A fast recursive total least squares algorithm for adaptive IIR filtering

2005 ◽  
Vol 53 (3) ◽  
pp. 957-965 ◽  
Author(s):  
Dong-Xia Chang ◽  
Da-Zheng Feng ◽  
Wei-Xing Zheng ◽  
Lei Li
Keyword(s):  
Least Squares ◽  
Total Least Squares ◽  
Least Squares Algorithm

Position Estimation of Single Camera Visual System Based on Total Least Squares Algorithm

2012 ◽  
Vol 239-240 ◽  
pp. 1352-1355
Author(s):  
Jing Zhou ◽  
Yin Han Gao ◽  
Chang Yin Liu ◽  
Ji Zhi Li
Keyword(s):  
Visual System ◽  
Least Squares ◽  
Total Least Squares ◽  
Position Estimation ◽  
Feature Points ◽  
Perspective Theory ◽  
Optical Feature ◽  
The Matrix ◽  
Least Squares Algorithm ◽  
Set Up

The position estimation of optical feature points of visual system is the focus factor of the precision of system. For this problem , to present the Total Least Squares Algorithm . Firstly , set up the measurement coordinate system and 3D model between optical feature points, image points and the position of camera according to the position relation ; Second , build the matrix equations between optical feature points and image points ; Then apply in the total least squares to have an optimization calculation ; Finally apply in the coordinate measuring machining to have a simulation comparison experiment , the results indicate that the standard tolerance of attitude coordinate calculated by total least squares is 0.043mm, it validates the effectiveness; Compare with the traditional method based on three points perspective theory, measure the standard gauge of 500mm; the standard tolerance of traditional measurement system is 0.0641mm, the standard tolerance of Total Least Squares Algorithm is 0.0593mm; The experiment proves the Total Least Squares Algorithm is effective and has high precision.

scholarly journals A Recursive Restricted Total Least-Squares Algorithm

2014 ◽  
Vol 62 (21) ◽  
pp. 5652-5662 ◽  
Author(s):  
Stephan Rhode ◽  
Konstantin Usevich ◽  
Ivan Markovsky ◽  
Frank Gauterin
Keyword(s):  
Least Squares ◽  
Total Least Squares ◽  
Least Squares Algorithm

New Total Least Squares Algorithm and Model with Applications to the Transformation among ITRF Realizations

2020 ◽  
Author(s):  
Jianqing Cai ◽  
Dalu Dong ◽  
Nico Sneeuw
Keyword(s):  
Least Squares ◽  
Coordinate Transformation ◽  
Total Least Squares ◽  
Design Matrix ◽  
Matrix Elements ◽  
Least Squares Problem ◽  
Transformation Parameters ◽  
Least Squares Algorithm

<p>A newly developed Converted Total Least Squares (CTLS) algorithm is introduced, which is to take the stochastic design matrix elements as virtual observations, and to transform the TLS problem into a traditional Least Squares problem. This new algorithm has the advantages that it can not only easily consider the weight of observations and the weight of stochastic design matrix, but also deal with TLS problem without complicated iteration processing, which enriches the TLS algorithm and solves the bottleneck restricting the application of TLS solutions. The notable development of the CTLS reveals also that CTLS estimator is identical to Gauss-Helmert model estimator in dealing with EIV model, especially in the case of similarity coordinate transformation. CTLS has been successfully applied to the estimation of the transformation parameters, their rates and related transformed residuals between actual ITRF realizations of ITRF2014 and ITRF2008 with obvious improvement of their accuracies.</p>

Robust structured total least squares algorithm for passive location

2015 ◽  
Vol 26 (5) ◽  
pp. 946-953 ◽  
Author(s):  
Hao Wu ◽  
Shuxin Chen ◽  
Yihang Zhang ◽  
Hengyang Zhang ◽  
Juan Ni
Keyword(s):  
Least Squares ◽  
Total Least Squares ◽  
Passive Location ◽  
Structured Total Least Squares ◽  
Least Squares Algorithm
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