INTRODUCTION OF EIO MODEL IN TLS METHOD TO CALCULATE THE COORDINATES TRANSFORMATION BY HELMERT’S FORMULA

InterConf ◽  
2021 ◽  
pp. 256-266
Author(s):  
Huynh Nguyen Dinh Quoc ◽  
Dang Xuan Truong ◽  
Tran Thi Bao Tram
Keyword(s):  
Least Squares ◽  
Iterative Algorithm ◽  
Coordinate Transformation ◽  
Least Squares Method ◽  
Total Least Squares ◽  
Geodetic Data ◽  
Large Dimension ◽  
Accuracy Evaluation ◽  
Matrix Inverse ◽  
Coordinates Transformation

The EIO (Errors In Observations) model is used in the total least squares method to calculate, process geodetic data. Next to the classical least squares method, it is applied to solve more solutions. When we use the EIO model in calculus and process, performing a matrix inverse has a large dimension will be avoided. Moreover, the calculation and accuracy evaluation steps are based on the iterative algorithm to get the results. In this paper, the authors use the procedure of calculating and evaluating the accuracy of the EIO model in the experimental calculation of the coordinate transformation according to the Helmert formula

scholarly journals On weighted total least squares adjustment for solving the nonlinear problems

2014 ◽  
Vol 4 (1) ◽  
Author(s):  
C. Hu ◽  
Y. Chen ◽  
Y. Peng
Keyword(s):  
Data Processing ◽  
Least Squares ◽  
Least Squares Method ◽  
Nonlinear Problems ◽  
Total Least Squares ◽  
Geodetic Data ◽  
Least Square ◽  
Weight Matrix ◽  
Weighted Total Least Squares ◽  
Least Squares Adjustment

AbstractIn the classical geodetic data processing, a non- linear problem always can be converted to a linear least squares adjustment. However, the errors in Jacob matrix are often not being considered when using the least square method to estimate the optimal parameters from a system of equations. Furthermore, the identity weight matrix may not suitable for each element in Jacob matrix. The weighted total least squares method has been frequently applied in geodetic data processing for the case that the observation vector and the coefficient matrix are perturbed by random errors, which are zero mean and statistically in- dependent with inequality variance. In this contribution, we suggested an approach that employ the weighted total least squares to solve the nonlinear problems and to mitigate the affection of noise in Jacob matrix. The weight matrix of the vector from Jacob matrix is derived by the law of nonlinear error propagation. Two numerical examples, one is the triangulation adjustment and another is a simulation experiment, are given at last to validate the feasibility of the developed method.

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).

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