(5)The distance IM and BQ should be equal to the trusty radius T

(5)The distance IM and BQ should be equal to the trusty radius. Then,Rtrusty=AE24+AB2AD2AB2+AD2=AB2+AD22.(6)As described in literature the site [34], the ratio of AB and AD should be 1?:?3. According to (6),Rtrusty?:?AE?:?AB?:?AD=1?:?1?:?1?:?3.(7)Figure 4Example of the hexahedron.The whole process of localization can be described as follows.Step 1 ��The unknown nodes are randomly deployed in the three-dimensional space.Step 2 ��The anchor moves along the trajectory according to the radius and broadcasts its location information and ID.Step 3 ��The nodes receive and record information from the anchor (including signal strength).Step 4 ��Each node finds out the nearest reference points on each of the three kinds of trajectory according to the RSSI.Step 5 ��Implement the HL and calculate estimated position.

Step 6 ��The localization is finished.The flow chart of IAPIT-3D is shown in Figure 5.Figure 5The flow chart of HL.The Matlab pseudocode of localization period is displayed in Pseudocode 1.4. Simulation and ResultIn order to verify the theoretical feasibility of HL, the scientific tool MATLAB is adopted for the simulation. Take the conclusion of Section 3.1 for premise, we deploy 400 unknown nodes in the space of size 100m �� 100m �� 100m. The experiment is separately simulated by the moving step length of 1m, 2m, 3m, 5m, 6m, 10m, and 15m. The result is described by the average absolute error and normalized average error (which is normalized to the ratio of the absolute average error to the radio range).As Figures Figures66 and and77 show, the errors are increasing as the moving step length increases.

In another word, the longer the length of step is, the more inaccurate the localization is. The reason is obvious that the shorter the step, is the more virtual beacon nodes are deployed. The location error is shown in Tables Tables22 and and33.Figure 6The average absolute error under different moving step lengths.Figure 7The average normalized error under different moving step lengths.Table 2The absolute error (m) under different radii and lengths of step.Table 3The normalized error under different radii and length of step.5. The Relationship among the Parameters5.1. The Radius and the Absolute ErrorIn Figure 6, the seven curves that present absolute errors under different radius almost coincide. That means, as long as lengths of step are same, the absolute error is changeless although the radius is different.

We can explain this phenomenon as follows: though radius is related to the deployment of virtual beacon, it does not influence the trusty coverage of mobile beacon in the total space. In another word, the change of radius cannot effect whether unknown nodes are covered in the trusty communication AV-951 extension as long as the step of movement is definite.

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