THE SELECTION OF POLE AND CONDITION EQUATION IN THE LEAST SQUARES ADJUSTMENT OF LINEAR DIMENSIONS IN A GEODETIC QUADRILATERAL

1960 ◽  
Vol 15 (116) ◽  
pp. 266-270 ◽  
Author(s):  
B. T. Murphy
Keyword(s):  
Least Squares ◽  
Linear Dimensions ◽  
Least Squares Adjustment ◽  
Condition Equation ◽  
Selection Of

LEAST SQUARES ADJUSTMENT OF LINEAR DIMENSIONS IN A GEODETIC QUADRILATERAL

1957 ◽  
Vol 14 (106) ◽  
pp. 175-184 ◽  
Author(s):  
B. T. Murphy ◽  
G. J. Thornton-Smith
Keyword(s):  
Least Squares ◽  
Linear Dimensions ◽  
Least Squares Adjustment

Bridging the Gap between Quantitative and Qualitative Historical Research: an application of multiple regression analysis and homogeneity analysis with alternating least squares

1996 ◽  
Vol 8 (3) ◽  
pp. 133-144 ◽  
Author(s):  
María del Mar del Pozo Andrés ◽  
Jacques F A Braster
Keyword(s):  
Least Squares ◽  
Multiple Regression ◽  
Historical Research ◽  
Alternating Least Squares ◽  
Categorical Variables ◽  
Two Dimensional ◽  
Homogeneity Analysis ◽  
Regression Approach ◽  
Dimensional Picture ◽  
Selection Of

In this article we propose two research techniques that can bridge the gap between quantitative and qualitative historical research. These are: (1) a multiple regression approach that gives information about general patterns between numerical variables and the selection of outliers for qualitative analysis; (2) a homogeneity analysis with alternating least squares that results in a two-dimensional picture in which the relationships between categorical variables are graphically presented.

scholarly journals Using Least-Squares Residuals to Assess the Stochasticity of Measurements—Example: Terrestrial Laser Scanner and Surface Modeling

2021 ◽  
Vol 5 (1) ◽  
pp. 59
Author(s):  
Gaël Kermarrec ◽  
Niklas Schild ◽  
Jan Hartmann
Keyword(s):  
Least Squares ◽  
Laser Scanner ◽  
Real Data ◽  
Point Clouds ◽  
Statistical Testing ◽  
Normal Vector ◽  
Engineering Structures ◽  
3D Point Clouds ◽  
Least Squares Adjustment ◽  
Correlation Parameters

Terrestrial laser scanners (TLS) capture a large number of 3D points rapidly, with high precision and spatial resolution. These scanners are used for applications as diverse as modeling architectural or engineering structures, but also high-resolution mapping of terrain. The noise of the observations cannot be assumed to be strictly corresponding to white noise: besides being heteroscedastic, correlations between observations are likely to appear due to the high scanning rate. Unfortunately, if the variance can sometimes be modeled based on physical or empirical considerations, the latter are more often neglected. Trustworthy knowledge is, however, mandatory to avoid the overestimation of the precision of the point cloud and, potentially, the non-detection of deformation between scans recorded at different epochs using statistical testing strategies. The TLS point clouds can be approximated with parametric surfaces, such as planes, using the Gauss–Helmert model, or the newly introduced T-splines surfaces. In both cases, the goal is to minimize the squared distance between the observations and the approximated surfaces in order to estimate parameters, such as normal vector or control points. In this contribution, we will show how the residuals of the surface approximation can be used to derive the correlation structure of the noise of the observations. We will estimate the correlation parameters using the Whittle maximum likelihood and use comparable simulations and real data to validate our methodology. Using the least-squares adjustment as a “filter of the geometry” paves the way for the determination of a correlation model for many sensors recording 3D point clouds.

Supermatrix Approach to Least-Squares Adjustment

1968 ◽  
Vol 22 (5) ◽  
pp. 22
Author(s):  
Irving H. Siegel
Keyword(s):  
Least Squares ◽  
Least Squares Adjustment

Variable-Frequency Prony Method in the Analysis of Electrical Power Quality

2012 ◽  
Vol 19 (1) ◽  
pp. 39-48 ◽  
Author(s):  
Jarosław Zygarlicki ◽  
Janusz Mroczka
Keyword(s):  
Least Squares ◽  
Power Quality ◽  
Electrical Power ◽  
Electric Energy ◽  
Variable Frequency ◽  
Prony Method ◽  
Analysis Window ◽  
Proposed Modification ◽  
Selection Of

Variable-Frequency Prony Method in the Analysis of Electrical Power QualityThe article presents a new modification of the the least squares Prony method. The so-called variable-frequency Prony method can be a useful tool for estimating parameters of sinusoidal components, which, in the analyzed signal, are characterized by time-dependent frequencies. The authors propose use of the presented method for testing the quality of electric energy. It allows observation of phenomena which, when using traditional methods, are averaged in the analysis window. The proposed modification of least squares Prony method is based on introduction and specific selection of a frequency matrix. This matrix represents frequencies of estimated components and their variability in time.

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