-squares-Stokes' function solution when the conventional solution utilizes properly weighted zero a priori estimates. The mathematical and physical assumptions underlying the least squares collocation estimator are described, and its numerical properties are compared with the numerical properties of the conventional least squares estimator.

Argentiero, P.↗
NASA NTRS1971

Foundations for estimation by the method of least squares

Least squares estimation is discussed from the point of view of a statistician. Much of the emphasis is on problems encountered in application and, more specifically, on questions involving assumptions: what assumptions are needed, when are they needed, what happens if they are not valid, and if they are invalid, how that fact can be detected.

Hauck, W. W., Jr.↗
NASA NTRS1977

On estimating gravity anomalies - A comparison of least squares collocation with conventional least squares techniques

The least squares collocation algorithm for estimating gravity anomalies from geodetic data is shown to be an application of the well known regression equations which provide the mean and covariance of a random vector (gravity anomalies) given a realization of a correlated random vector (geodetic data). It is also shown that the collocation solution for gravity anomalies is equivalent to the conventional least-squares-Stokes' function solution when the conventional solution utilizes properly weighted zero a priori estimates. The mathematical and physical assumptions underlying the least squares collocation estimator are described.

Argentiero, P.↗
NASA NTRS1996

Domain Decomposition Algorithms for First-Order System Least Squares Methods

Least squares methods based on first-order systems have been recently proposed and analyzed for second-order elliptic equations and systems. They produce symmetric and positive definite discrete systems by using standard finite element spaces, which are not required to satisfy the inf-sup condition. In this paper, several domain decomposition algorithms for these first-order least squares methods are studied. Some representative overlapping and substructuring algorithms are considered in their additive and multiplicative variants. The theoretical and numerical results obtained show that the classical convergence bounds (on the iteration operator) for standard Galerkin discretizations are also valid for least squares methods.

Pavarino, Luca F.↗
NASA NTRS1980

Stratospheric NO2 and H2O mixing ratio profiles from high resolution infrared solar spectra using nonlinear least squares

Nonlinear least squares spectral curve fitting has been used to derive vertical mixing ratio profiles for NO2 and H2O above 16 km from high resolution (0.2/cm) solar spectra collected during sunset with a balloon borne interferometer. The NO2 profile shows a sharp peak of 8 ppbv at 32 km falling rapidly to less than 0.5 ppbv at 17 km. The H2O profile shows a broad peak of 6.5 ppmv at 30 km falling to less than 4 ppmv at 17 km.

Niple, E.↗
NASA NTRS1990

Least-Squares Curve-Fitting Program

Least Squares Curve Fitting program, AKLSQF, easily and efficiently computes polynomial providing least-squares best fit to uniformly spaced data. Enables user to specify tolerable least-squares error in fit or degree of polynomial. AKLSQF returns polynomial and actual least-squares-fit error incurred in operation. Data supplied to routine either by direct keyboard entry or via file. Written for an IBM PC X/AT or compatible using Microsoft's Quick Basic compiler.

Kantak, Anil V.↗
NASA NTRS1981

On the method of least squares. II

A least squares method proposed previously for solving a general class of problems is expanded in two ways. First, covariance matrices related to the solution are calculated and their interpretation is given. Second, improved methods of solving the normal equations related to those of Marquardt (1963) and Fletcher and Powell (1963) are developed for this approach. These methods may converge in cases where Newton's method diverges or converges slowly.

Jefferys, W. H.↗
NASA NTRS1978

On least squares collocation

It is shown that the least squares collocation approach to estimating geodetic parameters is identical to conventional minimum variance estimation. Hence, the least squares collocation estimator can be derived either by minimizing the usual least squares quadratic loss function or by computing a conditional expectation by means of the regression equation. When a deterministic functional relationship between the data and the parameters to be estimated is available, one can implement a least squares solution using the functional relation to obtain an equation of condition. It is proved the solution so obtained is identical to what is obtained through least squares collocation. The implications of this equivalance for the estimation of mean gravity anomalies are discussed.

Argentiero, P. D.↗
NASA NTRS1986

On realizations of least-squares estimation and Kalman filtering by systolic arrays

Least-squares (LS) estimation is a basic operation in many signal processing problems. Given y = Ax + v, where A is a m x n coefficient matrix, y is a m x 1 observation vector, and v is a m x 1 zero mean white noise vector, a simple least-squares solution is finding the estimated vector x which minimizes the norm of /Ax-y/. It is well known that for an ill-conditioned matrix A, solving least-squares problems by orthogonal triangular (QR) decomposition and back substitution has robust numerical properties under finite word length effect since 2-norm is preserved. Many fast algorithms have been proposed and applied to systolic arrays. Gentleman-Kung (1981) first presented the trianglular systolic array for a basic Givens reduction. McWhirter (1983) used this array structure to find the least-squares estimation errors. Then by geometric approach, several different systolic array realizations of the recursive least-squares estimation algorithms of Lee et al (1981) were derived by Kalson-Yao (1985). Basic QR decomposition algorithms are considered in this paper and it is found that under a one-row time updating situation, the Householder transformation degenerates to a simple Givens reduction. Next, an improved least-squares estimation algorithm is derived by considering a modified version of fast Givens reduction. From this approach, the basic relationship between Givens reduction and Modified-Gram-Schmidt transformation can easily be understood. This improved algorithm also has simpler computational and inter-cell connection complexities while compared with other known least-squares algorithms and is more realistic for systolic array implementation.

Chen, M. J.↗
NASA NTRS1991

Optimal least-squares finite element method for elliptic problems

An optimal least squares finite element method is proposed for two dimensional and three dimensional elliptic problems and its advantages are discussed over the mixed Galerkin method and the usual least squares finite element method. In the usual least squares finite element method, the second order equation (-Delta x (Delta u) + u = f) is recast as a first order system (-Delta x p + u = f, Delta u - p = 0). The error analysis and numerical experiment show that, in this usual least squares finite element method, the rate of convergence for flux p is one order lower than optimal. In order to get an optimal least squares method, the irrotationality Delta x p = 0 should be included in the first order system.

Jiang, Bo-Nan↗
NASA NTRS2017

Wind Tunnel Strain-Gage Balance Calibration Data Analysis Using a Weighted Least Squares Approach

A new approach is presented that uses a weighted least squares fit to analyze wind tunnel strain-gage balance calibration data. The weighted least squares fit is specifically designed to increase the influence of single-component loadings during the regression analysis. The weighted least squares fit also reduces the impact of calibration load schedule asymmetries on the predicted primary sensitivities of the balance gages. A weighting factor between zero and one is assigned to each calibration data point that depends on a simple count of its intentionally loaded load components or gages. The greater the number of a data point's intentionally loaded load components or gages is, the smaller its weighting factor becomes. The proposed approach is applicable to both the Iterative and Non-Iterative Methods that are used for the analysis of strain-gage balance calibration data in the aerospace testing community. The Iterative Method uses a reasonable estimate of the tare corrected load set as input for the determination of the weighting factors. The Non-Iterative Method, on the other hand, uses gage output differences relative to the natural zeros as input for the determination of the weighting factors. Machine calibration data of a six-component force balance is used to illustrate benefits of the proposed weighted least squares fit. In addition, a detailed derivation of the PRESS residuals associated with a weighted least squares fit is given in the appendices of the paper as this information could not be found in the literature. These PRESS residuals may be needed to evaluate the predictive capabilities of the final regression models that result from a weighted least squares fit of the balance calibration data.

calibration analysis↗
NASA NTRS1992

Multi-element array signal reconstruction with adaptive least-squares algorithms

Two versions of the adaptive least-squares algorithm are presented for combining signals from multiple feeds placed in the focal plane of a mechanical antenna whose reflector surface is distorted due to various deformations. Coherent signal combining techniques based on the adaptive least-squares algorithm are examined for nearly optimally and adaptively combining the outputs of the feeds. The performance of the two versions is evaluated by simulations. It is demonstrated for the example considered that both of the adaptive least-squares algorithms are capable of offsetting most of the loss in the antenna gain incurred due to reflector surface deformations.

Kumar, R.↗
NASA NTRS1986

Fast frequency acquisition via adaptive least squares algorithm

A new least squares algorithm is proposed and investigated for fast frequency and phase acquisition of sinusoids in the presence of noise. This algorithm is a special case of more general, adaptive parameter-estimation techniques. The advantages of the algorithms are their conceptual simplicity, flexibility and applicability to general situations. For example, the frequency to be acquired can be time varying, and the noise can be nonGaussian, nonstationary and colored. As the proposed algorithm can be made recursive in the number of observations, it is not necessary to have a priori knowledge of the received signal-to-noise ratio or to specify the measurement time. This would be required for batch processing techniques, such as the fast Fourier transform (FFT). The proposed algorithm improves the frequency estimate on a recursive basis as more and more observations are obtained. When the algorithm is applied in real time, it has the extra advantage that the observations need not be stored. The algorithm also yields a real time confidence measure as to the accuracy of the estimator.

Kumar, R.↗
NASA NTRS1986

Fast frequency acquisition via adaptive least squares algorithm

A new least squares algorithm is proposed and investigated for fast frequency and phase acquisition of sinusoids in the presence of noise. This algorithm is a special case of more general, adaptive parameter-estimation techniques. The advantages of the algorithms are their conceptual simplicity, flexibility and applicability to general situations. For example, the frequency to be acquired can be time varying, and the noise can be non-Gaussian, nonstationary and colored. As the proposed algorithm can be made recursive in the number of observations, it is not necessary to have a priori knowledge of the received signal-to-noise ratio or to specify the measurement time. This would be required for batch processing techniques, such as the fast Fourier transform (FFT). The proposed algorithm improves the frequency estimate on a recursive basis as more and more observations are obtained. When the algorithm is applied in real time, it has the extra advantage that the observations need not be stored. The algorithm also yields a real time confidence measure as to the accuracy of the estimator.

Kumar, Rajendra↗
NASA NTRS1995

Estimating errors in least-squares fitting

While least-squares fitting procedures are commonly used in data analysis and are extensively discussed in the literature devoted to this subject, the proper assessment of errors resulting from such fits has received relatively little attention. The present work considers statistical errors in the fitted parameters, as well as in the values of the fitted function itself, resulting from random errors in the data. Expressions are derived for the standard error of the fit, as a function of the independent variable, for the general nonlinear and linear fitting problems. Additionally, closed-form expressions are derived for some examples commonly encountered in the scientific and engineering fields, namely ordinary polynomial and Gaussian fitting functions. These results have direct application to the assessment of the antenna gain and system temperature characteristics, in addition to a broad range of problems in data analysis. The effects of the nature of the data and the choice of fitting function on the ability to accurately model the system under study are discussed, and some general rules are deduced to assist workers intent on maximizing the amount of information obtained form a given set of measurements.

Richter, P. H.↗