Optimal Placements for Minimum GDOP With Consideration on the Elevations of Access Nodes

Minimum geometric dilution of precision (GDOP) is desired for a high accuracy in the localization of an unknown node. The optimal placements for the access nodes (or sensing nodes) to achieve the minimum GDOP can be configured by combinations of symmetric cones or regular polyhedrons. The minimum GDOP occurs at the tips of the cones or the center of the polyhedrons. These points are referred to as the designated min-GDOP-points. To benefit the minimum GDOP, the unknown node needs to be at the min-GDOP-points. However, that is hardly the case in practice, because the unknown node could be anywhere in a 3-D working volume or a 2-D area. It is shown that the minimum value of GDOP is determined by the number of access nodes and the dimensions of the measurement, and it does not depend on the elevations of access nodes as long as the topology of the placement is not altered. This motivates the proposed design to use the elevations as an extra degree of freedom to improve the overall localization accuracy in the volume. The goal is to seek the optimal elevations of access nodes to reduce the averaged GDOP values over the volume while keeping the theoretical minimum GDOP value unchanged. The obtained solutions are verified by extensive simulations.