Understanding Error Propagation in Multihop Sensor Network Localization

In multihop localization procedures where not every node at unknown positions (i.e., sensors) can directly measure distances to nodes at known positions (i.e., anchors), sensor localization errors normally propagate (i.e., increase) as sensors progressively more distant from anchors are localized. To understand error propagation, we consider a primitive localization scenario: Nodes are deployed within a disk according to a homogeneous Poisson point process, the nodes around the disk center are anchors, the other nodes are sensors, and sensors are localized from the disk center to the outside in a hop-by-hop manner. Supposing noisy distance measurements between adjacent nodes, we analyze the quantitative relationship among sensor localization errors, minimal hop counts from sensors to anchors, the sensor density, and the noise level of distance measurements. This relationship clearly reflects the properties of error propagation and is greatly helpful to the design and deployment of large-scale sensor networks. Finally, a simulation analysis based on actual localization procedures and the Cramér-Rao lower bound confirms our results.