scholarly journals Closed form least-squares solution to 3D symmetric Helmert transformation with rotational invariant covariance structure

2015 ◽  
Vol 51 (2) ◽  
pp. 237-244 ◽  
Author(s):  
Guobin Chang
Keyword(s):  
Least Squares ◽  
Closed Form ◽  
Covariance Structure ◽  
Helmert Transformation ◽  
Least Squares Solution ◽  
Rotational Invariant

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.

scholarly journals 2-Norm-Based Iterative Design of Filterbank Transceivers: A Control Perspective

2008 ◽  
Vol 2008 ◽  
pp. 1-7 ◽  
Author(s):  
Yang Shi ◽  
Tongwen Chen
Keyword(s):  
Optimal Design ◽  
Least Squares ◽  
Closed Form ◽  
Design Procedure ◽  
Perfect Reconstruction ◽  
Good Frequency ◽  
Noise Attenuation ◽  
Error Criterion ◽  
Iterative Design ◽  
Least Squares Solution

This paper considers design of filterbank-based transceivers. A composite error criterion is proposed to capture all the three traditional distortions. Incorporating noise attenuation and filter bandlimiting properties into this error criterion, an optimal design procedure is developed and applied to a transceiver design example, yielding an FIR transceiver that has good frequency-selective properties and is close to perfect reconstruction. As a least-squares solution is given in closed form in each iteration, the algorithm is easy to implement.

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