Introducing scale parameters for adjusting area objects in GIS based on least squares and variance component estimation

Xiaohua Tong, Wen Zhong Shi, Dajie Liu

Research output: Journal article publicationJournal articleAcademic researchpeer-review

11 Citations (Scopus)


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.
Original languageEnglish
Pages (from-to)1413-1432
Number of pages20
JournalInternational Journal of Geographical Information Science
Issue number11
Publication statusPublished - 1 Nov 2009


  • Accuracy analysis
  • Cadastral parcel
  • Hypothesis testing
  • Least squares
  • Scale parameter
  • Variance component estimation

ASJC Scopus subject areas

  • Geography, Planning and Development
  • Information Systems
  • Library and Information Sciences

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