Simulation and Representation of the Positional Errors of Boundary and Interior Regions in Maps

Abstract

The main goal was to describe the positional errors in maps. Although the errors of spatial data are mainly normally distributed, their character often contains admixtures of poorly explained heterogeneities and other uncertainties that are not simply described. Better understanding the error distributions requires performing quantitative and qualitative tests. Portions of the error distributions that can be explained with stochastic behavior were modelled by Monte Carlo simulations. Two principles for the evaluation of projected error models and types were applied: boundary and surface simulation. Both principles address random, locally systematic, and systematic (with the limits at the gross) error distributions. The boundary error was simulated with vector lines and polygons. The surface error was simulated by producing error surfaces that shift every grid point or square-shaped polygon. Visualisations of the simulations include fuzzification process and allow additional understanding of the nature of errors. The study sets were historical maps and land use data derived from them. Additionally we propose a strategy for reconstructing data models and the error models dependent on them.