Abstract: A grid-based transmission system for determining relative positions of vehicles in a grid quadrangle of a reference grid, each vehicle having a transmitter and a receiver, comprising determining an absolute position of a vehicle. A reference grid is obtained. A reference point for the reference grid is assigned; and a relative position of the vehicle relative to the reference point is generated. The reference grid is a stored and previously generated reference grid, or is generated based on the absolute position and a transmission range of a transmitter. The vehicle sends a position message containing the relative position; the transmission range; an identity of the vehicle; an identity for all other vehicles that have previously sent a position message received by the vehicle; and the relative position of the all other vehicles.

Abstract: A re-routing apparatus and method for calculating an optimum path from a path deviated position to an original path in a navigation system, and a navigation system using this apparatus and method are disclosed. When a movable body traveling on a predetermined path provided from a navigation system has deviated from the path, links are selected which meet links extending in a direction having small accumulated travel cost from the deviated position link from among links included in the original path, and then paths traveling from the deviated position to the destination via the selected links are determined as re-routing paths.

Abstract: Navigation apparatus, methods, and programs merge and correct a plurality of types of past traffic information. The apparatus, methods, and programs may store a plurality of types of past traffic information, each type of past traffic information having a priority and may merge the stored past traffic information in accordance the priorities. The apparatus, methods, and programs may detect adjacency relationships among the plurality of links; and, if a detected link number indicates that the corresponding link is not adjacent to adjacent links, replaces the detected link number for the link, the replaced link number indicating that the link is adjacent to the adjacent links.