The algorithms of wireless sensor networks(WSN) position can be divided into two main categories [1]—Range-based position and Range-free position. in the Range-based position algorithm, we need to measure the distance and angle between the mobile nodes and the beacon nodes, and then count out the position of the mobile nodes by Tri-lateral measurements, Triangular measurements or Maximum likelihood estimation method. Yet, in the Range-free position algorithm, we need only information of the network-connectivity and signal strength. Here, non-distance-position method has a great superiority owing to that it has no requirements for accurate distance-measuring so that the cost of the hardware establishments will be greatly reduced and thus can be large-scale installed, and the precision of the position can be improved by algorithm. At present, the Range-free method has been widely used in the convex program [2], the DV-Hop [3] and etc. However, the convex program method requires that the reference nodes located on the edge of the network, otherwise the position will deflect towards the center; while the DV-Hop algorithm can carry out accurate position only in intensive isotropy networks [4]. The so-called isotropy here means that the signal strength will not change with the orientation of measures. However, it is hardly to guarantee the isotropy of the network in the indoor. Thus, the SSDV (Signal Strengthening Dynamic Value) scheme discussed in this article is born out of an algorithm of positioning which uses the Range-free techniques, and can accurately perceive the movements of the measuring objects. Thus it is very suitable to be used indoor. In our discussing, we assume that the wireless-signals can be kept steady and the signal covering scale of the nodes is a standard round area.

An important feather of wireless signal transmission is that the signal strength decreases as the distance increase. The principle of distance measurements of RSSI is to change attenuation of the signal strength into distance of signal transmission, using the functional relation between attenuation of the signal and the distance approximately. Researchers have done some effective researches about signals in different transmission environment [5], and conclude some good empirical formula:

is Transmitting antenna gain, is Receiver antenna gain, c is velocity of light, f is carrier frequency, is Channel attenuation coefficient (2～6）, v is the Gaussian random variable which considered the shadow effect, then v～, d is the distance, is the channel loss after the distance d.

In practice, we get the relation between RSSI and the distance through the measurement of transmission power and receiving power. Most of the chips which provide RSSI measurement show the relation of transmission power and receiving power by the following formula: [6]

After the conversion was:

is the receiving power of the wireless signal, is transmission power, n is the Propagation factor, r is the distance between Transceiver Unit. A is the receiving signal power when the signal transmit 1 meter. The numerical value of constant A and n determined the relation between receiving signal strength and signal transmission distance.

As to different chips, the empirical formula has corresponding different form due to different hardwire and modulation. The chip CC2430 used in our experiment is based on the IEEE802.15.4 agreement, using the DSSSO-QPSK modulation technology in the physical layer. IEEE802. 15. 4 gives the simplified channel model [7]

Most of theoretical analysis and empirical formula show that the relationship between RSSI and the transmission distance of wireless signal is apparent. The measurement of RSSI has repeatability and interchange ability, and there is a pattern in the application environment when RSSI does appropriate changes. After having finished the environmental factors, RSSI can do the distance measurement of indoor and outdoor.

In order to do a comprehensive discussion of RSSI ranging, we designed the following experiment. Do four groups ranging experiment which is mutually perpendicularity on an empty space, the nodes are above the ground one meter. The mobile node and fixed node start the ranging from the position one meter away, every 0.1 meter as a measuring point, and every measuring point will be measured 10 times. After 42 meters measured, part of the signals is not detected, because the RSSI values is obtained from complete receiving data packets, so the test is meaningless to continue. The four groups of experimental results are shown in the Figure 1.

We have collected 16000 experimental data, and the analysis on those statistics shows that: Each RSSI value corresponds to an distance scope, and high-intensity values has small probability, low-intensity values has large probability. So we can find the highest density peaks and filter out most wrong dates by doing Gaussian fitting. The probability distribution Restructure is shown in the Figure 2. There is only one peak for each different RSSI measurement value, and the peak is steeper as the value is bigger, then the error is small, the peak is more slowly as the value is smaller, then the error become big. We get the fitting function:

It is hard to find out the RSSI peak value of each measurement point. The value can be substituted into (6), when 0.5 ≤ y ≤ 1,we consider it is a large probability event and can be reserved, then we obtain the determined RSSI value by taking the average of the reserved RSSI values. and A are undetermined coefficients(can be determined by the relation between beacon nodes’ location and RSSI), k is the number of received beacon nodes.

Gaussian fitting reduced the influence of some low probability and large disturbance events by using Gaussian fitting to do data processing, and reduced the ranging error. Figure 3 is the data processing results compared to Gaussian fitting and mean approach. The result shows that Gaussian fitting is better than mean model in improving ranging precise, especially when we measure close distance, and the error can be control within 1.2 meters on open space.

Suppose the positioning region is a square plane with an area of 50 × 50 m², and on it an square region with an area of 40 × 40 m² is distributed equably with reference region and the space between the reference nodes is 5 m. the exchange nodes are positioned in the four point angles A, B, C, D of the positioning region.

The simulation result is shown in figure 6. The black line is the assistant positioning-line, the larger the value, the wider the line. The assistant with no value will not be shown. And the triangular shapes refer the focus reference nodes region while the small square shapes refer the actual spot of the mobile nodes, and the stars are the places that are determined by calculation. In figure 6(a), the mobile node is positioned at coordinate (41, 39). The positioning result which is calculated by node-matching is coordinate (40, 40) with an error of 1.4142 m and timecost of 28 ms. In figure 6(b), the mobile node is positioned at coordinate (26, 28), and the calculated positioning result is coordinate (25, 27.5) with an error of 1.118 m and time-cost of 43 ms. In figure 6(c), the mobile node is positioned at coordinate (13, 17), and the calculated positioning result is coordinate(12.5, 17.5) with an error of 0.7071 m and time-cost of 41 ms. In figure 6(d), the mobile node is positioned at coordinate (48, 24), and the calculated positioning result shows that it does not exist in the positioning region with a time-cost of 29 ms.

From figures 6(a) and (b), we can see that the SSDV can determine the mobile nodes on special positions accurately; As from figure 6(c), it shows that most mobile nodes on normal positions can be determined accurately by this algorithm. From figure 6(d), we can see that when the mobile node is located out of the positioning region, the SSDV can find this out correctly. While comparing (a), (d) with (b), (c), we can see that the less the steps of the positioning, the less of the time-cost; while comparing (b) with (c), we can see that the closer is the mobile node near to any random reference node, the smaller the focus positioning region will be while the time cost is cut only with a very small quantity. On the contrary, the focus positioning region will get larger and the time-cost increase also has a very little quantity.

This paper presents a new algorithm of SSDV. This algorithm needs only the strength of the radio signals as foundation to position the mobile nodes. The establishment is rather simple and there is no blind spot in positioning region, and the accuracy and the time of positioning can both be adjusted by the users. The result of simulation proves the validity of this algorithm.