Range tracking in wireless networks.

Machedon Pisu, Mihai

1. INTRODUCTION

The recent development of wireless sensor networks (WSN) makes it possible for applications such as industrial monitoring and control, automations in buildings, or target tracking to be implemented with low cost, low power and reduced complexity. GPS cannot comply with these requirements but its principle of triangulation can be used with other wireless technologies for range tracking inside buildings. Position information can play a major role in wireless networks, and many methods for localization within WSNs have been proposed. Similar to triangulation tracking, these methods calculate the position of a mobile node based on the locations of more than three reference nodes and the distance between a mobile node and a reference node can be determined by the received signal strength or quality, which is evaluated with the link quality indicator (LQI). Such estimation depends on the signal propagation phenomena, which affect the radio link quality. A proper correlation should adapt to the unpredictable changes in LQI. Also, the localization errors are greatly reduced by using the best localization algorithm. Combining these strategies with the results from the field tests, a simulator is developed and run.

2. THE CORRELATION BETWEEN DISTANCE AND LQI

Different values of LQI are obtained from packets sent at the same distance. Averaging these values gives unsatisfactory results. Using the Probability Theory, the value of LQI for that distance is better determined in the following way:

[LQI.sub.FINAL] = ([summation]P([LQI.sub.i]) * [LQI.sub.i]) / [summation]P([LQI.sub.i]) (1)

Where [LQI.sub.i] are the LQI values, P([LQI.sub.i]) the probability of a LQI value to occur for that distance, and it is equal to 1/ [k.sub.MIN] if NP([LQI.sub.i]) >= [NP.sub.ALL]/[k.sub.MIN], where NP([LQI.sub.i]) is the number of packets received with that LQI value and [NP.sub.ALL] is the total number of packets sent (as seen in Fig. 1), where k=2,3,4 ... (integer values).

[FIGURE 1 OMITTED]

LQI measurements provide the means to estimate the performance of the link. The changes in LQI do not depend only on the communication distance, but also on factors such as the transmission medium and the surrounding environment. The effects of these factors for radio propagation are related to attenuation, multipath and interference. A correlation between LQI and distance is needed in order to adapt to these effects, and by approximating the LQI value as close as possible to the measured distance, it should be achieved (Fig. 2). The power correlation refers to the Friis' free space transmission equation, where the power at the receiver follows an inverse square law related to the distance value. Due to dynamic and uncertain propagation conditions, this approach does not work, and a more adaptive solution is given by the logarithmic correlation. The link performance is tested in different indoor and outdoor scenarios and the errors obtained with the two correlations are compared.

[FIGURE 2 OMITTED]

For a 10m x 10m grid, the logarithmic correlation gives a mean error of 1.49% and a maximum error of 3.9%. The power correlation mean error is 2.28% and the maximum is 5.47%. The formulas for logarithmic (2) and power correlation (3) are the following (with d as distance):

-77.9 * log (d) + 190 = LQI (2)

185 * [d.sup.-0.206] = LQI (3)

3. IMPLEMENTING LOCALIZATION METHODS IN WIRELESS NETWORKS

Before implementing the localization method, the algorithm used for tracking must be tested in order to establish its precision. ML estimates the position of the target by minimizing the differences between estimated and measured distances, by using the minimum mean square error (MMSE). An algorithm that uses ML can determine the target's position, for 10m distance between the neighbour reference nodes, in the following way ([D.sub.i] represents measured distances):

[X.sub.TARGET] = [([D.sub.4.sup.2]) - ([D.sub.3.sup.2]) + 100] / 20 (4)

[Y.sub.TARGET] = [([D.sub.1.sup.2]) - ([D.sub.4.sup.2]) + 100] / 20 (5)

The WCL algorithm proposes a method in which the distances measured are encapsulated as weighted functions: w = 1 / [D.sup.k] where k=1,2,3 ... (integer values). The target's position is estimated ([X.sub.i] [Y.sub.i] are reference node coordinates):

[X.sub.TARGET] = ([summation] [X.sub.i] / [D.sub.i.sup.k]) / [summation] 1 / [D.sub.i.sup.k] (6)

[Y.sub.TARGET] = ([summation] [Y.sub.i] / [D.sub.i.sup.k]) / [summation] 1 / [D.sub.i.sup.k] (7)

ML and WCL algorithms are tested within a 10m x 10m grid, with 4 reference nodes, one in each corner and 121 points are used for position measurement (Fig. 3).

[FIGURE 3 OMITTED]

Both algorithms are scalable but the tracking error should not exceed 1%. The tracking errors are illustrated in Figures 4 and 5:

[FIGURE 4 OMITTED]

[FIGURE 5 OMITTED]

For a 100m x 100m test grid, the maximum tracking error of ML is 0.94 %, while the mean error is 0.39%. The tracking errors for WCL are far greater, the maximum exceeding 3%, while the mean error is around 1.7%, for a 10m x 10m test grid.

4. SIMULATION RESULTS

WSNs are special networks which deploy hundreds of tiny sensors. Due to range limitations, a range-based approach for tracking in WSNs gives poor results. A more adequate approach should be a range-free tracking with a large number of reference nodes. Therefore, tracking simulation uses 121 reference nodes for a 100m x 100m test grid, with a distance of 10 m between neighbour reference nodes. There are 100 test points and their position is determined by tracking with the most near four reference nodes, for which the LQI value is the greatest (Fig. 6).

[FIGURE 6 OMITTED]

The errors provided by the field tests have shown that the logarithmic correlation and the ML algorithm can be used for precise tracking in wireless networks. The proposed solution combines the two methods within the simulator, which gives a maximum error of 1.91% and a mean error of 0.97%.

5. CONCLUSION

Range tracking is one of the main applications that can be implemented with wireless sensor networks. The present research has provided the solutions for obtaining precision in position estimation, and as an effect of the simulation, we can see that GPS for large buildings is possible by considering the proposed tracking method.

6. REFERENCES

Blumenthal, J., Grossmann, R., Golatowski, F. & Timmermann, D. (2007), Weighted Centroid Localization in ZigBee-based Sensor Networks, Proceedings of Intelligent Signal Processing, pp. 14-17, ISBN: 978-1-4244-0830-6

Ferrari, G., Medagliani, P., Di piazza, S.& Martalo, M. (2007), Wireless Sensor Networks: performance analysis in indoor scenarios, Eurasip Journal on Wireless Communications and Networking, Vol. 2007, No. 1, pp. 41, ISSN 1687-1472

Machedon-Pisu, M., Szekely, I., Gavrus, R. (2008), Efficient Data Propagation Techniques and Security Concerns in Low Rate Wireless Personal Area Networks in Outdoor and Indoor Scenarios, In: OPTIM 2008, Vol.3: Industrial Automation and Control, pp.201-207, ISSN 1842-0133