When kinase inhibitor Vorinostat the mobile beacon tracks along a straight line, the nearest point of the unknown node is the foot point of the trajectory. At the same time, the RSSI is the largest.Different from literature [34], the purpose of our experiment is to get the suitable distance that the RSSI is available. From Figure 1, we can obtain the trusty distance is 30m when the radius is about 50m. And we continue to do the similar but more accurate experiment under the radius from 40�C100m by the step of the 10m. The result is shown in Table 1. Table 1The trusty radius of different radii.According to Table 1, the trusty radius analogously equal to 60% of the radius.3.2. The Model of the HLThe observation above motivates the design of HL. We project HL as shown in Figure 2.Figure 2The model of HL.

The mobile beacon moves along the given trajectory and broadcasts its own position periodically. Via RSSI, the unknown node selects the nearest reference points on the trajectory. The coordinate of the reference point is (xa, ya, za)(xb, yb, zb)(xc, yc, zc) .And the unknown node is (x, y, z).The direction vector of ��, ��, �� is given as (i1, j1, k1)(i2, j2, k2)(i3, j3, k3). Then, we have the following N=(i1xa+j1ya+k1zai2xb+j2yb+k2zbi3xc+j3yc+k3zc).(2)According??equations:i1(x?xa)+j1(y?ya)+k1(z?za)=0i2(x?xb)+j2(y?yb)+k2(z?zb)=0i3(x?xc)+j3(y?yc)+k3(z?zc)=0?M(xyz)=N,M=(i1j1k1i2j2k2i3j3k3), to the least square method,(xyz)=(MTM)?1MTN.(3)There must be a lot of errors in the process of calculation via the least square method. We will analyze that in Section 6.3.3.

The Optimization of the TrajectoryWe have given out the trajectory of the HL. But how to make the model reasonable is an important issue. From literature [34], it can be known that the equilateral triangle is the best trajectory on the two-dimensional flat. And interestingly, we find that the equilateral triangles can be connected and divided into rectangles like Figure 3. The trajectory we proposed is more controllable at the same time.Figure 3The transformation of the two-dimensional trajectory.As the trajectory described in Section 3.2, according to the radius R, the ratio of the hexahedron’s edges should be optimized.In Figure 4, take the red hexahedron, for example, AC, BD, HE, GF, AE, BF, DG, and CH are all the trajectories of the mobile beacon. To ensure the coverage of mobile beacons, the extension that the signal propagates should be equal.

In another word, the point in the hexahedron which is furthest from the trajectory should be covered in the extension. According to the trusty radius, the largest distance should be equal to the trusty radius. As the trajectories are deployed symmetrically as shown in Figure 4, we find that the points I, J, K, L are the furthest points to the bevel trajectory like AC, BD, HE, and GF. And the point on PQ is the furthest point to the vertical Batimastat trajectory like AE, BF, DG, and CH.