| 二维直角建筑物规则化的加权总体最小二乘平差方法 |
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| 引用本文： | 李林林,周拥军,周瑜.二维直角建筑物规则化的加权总体最小二乘平差方法[J].武汉大学学报(信息科学版),2019,44(3):422-428. |
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| 作者姓名： | 李林林 周拥军 周瑜 |
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| 作者单位： | 1.上海交通大学船舶海洋与建筑工程学院, 上海, 200240 |
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| 基金项目： | 国家自然科学基金41274012 |
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| 摘 要： | 针对基于遥感数据的二维建筑物的直角化问题，以建筑物边界点的坐标为观测值，以顾及边界正交限制条件的直线斜率和截距为参数，建立附有限制条件的变量误差（errors-in-variables，EIV）模型。考虑观测向量和设计矩阵相关的情况，给出了增广设计矩阵的协方差阵的计算方法，推导了附限制条件的通用加权总体最小二乘（weighted total least squares，WTLS）平差算法，以及近似精度评定算法和仅含二次型限制条件的WTLS平差方法。理论和算例分析表明，在建筑物重建问题中，附有限制条件的EIV模型比经典附有限制条件的Gauss-Helmert模型易于构建，所提的WTLS算法快速收敛速度快，对拓展WTLS平差方法的应用具有理论与实践意义。
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| 关 键 词： | 限制条件 EIV模型 加权总体最小二乘 建筑物直角化 |
| 收稿时间： | 2017-04-21 |
A Weighted Total Least Squares Adjustment Method for Building Regularization |
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| Affiliation: | 1.School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiaotong University, Shanghai 200240, China2.Xi'an Institute of Surveying and Mapping, Xi'an 710054, China3.State Key Laboratory of Geo-Information Engineering, Xi'an 710054, China |
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| Abstract: | An errors-in-variable (EIV) with arbitrary constraints is proposed for the purpose of building regularization from remote sensed data, in which the edge points are treated as measurements, the constrained slopes and intercepts of each edge are chosen as parameters. Assuming the measurement vector and the design matrix are mutually correlated, the scheme of calculating the dispersion matrix of augmented matrix is suggested. A generic constrained weighted total least squares(WTLS) algorithm is derived with an approximate accuracy assessment method, and the WTLS algorithm of a quadratic constrained EIV problem is given as a specific case. Theoretic analysis and data experiment demonstrate the advantages of an EIV model compared with a Gauss-Helmert model in building regularization problem, and the rapid convergence rate of proposed WTLS algorithm. It aims to promote WTLS adjustment methods, and to expand the applications of total least squares method in new surveying technology with a certain theoretical and practical significance. |
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