| 不等式约束最小二乘问题的解及其统计性质 |
| |
| 引用本文： | 彭军还,张亚利,章红平,刘星.不等式约束最小二乘问题的解及其统计性质[J].测绘学报,2007,36(1):50-55. |
| |
| 作者姓名： | 彭军还 张亚利 章红平 刘星 |
| |
| 作者单位： | 重庆大学,土木工程学院,重庆,400045;中国地质大学,土地科学与技术系,北京,100000;重庆大学,土木工程学院,重庆,400045;中国地质大学,土地科学与技术系,北京,100000;上海天文台,上海,200030 |
| |
| 基金项目： | 国家自然科学基金
,
中国科学院测量与地球物理研究所动力大地测量重点实验室开放基金
,
重庆市自然科学基金
,
广西自然科学基金 |
| |
| 摘 要： | 对不等式约束最小二乘平差问题,借助非线性规划中的凝聚约束方法把多个不等式约束转化为一个等式约束,采用拉格朗日极值法求解,解与贝叶斯解或单纯形解一致。其优点在于该解能够表示为观测的明显表达式,由此解的统计性质与最优性可以确定。给出演示该方法的GPS单点定位算例。
|
| 关 键 词： | 不等式约束最小二乘 贝叶斯估计 非线性规划 凝聚约束方法 GPS |
| 文章编号： | 1001-1595（2007）01-0050-06 |
| 修稿时间： | 2005-04-012006-10-30 |
The Solution of Inequality-constrained Least Squares Problem and Its Statistical Properties |
| |
| PENG Jun-huan,ZHANG Ya-li,ZHANG Hong-ping,LIU Xing.The Solution of Inequality-constrained Least Squares Problem and Its Statistical Properties[J].Acta Geodaetica et Cartographica Sinica,2007,36(1):50-55. |
| |
| Authors: | PENG Jun-huan ZHANG Ya-li ZHANG Hong-ping LIU Xing |
| |
| Institution: | 1. School of Civil Engineering, Chongqing University, Chongqing 400044, China ; 2. Department of Land Science and Technology, China Geology University, Beijing 100000, China; 3. Shanghai Astronomical Observatory, Shanghai 200030, China |
| |
| Abstract: | To the inequality constrained least squares adjustment problem,this paper converts many inequality constraints into one equality constraint by using aggregate function of non-linear programming;a basic augmented Lagrangean algorithm can obtain the solutions for equality constrained non-linear programming problem and the solutions are identical to those obtained by the Bayesian method and/or simplex algorithm.The new approach features the advantage that the solutions are the explicit expression of observations,and thus the statistical properties can be easily determined and the general conclusions about the superiority of the estimator can be made.A numerical example on GPS point positioning is given to show the interesting method. |
| |
| Keywords: | Inequality Constrained Least Squares(ICLS) Bayesian estimation non-linear programming aggregate constraint method GPS |
| 本文献已被 CNKI 维普 万方数据 等数据库收录！ |
|
