An Anchor-Free Location Algorithm Based on Transition Coordinates

In some location scenarios where the location information of nodes cannot be mastered in advance, the anchor-free location technology is particularly important. In order to reduce the complicated calculation and eliminate the accumulated error in the traditional anchor-free location algorithm, a new anchor-free location algorithm based on transition coordinates is proposed in this paper. This algorithm is different from the traditional methods such as minimum cost function or inverse matrix. Instead, N initial coordinates are randomly generated as the starting position of the transition coordinates, and the position increment between the transition coordinates and the real coordinates of the node is constantly modified. After K iterations, the convergent position coordinates are finally infinitely close to the real position coordinates of N nodes, and the computational complexity is less than most existing algorithms. As follows, the factors that affect the performance of the algorithm are investigated in the simulation experiment, including the topology structure, positioning accuracy and the total number of nodes, etc. The results show great advantages compared with the traditional anchor-free positioning algorithm. When the topology structure of the initial coordinates changes from a square to a random graph, the number of iterations increases by 15.79%. When the positioning accuracy increased from 1% to 1 parts per thousand, the number of iterations increased by 36.84%. When the number of nodes N is reduced from 9 to 4, the number of iterations is reduced by 63.16%. In addition, the algorithm can also be extended to the field of moving coordinates or three-dimensional spatial positioning, which has broad application prospects.