The Research On Uncertainty Propagation In GIS

Uncertainty propagation of spatial databases is one of the most major problems, and alsoa focus of research in GIS. It is well known that uncertainty can be described by error, whichis inevitable for spatial data. It should be noted that error would be propagated andaccumulated along with the GIS operations, lastly has an important effect on the results ofdecision analysis. At present, the research on error propagation has achieved greatdevelopments. However, most of them are based on the linear propagation theory, while thenonlinearity of system function such as many GIS operations is seldom considered. Thus thedeep study of methods of error propagation, especially the nonlinear propagation, istheoretically of significant academic contributions and application values.In order to improve the theoretical precision of propagation process, in this paper, westart by increasing the approximate degree of Taylor-series expansions, and focus on thestudy of error propagation methods based on the high-order Taylor-series expansion. Then thevalidity of these methods is checked by comparing them with Monte Carlo simulations andthe moment-design method through several simulation experiments. Finally, these methodsare applied to the uncertainty evaluation of practical problems in GIS. The main researchworks are as follows:(1) We study the existing basic theories and methods, and summarize and compare thesemethods by simulation experiments in order to provide guidance for practical applications inGIS.(2) Based on the high-order Taylor-series expansion method, we present the errorpropagation methods for the line-on-line, line-on-polygon, and polygon-on-polygon ofoverlay operations in GIS. And the effectiveness of the proposed methods in improvingprecision are verified and compared by simulation experiments.(3) To use the spatial correlation of geographic variables, high-order Taylor-seriesexpansion methods are extended to the situations involving multi-dimensional output vectors,which provide strict theoretical support for the study of error propagation in polygon overlayoperations in GIS. The significance of the proposed methods is shown. (4) According to the matrix-form formulae of Taylor-series expansion methods, errorpropagation formulae for area measurement in GIS is given correspondingly and validated bytheoretical derivation and simulation experiments.