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.

TOTAL LEAST SQUARES FOR ESTIMATION OF THE GROSS OUTPUT VECTOR

2020 ◽  
Author(s):  
Dmitriy Vladimirovich Ivanov ◽  
Keyword(s):  
Least Squares ◽  
Least Squares Method ◽  
Direct Costs ◽  
Total Least Squares ◽  
Test Cases ◽  
Output Vector ◽  
Final Consumption ◽  
The Matrix

The article proposes the estimation of the gross output vector in the presence of errors in the matrix of direct costs and the final consumption vector. The article suggests the use of the total least squares method for estimating the gross output vector. Test cases showed that the accuracy of the proposed estimates of the gross output vector is higher than the accuracy of the estimates obtained using the classical least squares method (OLS).

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

On Total Least Squares Estimation for Longitudinal Errors-in-Variables Models

2021 ◽  
pp. 359-380
Author(s):  
Rauf Ahmad ◽  
Silvelyn Zwanzig
Keyword(s):  
Least Squares ◽  
Repeated Measures ◽  
Measurement Errors ◽  
Mixed Model ◽  
Linear Mixed Model ◽  
Total Least Squares ◽  
Special Focus ◽  
Design Matrix ◽  
Fixed Part ◽  
Set Up

The objective of this study is to evaluate the total least squares (TLS) estimator for the linear mixed model when the design matrix is subject to measurement errors, with special focus on models for longitudinal or repeated-measures data. We consider measurement errors only in the design matrix concerning the fixed part of the model and estimate its corresponding parameter vector under the TLS set up. After treating two variants of the general case, the random coefficient model is discussed as a special case. We evaluate conditions, on the design matrices as well as on variance component parameters, under which a reasonable TLS estimator can be expected in such models. Analysis of a real data example is also provided.

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>

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