Geometric Buildup Algorithms for Sensor Network Localization

Algorithm 2

The extended geometric buildup algorithm.

Input: The positions of the anchors, the distances 𝑑_𝑖,𝑗,(𝑖,𝑗)∈𝑁_𝑥∪𝑁_𝑎.

Output: The positions of a set of determined sensors.

Step 1: Set the anchors to be the initial set of determined sensors.

Step 2: Repeat:

    For each undetermined sensor:

     If the sensor has distances to ℓ (ℓ≥3) required determined sensors,

      determine the positions of all ℓ+1 sensors by solving (2.8),

      and update the coordinates of all ℓ+1 sensors by proper

      translation and orthogonal transformation.

     End

    End

    If no sensor can be determined in the loop, stop.

    If all the sensors are determined, stop.