An application of generalized matrix inversion to sequential least squares parameter estimation
Generalized matrix inversion theory used in formulating recursive algorithm for least squares parameter estimation
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Generalized matrix inversion theory used in formulating recursive algorithm for least squares parameter estimation
Equations for mean error and standard deviation in output of least squares quadratic filter - radar
Approximation optimal trajectories - selection of estimation variables in least squares program, and computer program application
Least integral square error method for antenna array synthesis
Additional observations effect on previous least squares estimate
Error analysis of weighted least squares method to determine lunar gravitational field
Fortran subroutines for least squares curve fitting and solution of simultaneous equations
Mathematical models for effect of tracking systems on RMS errors in spacecraft position and velocity - least squares method
Iterative methods for solving nonlinear least squares problems
Least squares analysis of unified S-band system high speed range rate and X-Y angular data from AS-202 mission
Multivariate functional models for least squares approximation of error tolerance
Maximum possible error in position in least squares elliptical orbit
Convergence acceleration for least squares differential corrections
Least squares gradient method for boundary value and optimization problems found in flight mechanics and astrodynamics
Least squares deconvolution technique for reducing Fabry-Perot spectrometer data to Voigt profiles
The distribution of stress in the cover sheets of thin-wall box beams is analyzed, with regard to the effect of shear deformation in the cover sheets, by the method of least work. Explicit results are obtained for a number of representative cases that show the influence of the following factors on the stress patterns. (1) Variation of stress in spanwise direction as given by elementary beam theory. (2) Value of a parameter called shear-lag aspect ratio which designates the product of span-width ratio of the beam and of the square root of the ratio of effective shear modulus and tensing modulus of the cover sheets. (3) Value of ratio of cover-sheet stiffness to side-web stiffness. (4) Variation of beam height in span direction. (5) Variation of beam width in span direction. (6) Variation of cover-sheet thickness in span direction. General conclusions are drawn from the results obtained. Among them the most important one appears to be the fact that the shear-lag effect depends primarily on the following tow quantities: (1) the value of the shear-lag aspect ratio. (2) the shape of the curve representing the product of the stress of elementary beam theory and of the cover-sheet thickness.
The Space Interferometry Mission (S1M) will measure optical path differences (OPDs) with an accuracy of tens of picometers, requiring precise calibration of the instrument. In this article, we present a calibration approach based on fitting star light interference fringes in the interferometer using a least-squares algorithm. The algorithm is first analyzed for the case of a monochromatic light source with a monochromatic fringe model. Using fringe data measured on the Micro-Arcsecond Metrology (MAM) testbed with a laser source, the error in the determination of the wavelength is shown to be less than 10pm. By using a quasi-monochromatic fringe model, the algorithm can be extended to the case of a white light source with a narrow detection bandwidth. In SIM, because of the finite bandwidth of each CCD pixel, the effect of the fringe envelope can not be neglected, especially for the larger optical path difference range favored for the wavelength calibration.
We show that a semi-definite programming approach can be adopted to determine the least order dynamic output feedback which stabilizes a given linear time invariant plant.