Introducing scale parameters for adjusting area objects in GIS based on least squares and variance component estimation |
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| Authors: | Xiaohua Tong Wenzhong Shi Dajie Liu |
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| Institution: | 1. Department of Surveying and Geo‐informatics , Tongji University , 1239 Siping Road, Shanghai 200092, China xhtong@mail.tongji.edu.cn;3. Advanced Research Center for Spatial Information Technology, Department of Land Surveying and Geo‐informatics , The Hong Kong Polytechnic University , Hong Kong, China;4. Department of Surveying and Geo‐informatics , Tongji University , 1239 Siping Road, Shanghai 200092, China |
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| Abstract: | In this paper, a least‐squares based cadastral parcel area adjustment in geographic information systems (GIS) is developed based on (1) both the areas and coordinates being treated as observations with errors; and (2) scale parameters being introduced to take the systematic effect into account in the process of cadastral map digitization. The area condition equation for cadastral parcel considerations of scale parameters and geometric constraints is first constructed. The effects of the scale error on area adjustment results are then derived, and statistical hypothesis testing is presented to determine the significance of the scale error. Afterwards, Helmert's variance component estimation based on least‐squares adjustment using the condition equation with additional parameters is proposed to determine the weight between the coordinate and area measurements of the parcel. Practical tests are conducted to illustrate the implementation of the proposed methods. Four schemes for solving the inconsistencies between the registered areas and the digitized areas of the parcels are studied. The analysis of the results demonstrates that in the case of significant systematic errors in cadastral map digitization, the accuracies of the adjusted coordinates and areas are improved by introducing scale parameters to reduce the systematic error influence in the parcel area adjustment. Meanwhile, Helmert's variance component estimation method determines more accurate weights of the digitized coordinates and parcel areas, and the least‐squares adjustment solves the inconsistencies between the registered areas and the digitized areas of the parcels. |
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| Keywords: | Scale parameter Variance component estimation Hypothesis testing Accuracy analysis Least squares Cadastral parcel |
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