Path planning of mobile landmarks for localization in wireless sensor networks

Many applications of wireless sensor networks require the sensor nodes to obtain their locations. The main idea in most localization methods has been that some statically deployed nodes (landmarks) with known coordinates (e.g., GPS-equipped nodes) transmit beacons with their coordinates in order to help other nodes to localize themselves. A promising method that significantly reduces the cost is to replace the set of statically deployed GPS-enhanced sensors with one mobile landmark equipped with a GPS unit that moves to cover the entire network. In this case, a fundamental research issue is the planning of the path that the mobile landmark should travel along in order to minimize the localization error as well as the time required to localize the whole network. These two objectives can potentially conflict with each other.In this paper, we first study three different trajectories for the mobile landmark, namely Scan, Double Scan, and Hilbert. We show that any deterministic trajectory that covers the whole area offers significant benefits compared to a random movement of the landmark. When the mobile landmark traverses the network area at a fine resolution, Scan has the lowest localization error among the three trajectories, followed closely by Hilbert. But when the resolution of the trajectory is larger than the communication range, the Hilbert space-filling curve offers significantly better accuracy than the other two trajectories. We further study the tradeoffs between the trajectory resolution and the localization accuracy in the presence of 2-hop localization, in which sensors that have already obtained an estimate of their positions help to localize other sensors. We show that under moderate sensor mobility, 2-hop localization along with a good trajectory reduces the average localization error over time by about 40%.