62 Chih-Ning Huang and Chia-Tai Chan / Procedia Computer Science 5 (2011) 58–65

3.2.3.Online position calculation phase

After all the RSSI values are transmitted to the computer, the mobile position will be calculated by ZigBEACON system. Suppose we have M fixed reference nodes, N fixed RF generators and one mobile node in AmI environment. We define the RSSI vector of the mobile node is M = (M1, …, MN), and the corresponding RSSI vector of the i-th reference node is Ri = (Ri1, …, RiN). The Euclidean distance between the mobile node and the reference node i is defined as NEi ¦ M

j 1j Rij 2. (2)

The mobile node will have a Euclidean distance vector E = (E1, …, EM) that shows the similarity between the mobile node and all reference nodes. The smallest Ei means that the reference node i is the nearest reference node surrounding the mobile node. Nevertheless, as shown in Figure 2, the result calculated by Equation (2) is difficult to recognize the real distance, since the term (MjЁRij) is blurred. For example, (160Ё140) and (100Ё80) have the same result but the distance of the former is about 0.5m and the longest distance of latter would reach 5m. In order to solve this problem, the RSSI should be adjusted before calculating the Euclidean distance by

RSSI' A ratiou RSSI B .

Table 2. The values of parameters for each class

A ratio B Class I

Class II

Class III

Class IV 176 (0xB0) 112 (0x70) 60 (0x3C) 0 (0x00) 0.05 0.3 0.6 1 144 (0x90) 112 (0x70) 60 (0x3C) 0 (0x00) (3) Table 2 shows the parameter values of A, ratio and B according to each class from the offline path loss survey phase. The values of parameter B are the baseline of each class that are 144(0x90) for Class I, 112(0x70) for Class II, 60(0x3C) for Class III and 0(0x00) for Class IV. The parameter ratio can reduce the difference when the RSSI values belong to the same class, and this value depends upon the distance coverage of its class. So, the values of ratio are 0.05, 0.3, 0.6 and 1 for Class I, II, III and IV respectively. The numbers of parameter A are equal to B for Class II, III and IV. But the gap between two baselines of Class I and Class II is too small, so we set the A value of Class I to 176(0xB0) that makes this gap is similar to the other gaps between two classes. Then we replace the original RSSI in Equation (2) by the wighted RSSI, M’ = (M1’, …, MN’) andRi’ = (Ri1’, …, RiN’), to obtain the Euclidean distance vector. Finally, the ZigBEACON system will choose p-nearest reference nodes to calculate the unknown position of the mobile node by

x,y ¦wk xk,yk ,

k 1p(4)

the wk means the weight of the k-th nearest reference node sorted by the E, the (xk,yk) is the coordinate of this reference node and the (x,y) is the estimation position of mobile node. The weight that depends on the p-nearest reference nodes’ Euclidean distance of the mobile node is defined as:

1wk 'Ek¦El 1p1'

l, (5)