with multiple power-levels of RNs
4.3 Positioning accuracy for multiple power-levels of RNsof RNs
4.3.5 Comparison with other positioning methods
We consider the simulation environment that RNs are randomly deployed in a 1000*1000 working area for variety of number of RNs. For the same simulation environment, the average accuracy of centroid method [16], range-free method [17], and our method are shown in Figure 4.14. These methods are range-free positioning methods that utilize the beacon signal to estimate node’s position without ranging technologies. For 100 RNs, the average accuracy of these positioning methods is larger than 0.3. As the number of RNs increase, the average accuracy of them can be improved.
The average accuracy of proposed method is slightly better than others besides the simulation environment of 200 RNs. In low density of RNs (i.e. number of RNs
< 300), the entire working area cannot be covered by all RNs that was deployed randomly. Because the uncovered area cause the area-based positioning method failed to work, the improvement of average accuracy is limited. In high density of
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Precision
Accuracy
100 RNs 200 RNs 300 RNs 400 RNs 500 RNs
Figure 4.13: The average accuracy for various numbers of RNs with random de-ployment strategy.
RNs, range-free and cell-based methods are almost the same.
However, the range-free positioning method uses the approximate point-in-triangulation test (APIT) algorithm to estimate node’s location. This algorithm calculates the center of gravity of the intersection of all of the triangles to deter-mine its estimated position. Note that the triangle is formed by selecting heard RNs in which a SN resides. For high density of RNs, the computation cost of APIT is higher than our method. Therefore, considering the computation power, com-plexity of positioning algorithm, and positioning accuracy, our method is better than others.
100 200 300 400 500 0
0.1 0.2 0.3 0.4 0.5 0.6 0.7
Number of RNs
Average accuracy
Centroid[16]
Range−free[17]
Cell−based with multiple power−levels
Figure 4.14: The average accuracy of centroid[16], range-free[17] and proposed positioning methods for various numbers of RNs.
Chapter 5 Conclusion
We proposed a cell-based positioning method with single power level for wire-less networks. In our method, a set of RNs with overlapping regions of coverage are arranged in a regular (hexagonal) structure [14] and irregular (random) struc-ture [29] and broadcast the beacon frames. Sensor nodes only collect the beacon frames from RNs and use the localization data in the beacon frame to calcu-late their locations. The worst-case and average-case accuracy are analyzed with perfect RNs and ideal radio model. For reality, unstable radio model and imper-fect RNs are considered. The simulation results show that the proposed method worked well in the outdoor, shadowed urban area. Cell-based positioning method with backup RNs is also presented to reduce the number of un-located SNs when one or more RNs are failed. We have implemented our positioning method on a sensor network test bed to verify its feasibility [24].
In order to improve the positioning accuracy, an extension of cell-based posi-tioning method, multiple power-levels approach for wireless network posiposi-tioning, is proposed. It uses simple algorithm without additional device to locate sensor nodes. In addition, we proposed an equal-area ring strategy setting up the power-level set to provide the higher average accuracy. The average accuracy using this
strategy is similar to the one using optimal power-level set that is obtained by brute-force approach. By simulation, using four power-levels in ideal propagation model, the average accuracy is less than 0.07 unit distance. The robustness of proposed algorithm is shown by simulation that contains the factor of reference node failure, beacon frame loss, and unstable radio environment.
The main advantages of the proposed method are that (1) the proposed method is a distributed positioning method; (2) sensor node requires little computation to localize by itself; (3) it is suitable for wireless networks, especially for wireless sensor networks, for low cost and easy computation; (4) it has high average accuracy; and (5) it is suitable for real world applications.
The following directions might be interesting for possible future work:
• Find an optimal layout for irregular network structure by tuning RNs’ trans-mitting power.
• Find a power-saving mechanism to prolong lifetime of RNs.
• Find a secure message communication and positioning estimation algorithm for untruthful environment.
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Vita