A Combined Localization Algorithm for Wireless Sensor Networks

Algorithm 1

The MA-MDS algorithm.

Inputs

(i) A: the set of anchor nodes locations.

(ii) k: threshold.

(iii) : the estimated coordinates of i-level nodes.

Outputs

(i) : the estimated coordinates of all nodes in the entire WSNs.

tep 1: Low-level nodes positioning

For i=1 to k do

(i) Find the set of i-level nodes.

(ii) Running the multilateral algorithm to obtain the estimated coordinates of the i-level nodes, ;

(iii) Refresh the set of anchor nodes coordinates, ;

End for.

tep 2: High-level nodes positioning

(i) Get the weighted shortest path distance matrix by using Floyd algorithm, ;

(ii) Running MDS algorithm, get relative coordinates for all nodes in WSNs, ;

the relative coordinates of anchor nodes are ;

(iii) Transform relative coordinates to absolute coordinates by PA algorithm,

get finally estimated coordinates of all nodes, ;

tep 3: Calculation error

(i) Calculate average localization error by Eq. (1);