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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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Maximum principle least squares /MPLS/ nonlinear filter scheme simplified, using digital simulation for stability and tracking performance
Least squares analyses of uranium and thorium alpha spectra
Exponential downweighting of past data in single stage, weighted least squares trajectory processor for coasting spacecraft
Least square distance curve fitting method
FORTRAN 4 program /FITLOS/ for fitting low-order polynomial splines of two and three degrees by least squares method
Attitude determination and sensor alignment via weighted least squares affine transformations
Biomathematical model and least square estimation from time series data of discrete particle population in stochastic compartmental system
Suboptimal design of closed loop least upper bound fuel control for dynamic systems, minimizing fuel consumption on basis of fixed ultimate error
Least squares and sequential estimation techniques application to Mariner 6 and 7 tracking data analysis, verifying Einstein relativity theory on electromagnetic radiation propagation
Vehicle attitude determination and guidance sensor orientation by vector space matrix method, minimizing errors by weighted least squares affine transformation technique
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.
Probability density functions were derived for errors in the evaluation of unknowns by the least squares method in system of nonhomogeneous linear equations. Coefficients of the unknowns were assumed correct and computational precision were also assumed. A vector space was used, with number of dimensions equal to the number of equations. An error vector was defined and assumed to have uniform distribution of orientation throughout the vector space. The density functions are shown to be insensitive to the biasing effects of the source of the system of equations.
Nonlinear least squares techniques can be used to determine effective thermal conductivity values from experimental data. Comparisons between measured and predicted conductivity values indicate that the analytically determined values can be used with confidence in performing thermal protection system analyses. A study was performed to compare the relative efficiencies of different minimizing techniques; techniques; the method of Peckham was the most efficient.
Investigation of the problem of replacing a certain time-varying linear system by a stationary one. Several quadratic criteria are proposed to aid in determining suitable candidate systems. One criterion for choosing the matrix B (in the stationary system) is initial-condition dependent, and another bounds the 'worst case' homogeneous system performance. Both of these criteria produce weighted least square fits.
The practical aspects of balancing real, flexible rotors were investigated through inclusion of rotor out-of-roundness data at the measurement probe locations. The computer program was demonstrated to be fully capable of handling out-of-roundness data in the investigation. Testing was performed predominantly with a machine having a 41-inch long, 126-pound rotor. This rotor was operated over a speed range encompassing three rotor-bearing system critical speeds. Both balancing procedures were evaluated for several different conditions of initial rotor unbalance. Safe (and slow) passage through all the critical speeds was obtained after two or three balancing runs in most cases. The Least Squares procedure was found to be generally equivalent in capability to the Exact Point-Speed procedure for the configurations studies. (U)
A least-square mixing model incorporating mare basalts, KREEP basalts, anorthosites, anorthositic gabbros, ultramafics, granites, and meteorites was used to estimate the abundances of rock components in lunar soil from the Apollo 11, 12, 15, Luna 16, and Surveyor 5 and 6 landing sites. The predominance of iron-rich mare basalt at the sites is indicated.
Nonlinear least squares techniques can be used to determine effective thermal conductivity values from experimental data. Comparisons between measured and predicted conductivity values indicate that the analytically determined values can be used with confidence in performing thermal protection system analyses. A study was performed to compare the relative efficiencies of different minimizing techniques; the method of Peckham was the most efficient.
Least squares adjustment problems are considered in which the condition equations are nonlinear in both the observations and the adjustment parameters ('unknowns'). A solution algorithm is presented which takes into account the second (as well as the first) order derivatives in the adjustment residuals (observation errors) and the corrections to the initially available approximations to the adjustment parameters. The inclusion of second-order terms in the adjustment residuals is necessary whenever the adjustment residuals themselves cannot be regarded as negligible as compared to the adjustment parameters, i.e., whenever the linearized condition equations would no longer be practically equivalent to the rigorous ones. The consideration of second-order terms in the parameter corrections is completely independent of the second-order terms in the adjustment residuals.