scholarly journals A total least squares solution to a 3D coordinate transformation parameters of large Euler angles with closure constrain

2020 ◽  
Vol 513 ◽  
pp. 012045
Author(s):  
Jian Qin ◽  
Jinyun Guo ◽  
Xiaofei Xu
Keyword(s):  
Least Squares ◽  
Coordinate Transformation ◽  
Total Least Squares ◽  
Euler Angles ◽  
Least Squares Solution ◽  
Transformation Parameters

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>

Comparing of Coordinate Transformation Based on Total Least Squares and Least Squares

2014 ◽  
Vol 522-524 ◽  
pp. 1211-1214
Author(s):  
Qing Wu Meng ◽  
Lu Meng
Keyword(s):  
Least Squares ◽  
Coordinate Transformation ◽  
Least Square Method ◽  
Coefficient Matrix ◽  
Total Least Squares ◽  
Least Square ◽  
Experimental Results ◽  
Transformation Models ◽  
Total Least Square

The coordinate transformation models based on least square method and total least square are built and discussed. The least square model only includes the errors of observation vectors, the total least square model simultaneously takes into consideration to the errors of observation vectors and the errors of coefficient matrix. The both models are verified and compared in experiment. The experimental results showed that the model of total least square is more in line with actual, and more reasonable than by least square theoretically, and the coordinate transformation solution result of total least square with least square is more near.

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