# An Anchor-Free Location Algorithm Based on Transition Coordinates
## 5 Simulation Result
### Relationship Between the Number of Nodes N and the Number of Iterations  
The problem considered in this paper is to locate the relative position graph between multiple members, and the randomly generated node coordinates should ensure that the connection degree is greater than the specified minimum connection degree. Usually the minimum connection degree is set as 3, that is, \(N\geq 3\). Next, we will change the value of  
Figure 4: The relationship between positioning accuracy and the number of iterations: (**a**) the real position several members; (**b**) initial hypothetical positions of several member iterations; (**c**) the 1 st iteration; (**d**) the 26 th iteration; (**e**) when the EP increases from 0.1 to 0.01, 0.001, 0.0001, the relationship between the number of iterations of the algorithm and EP.  
the number of nodes \(N\) in the first test, and the remaining simulation conditions remain unchanged. Taking \(N=6\) as an example, we will show the iterative process and give the relationship between the error proportion and the number of iterations when \(N\) takes different values. Figure 5 shows the simulation results.  
From Figure 5, we can see that when the number of nodes \(N\) is 4, the number of iterations is 7. When increasing from 4 to 6, the number of iteratio  
Figure 5: The relationship between the number of nodes \(N\) and the number of iterations: (**a**) the real position several members; (**b**) initial hypothetical positions of several member iterations; (**c**) the 1 st iteration; (**d**) the 11 th iteration; (**e**) when the number of nodes ranges from 4 to 6, 9, or 12, the relationship between the number of iterations of the algorithm and EP.  
increasing from 6 to 9, the number of iterations increases by 8; when increasing from 9 to 12, the number of iterations increases by 22. With the increase in the number of nodes \(N\), the number of iterations required by the algorithm in this paper also gradually increases, but the number of iterations increased each time by the algorithm, that is, the amount of computation required by the algorithm did not increase much with the increase in the number of nodes. Therefore, the algorithm can be applied to positioning in various complex scenarios and quickly obtain the position coordinates of nodes.  
As can be seen from Figure 6, the positioning error of the anchor-free location algorithm based on transition coordinates proposed in this paper decreases with the increase in the number of nodes. Compared with the classical algorithm, the AFL, R-AFL, and MDS-MAP algorithms have the smallest positioning error and the best positioning performance. Secondly, the positioning error of R-AFL algorithm is better than that of traditional AFL and MDS, because the coordinate system established by R-AFL in the positioning process is more accurate and the adopted algorithm optimizes the position of nodes in the network, so it has better positioning performance. The AFL algorithm performs better than MDS when the number of nodes is small, but its performance is surpassed by MDS when the number of nodes increases gradually. In general, the proposed algorithm has some advantages compared with the existing algorithms.