Universal Error Propagation Law

As an ubiquitous statistical theory, Gaussian Distribution (GD) or Gaussian Error Propagation Law (GEPL) has been widely used for modelling random errors in many engineering and application fields since 1809. In recent years, this theory has been extended to handle the uncertainties of spatial data in GIS, such as positional error modelling. But most of the results for spatial error modelling based on GD are contradictory with common senses and natural laws, such as energy law and Tobler’s First Law (TFL) in geography. This paper presents a novel statistical approach for rigorous modelling of positional errors of geometric features in spatial databases. Based on Generalized Gaussian Distribution (GGD) and using errors in local points as the fundamental building blocks, a new spatial statistical theory – Universal Error Propagation Law (UEPL) is presented to handle global error propagations for spatial random sets (or objects). Practical examples and simulations are given to illustrate the error propagations based on UEPL for various spatial objects. Finally, the relationships between UEPL and Newtown’s Universal Gravitation Law (NUGL) and TFL have been successfully established, which shows that UEPL is a new discovered natural law for spatial information field.