Vehicle Navigation with Hexagonal Hierarchical Spatial Index

Spatial index of geoinformation theory proposes a new possibility for development of navigation methods with global coverage and rich hierarchical addressing with different precision levels. Hexagonal Hierarchical Spatial Index (H3) and Open Location Codes (OLC) are the most frequently used spatial indexes. Global spatial indexes use indexes instead of geodetic coordinates of latitude and longitude to address any point or data associated with this place. Spatial indexes may use different shapes of cells and different projections could be applied for data transformation from WGS84 to cell space. In this paper, basic methods of vehicle navigation Time of Arrival and Angle of Arrival have been adopted for use in the global spatial index. We use a hexagonal hierarchical spatial index due to multiple advantages of cell shape for support navigation. Vehicle position is identified as a cell address based on available indexes of reference points and measured ranges between vehicle and reference points. Navigation in spatial index is grounded on set theory and logical operations only which makes positioning system cheap for computation in comparison to classical positioning methods. In numerical calculation we consider airplane positioning with Time of Arrival method in H3.