However, the influence of radius to the error is negligible relative to that of step length. We depict the relationship among radius, length of step, and the absolute error in a 3D picture. In Figure 8, the x-label and the y-label present radius and length of step. And the z-label presents the absolute error of the localization. From the piecemeal change of the color in Figure 8, we find selleck chemical Palbociclib that the influence of step length to the absolute error is greater than that of radius.Figure 8The 3D picture of the absolute error in localization.5.2. The Radius and the Normalized ErrorThe relationship between radius and the normalized error is shown in Figure 6 and Table 3. Different from Figure 6, we find that the normalized error is decreasing when the radius increases. The 3D picture of the normalized error is shown in Figure 9.

Figure 9The 3D picture of the normalized error in the localization.Normalized error is the ratio of the absolute error to the radius. As the absolute error increases, the radius increases. This phenomenon leads to a problem of balancing between radius and accuracy. In localization of WSN, there are two principle elements to be paid attention to: (1) the cost; (2) the accuracy and the precision [40]. In our scheme, the cost is reflected by the radius to a certain extent. Communication cost is influenced by two points: first, the size of model, which affects the number of the packages sent. Second, it is the transmitting power. And these two points are all relative to the radius. Next, we will analyze the relationship among these elements.

Take moving step of 1m for an example, the relationship between radius and number of packages sent is shown in Table 4.Table 4Relationship between radius and number of the packages sent.According to the formula of the signal space loss,[Lfs](dB)=32.44+20lg?d?(km)+20lg?f?(MHz).(8)The following equations should be established:Lfs(d)=32.44+20lg?(0.03)+20lg?f+20lg?(d0.03)=Lfs(0.03)+20lg?(d0.03).(9)In the light of the operating frequency = 2.4GHz and the receiving sensitivity = ?105dBm of the CC2420 receiver, and the transmitting power is W1 = ?35 (dBm) when the radius is 30m, the transmitting powers under different radius are shown in Table 5.Table 5The transmitting powers under different radii (step length = 1m).The formula of transforming dBm to mw obeys this equation:x?(dBm)=10lg?[p?(mw)].

(10)Combined with Table 4, we show the ratio of consumed energy under the same step length in Table 6.Table 6The ratio of consumed energy under the same step length.As described in Table 6, it is obvious that the consumed energy is lowest when the radius is 30m. So, the performance is increasingly excellent as the radius is reducing. At this moment, the traditional normalized error is meaningless. Entinostat However, there is a drawback that the trajectory is less controllable in the short-radius localization of our scheme.5.3.