Statistical Modeling Uncertainties of Three-dimensional GIS Features

This article presents a newly developed statistical approach for modeling positional uncertainties of geometric features in three-dimensional geographical information systems (GIS). These features include points, line segments and linear features. The developed approach provides a confidence volume model for each feature type. The true locations of these measured features are included within these volumes with probability larger than a pre-defined confidence level. With the assumptions that positional errors of the two endpoints are independent and follow two three-dimensional normal distributions, the error of any point on the line segment is derived and described by the distribution of the point. The confidence volume model of a line segment is hence derived. Based on this model, the confidence volume model of linear features is further derived.