参数带有区间约束的平差模型迭代算法

doi:10.11947/j.AGCS.2018.20160407

测绘学报 ›› 2018, Vol. 47 ›› Issue (8): 1141-1147.doi: 10.11947/j.AGCS.2018.20160407

参数带有区间约束的平差模型迭代算法

谢雪梅^1,2,3, 宋迎春^1,2, 肖兆兵²

1. 中南大学有色金属成矿预测与地质环境监测教育部重点实验室, 湖南长沙 410083;
2. 中南大学地球科学与信息物理学院, 湖南长沙 410083;
3. 中南林业科技大学土木工程学院, 湖南长沙 410004

收稿日期:2016-08-18 修回日期:2017-10-17 出版日期:2018-08-20 发布日期:2018-08-22
通讯作者: 宋迎春 E-mail:csusyc@csu.edu.cn
作者简介:谢雪梅(1977-),女,博士生,研究方向为测量平差数据处理。E-mail:xiexuemei_2003@126.com
基金资助:
国家自然科学基金（41574006；41674009）

Parameter Estimate Algorithm in Adjustment Model with Interval Constraint

XIE Xuemei^1,2,3, SONG Yingchun^1,2, XIAO Zhaobing²

1. Key Laboratory of Metallogenic Prediction of Nonferrous Metals and Geological Environment Monitoring of Ministry of Education, Central South University, Changsha 410083, China;
2. School of Geosciences and Info-physics, Central South University, Changsha 410083, China;
3. School of Civil Engineering, Central South University of Forestry and Technology, Changsha 410004, China

Received:2016-08-18 Revised:2017-10-17 Online:2018-08-20 Published:2018-08-22
Supported by:
The National Natural Science Foundation of China(Nos. 415074006;41674009)

摘要/Abstract

摘要： 测量平差模型中的参数通常存在一些不确定的附加信息或先验信息，充分利用它们可以对部分参数进行约束，从而保证参数解的唯一性和稳定性。本文主要研究参数带有区间约束的平差模型。即，利用矩阵正则分裂方法，将平差问题转化成一个简单的二次规划问题，建立了一种新的参数估计迭代算法，并证明了算法的收敛性。最后通过实例说明了新方法可以提高参数估计的效率，降低模型的不适定性，保持参数先验信息中的统计、几何或物理意义。

关键词: 不确定性, 先验信息, 区间约束, 平差模型, 病态问题

Abstract: There are usually some uncertain additional information or prior information on parameters in surveying adjustment models,which can constraint on the parameters,and guarantee uniqueness and stability of parameters solution.This paper mainly focused on the studies of adjustment model with box constraints.Firstly,using the regular splitting method of matrix,adjustment model is converted to a simple quadratic programming problem.Then a new iterative algorithm of parameter estimation is established.The algorithm convergence is given.Finally,with example,it is confirmed that the proposed method can improve efficiency of parameter estimation,reduce ill-posed characteristic of model and keep statistical,geometric or physical significance of prior information.

Key words: uncertainty, prior information, interval constraint, adjustment model, ill-posed problem

中图分类号:

P207

谢雪梅, 宋迎春, 肖兆兵. 参数带有区间约束的平差模型迭代算法[J]. 测绘学报, 2018, 47(8): 1141-1147.

XIE Xuemei, SONG Yingchun, XIAO Zhaobing. Parameter Estimate Algorithm in Adjustment Model with Interval Constraint[J]. Acta Geodaetica et Cartographica Sinica, 2018, 47(8): 1141-1147.

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参数带有区间约束的平差模型迭代算法

Parameter Estimate Algorithm in Adjustment Model with Interval Constraint

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