Toward Collinearity-Avoidable Localization for Wireless Sensor Network

Algorithm 1

2D LE-SA.

Input: : distance matrix between nodes; : coordinate of beacon nodes.

Output: : estimated location of the non-beacons.

  (1) Divide the beacon nodes collected by the unknown node into a series of LU groups in accordance with their IDs and

      by obtaining the combinatorial number, and calculate the DM value of each subgroup. Any one of Formulas (1)–(6)

      can be used to calculate the DM value.

  (2) Compare the DM value of each positioning unit with the set DM threshold value, eliminate the subgroups with poor

      unit quality (low measured value), only keep the subgroups with good quality, and record the DM value of the kept

      positioning units and corresponding estimated locations obtained by using trilateration or multilateration.

      It can be believed that the bigger the DM value is, the better the quality of positioning unit, and it

      has bigger contribution  to the accuracy of final positioning result. Assume there is such a multicollinearity

      weight after the positioning units with poor quality have been eliminated, and its expression is as the following:

  (3) At last, multiply the obtained weight with the estimated location of corresponding positioning unit, and add the

      corresponding products to obtain the final estimated location.