Generalized least squares estimators of linear functional relations with known error-covariance

1978 ◽  
Vol 9 (1) ◽  
pp. 9-26
Author(s):  
H.P. Höschel
Keyword(s):  
Least Squares ◽  
Linear Functional ◽  
Generalized Least Squares ◽  
Error Covariance ◽  
Least Squares Estimators ◽  
Functional Relations

NONLINEARITY AND LEAST SQUARES

CISM journal ◽  
1988 ◽  
Vol 42 (4) ◽  
pp. 321-330 ◽  
Author(s):  
P.J.G. Teunissen ◽  
E.H. Knickmeyer
Keyword(s):  
Least Squares ◽  
Covariance Structure ◽  
Point Of View ◽  
Helmert Transformation ◽  
Know How ◽  
Least Squares Estimators ◽  
Functional Relations ◽  
Geometric Point ◽  
Rotational Invariant ◽  
Almost All

Since almost all functional relations in our geodetic models are nonlinear, it is important, especially from a statistical inference point of view, to know how nonlinearity manifests itself at the various stages of an adjustment. In this paper particular attention is given to the effect of nonlinearity on the first two moments of least squares estimators. Expressions for the moments of least squares estimators of parameters, residuals and functions derived from parameters, are given. The measures of nonlinearity are discussed both from a statistical and differential geometric point of view. Finally, our results are applied to the 2D symmetric Helmert transformation with a rotational invariant covariance structure.

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