A Fast Search Algorithm in Adjustment Model with Inequality Constraint

XIE Xuemei; SONG Yingchun; XIAO Zhaobing

doi:10.13203/j.whugis20160435

Volume 43 Issue 9

Sep. 2018

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Geomatics and Information Science of Wuhan University > 2018 > 43(9): 1349-1354. > DOI: 10.13203/j.whugis20160435

XIE Xuemei, SONG Yingchun, XIAO Zhaobing. A Fast Search Algorithm in Adjustment Model with Inequality Constraint[J]. Geomatics and Information Science of Wuhan University, 2018, 43(9): 1349-1354. DOI: 10.13203/j.whugis20160435

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A Fast Search Algorithm in Adjustment Model with Inequality Constraint

1.
School of Geosciences and Info-Physics, Central South University, Changsha 410083, China
2.
School of Civil Engineering, Central South University of Forestry and Technology, Changsha 410004, China

Funds:

The National Natural Science Foundation of China 41574006

The National Natural Science Foundation of China 41674009

The National Natural Science Foundation of China 41674012

More Information

Author Bio:
XIE Xuemei, PhD candidate, lecturer, specializes in surveying data processing. E-mail:xiexuemei_2003@126.com
Corresponding author:
SONG Yingchun, PhD, professor. E-mail:csusyc@qq.com
Received Date: April 22, 2017
Published Date: September 04, 2018

Graphical Abstract

Abstract

Abstract

There usually exists some prior information with inequality constraint in the survey of adjustment model. The uniqueness and stability of the solution can be guaranteed by making full use of it. However, the existing adjustment algorithms with inequality constrain, which are mainly based on optimization theory, are usually complex. They need to select the effective constraint or establish penalty function. This paper mainly studies the adjustment model with inequality constraint, in which the inequality constraint is considered as a feasible region on the basis of the least squares adjustment rule and the Fisher function is used to search the optimal solution that minimizes the sum of squared errors, and sufficient necessary conditions for the optimal feasible solution are derived. A non-precise fast search based on Wolfe-Powell algorithm is given in the feasible region, which reduces the computational complexity, a new adjustment algorithm with inequality constraint is presented. The given algorithm, in which the adjustment criterion is consistent with that of the least squares adjustment criteria, does not require matrix inversion operation, and can solve some of the large dimension adjustment problem with inequality constrain.
- prior information,
- inequality constraint,
- adjustment model,
- quadratic programming,
- Fisher function

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References

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