Verified stochastic methods in geographic information system applications with uncertainty

• We discuss modeling of GPS data with uncertainty using interval arithmetic.
• We offer a complete workflow concept for GIS applications.
• We extended the DSI toolbox by functions to compute imprecise GPS localization.
• We develop an ontology-based semantic querying mechanism with geometric uncertainty.
• We discuss several approaches to visualize uncertain localization.

Modern localization techniques are based on the Global Positioning System (GPS). In general, the accuracy of the measurement depends on various uncertain parameters. In addition, despite its relevance, a number of localization approaches fail to consider the modeling of uncertainty in geographic information system (GIS) applications. This paper describes a new verified method for uncertain (GPS) localization for use in GPS and GIS application scenarios based on Dempster-Shafer theory (DST), with two-dimensional and interval-valued basic probability assignments. The main benefit our approach offers for GIS applications is a workflow concept using DST-based models that are embedded into an ontology-based semantic querying mechanism accompanied by 3D visualization techniques. This workflow provides interactive means of querying uncertain GIS models semantically and provides visual feedback.