3.1

Centroid: Consider a node with unknown coordinates located in a square region of side d, with four reference nodes on the corners of the square. Consider three cases, when the reference beacons can be received within circles of radius: (a) , (b) R = d, and (c) . In each case, identify the different unique centroid solutions that can be obtained (depending on the location of the unknown node) and the corresponding distinct regions. Estimate the worst case and average location estimate error in each case.

3.2

Centroid versus proximity: Consider three polygonal regions with reference nodes located at the vertices: (a) an equilateral triangle, (b) a square, and (c) a regular pentagon. Assume that an unknown node is uniformly likely to be located anywhere within the region, and that it is always within range of all reference nodes (and can correctly determine its nearest reference node if needed for a proximity determination). For each case compare the centroid localization technique with proximity localization, and indicate which performs better on average. Do you observe a trend in the three cases?

3.3

Overlapping geometric constraints: As in exercise 3.1, consider a node located in the square region of side d with four reference nodes A, B, C, and D located at the corners. Assuming R = d, identify the overlapping geometric region that the unknown node is constrained to be in if it can hear beacons...