Geometry Influence on GDOP in TOA and AOA Positioning Systems

Geometric dilution of precision (GDOP) is defined as the ratio of the root-mean-square position determination error to the root-mean-square measurement error. Based on the Cramer-Rao lower bound (CRLB), new mathematical expressions of GDOP are presented in Time-of-Arrival (TOA) and Angle-of-Arrival (AOA) positioning systems in this paper. The expressions obviously reveal that the geometrical shape of the anchor nodes make a significant influence on GDOP. Then the influence of adding a new anchor node at different locations is analyzed. Simulations show that in both positioning systems, two optimal placement angles exist to make the GDOP smallest, when the original anchor nodes are no uniformly scattered. However, when uniformly scattered, the GDOP keeps constant no matter what angle the new anchor node is placed at. In AOA positioning systems, the GDOP is also affected by the distance between the newly added anchor node and the target, and increases when the distance increases. Meanwhile, the GDOP is always reduced when more anchor nodes are used.