The Random Error Models Of Digital Elevation Model

In this thesis, the random error models of digital elevation model (DEM) are mainly studied. The generalized DEM includes line data, therefore we first study the random error models of spatial line feature. The error models are studied from the following several aspects:(1) Error measure for spatial line feature are provided that are pratically easy to implement by GIS user.(2) Two methods are employed for measuring the line accuracy, Method1, which assumes a normal distribution of residuals population, called Chi-squared approach. Method2is based on the non-parametric theory and no distribution of residuals population is assumed. This method is more generic than method1.(3) The error band models of spatial line feature are studied. This kind of error models provide a graphic visualization of the error of the spatial line feature. Two kinds of error band models are proposed:the first kind is the equivalent probability density error model; the second kind is the confidence model.(4) Methods for assessing the accuracy of DEM with emphasis on robust methods have been studied and are presented. Three methods are presented, the first method is based on the/distribution, the second and third methods are based on robust theory. An experimental study is conducted using Monte Carlo simulation to test the three methods.(5) Four geostatistical interpolation methods:ordinary kriging (OK), universal kriging (UK), kriging with external drift (KED) and ordinary cokriging (OCK) are applied to the generation of DEM error surfaces. The derived DEM slope is used as the exhaustive auxiliary variable for KED and OCK. In addition, the ability to predict the DEM error for the four geostatistical interpolation methods is evaluated by a cross validation method.(6) A new development technique in the estimation of the propagated error of DEM, interpolated by a nonlinear bicubic interpolation method is presented. Two approaches are applied to derive the propagated error of DEMs from nonlinear interpolation. The approaches are based on the error propagation law in statistics and methods in geo-statistics. The use of these two approaches enables the correctness of the derived DEM propagated error estimation results to be cross checked.(7) A new visualization method named confidence model in the description of the propagated error of the DEM, interpolated by (bi)linear method is presented. The analysis has just taken upon one patch firstly, further we extend the result from one patch to all patches, the entire terrain. That's what we do really matter.(8) The bilinear and bicubic interpolated DEM surface model errors are studied. Firstly, the qualitative relationship between the DEM model error and the sampling density for both bilinear interpolation and bicubic interpolation models has been described by convergence analysis. Secondly, the quantitative relationship between the DEM model error and the sampling density has been further derived by means of the numerical analysis.