Converted Total Least Squares Method and Gauss-Helmert Model with Applications to Coordinate Transformations

2020 ◽  
pp. 117-125
Author(s):  
Jianqing Cai ◽  
Dalu Dong ◽  
Nico Sneeuw ◽  
Yibin Yao
Keyword(s):  
Least Squares ◽  
Least Squares Method ◽  
Total Least Squares ◽  
Coordinate Transformations

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).

scholarly journals Array Pattern Synthesis Using a Hybrid Differential Evolution and Analytic Algorithm

Electronics ◽  
2021 ◽  
Vol 10 (18) ◽  
pp. 2227
Author(s):  
Rui Li ◽  
Le Xu ◽  
Xiaoqun Chen ◽  
Yong Yang ◽  
Xiaoning Yang ◽  
...  
Keyword(s):  
Differential Evolution ◽  
Least Squares ◽  
Antenna Array ◽  
Least Squares Method ◽  
Total Least Squares ◽  
Weight Matrix ◽  
Pattern Synthesis ◽  
Application Range ◽  
De Algorithm ◽  
Array Pattern

In this paper, a hybrid differential evolution and weight total least squares method (HDE-WTLSM) is proposed for antenna array pattern synthesis. A variable diagonal weight matrix is introduced in total least squares method. Then, the weight matrix is optimized by differential evolution (DE) algorithm to control the differences of the desired level and the obtained level in different directions. This algorithm combines the advantages of evolutionary algorithm and numerical algorithm, so it has a wider application range and faster convergence speed. To compare HDE-WTLSM with DE algorithm and typical numerical algorithms, these methods are applied to a linear antenna array and a conformal truncated conical array. Using our method, lower sidelobe levels and deeper nulls are obtained. The simulation results verify the validity and efficiently of HDE-WTLSM.

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