Enhancing Received Signal StrengthBased Localization through Coverage Hole Detection and Recovery^{ †}
Abstract
:1. Introduction
 To the best of our knowledge, this is the first paper to detect and recover coverage holes of WSNs based on RSSIbased localization techniques, and we will enhance RSSIbased localization through coverage hole recovery.
 We systematically investigate the coverage model of RSSIbased localization techniques, and ellipse coverage model is derived from theoretical analysis and experimental verification.
 An approximation algorithm is proposed to recover coverage holes in WSNs with ellipse coverage model. Simulation results show that our algorithm can recover all holes and can reach any set coverage rate, up to 100% coverage.
2. Related Work
2.1. RSSIBased Localization Techniques
2.2. Coverage Hole Detection and Recovery
3. Background
4. The Ellipse Coverage Model
4.1. Theoretical Model
4.2. Mathematic Model
4.3. Experimental Verification
5. Detecting and Recovering Coverage Holes
5.1. Detecting Coverage Holes
Algorithm 1: Procedure of Detecting Coverage Holes 
Input:

5.2. Recovering Coverage Holes
5.2.1. The Optimum Increase Coverage Problem (OICP) is NPComplete
5.2.2. Voronoi Tessellation
5.2.3. Delaunay Triangulation
Algorithm 2: Procedure of Recovering Coverage Holes 
Input:

5.2.4. Algorithm Description and Analysis
 Firstly, we divide the regions into several small enough cells and verify whether these small cells are covered one by one. Then the total area of covered regions can be calculated by adding up all covered small cells in the target regions. The time complexity of this step is $O\left(n\right)$, where n is the number of small cells, which is determined by the size of small cells.
 We then calculate the coverage rate of the target regions by calculating the ratio of the total area of covered regions with the area of the target regions. If the coverage rate achieves the requirement of the corresponding systems, then exit; if not, then continue.
 Partitioning the regions by Voronoi tessellation. According to the optimization proposed in [44], the worst case time complexity is $O\left(nlogn\right)$, where n is the number of sensors deployed in the target regions.
 According to the dual graph of Voronoi tessellation, we can obtain Delaunay triangle $T=\left\{{t}_{1},{t}_{2},\dots ,{t}_{i}\right\}$. Because the common border of adjacent Voronoi cells can be obtained in the process of Voronoi tessellation, the time complexity of the Delaunay triangle is $O\left(n\right)$, where n is the number of Delaunay triangles.
 We will next calculate the total area of all triangles of Delaunay triangulation and find the triangle with the largest area. The time complexity is determined by the sort algorithm, and it is $O\left(nlogn\right)$, where n is the number of Delaunay triangles.
 Finally, the new sensors will be deployed. Go back to Step 2.
6. Experiment and Evaluation
6.1. Experimental Setup
6.1.1. SingleLink Setup
6.1.2. MultiLink Setup
6.2. The Ellipse Coverage Model vs. the Disk Coverage Model
6.3. Results of Coverage Hole Recovery
7. Conclusions
Author Contributions
Funding
Conflicts of Interest
Appendix A
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${R}^{2}$  The target regions 
${d}_{max}$  The transmission range of sensors 
${s}_{i}$(${x}_{i}$, ${y}_{i}$)  The coordinate of sensor ${s}_{i}$ 
S = { ${s}_{1}$, ${s}_{2}$, ${s}_{3}$, …, ${s}_{n}$ }  The set of sensors in the target regions 
${d}_{ij}$  The Euclidean distance of sensor ${s}_{i}$ and sensor ${s}_{j}$ 
${f}_{ij}$  The ellipse coverage model determined by sensor ${s}_{i}$ and sensor ${s}_{j}$ 
$F=\left\{{f}_{ij}\mid i,j=1,2,\dots ,n,i\ne j\right\}$  The set of ellipse coverage model in the target regions 
${R}^{2}=\left\{{a}_{1},{a}_{2},{a}_{3},\dots ,{a}_{m}\right\}$  The set of square elements dividing the target regions 
${p}_{{a}_{i}}$  The square element ${a}_{i}$ is covered 
$\Re =\left\{{p}_{{a}_{1}},{p}_{{a}_{2}},{p}_{{a}_{3}},\dots ,{p}_{{a}_{t}}\right\}$  The set of covered square elements 
Parameter Name  Parameter Value 

Node type  Micaz 
Distance between nodes  4 m 
Height of nodes  1.5 m 
Frequency of sending packets  one second every packet 
Sampling distance  0.5 m 
Initial number of sensors  20  30  40  50  60 
Additional sensors  17  10  7  5  2 
Coverage rate of ellipse model  23.75%  21.05%  32.69%  41.3%  44.83% 
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Zhai, S.; Tang, Z.; Wang, D.; Li, Q.; Li, Z.; Chen, X.; Fang, D.; Chen, F.; Wang, Z. Enhancing Received Signal StrengthBased Localization through Coverage Hole Detection and Recovery. Sensors 2018, 18, 2075. https://doi.org/10.3390/s18072075
Zhai S, Tang Z, Wang D, Li Q, Li Z, Chen X, Fang D, Chen F, Wang Z. Enhancing Received Signal StrengthBased Localization through Coverage Hole Detection and Recovery. Sensors. 2018; 18(7):2075. https://doi.org/10.3390/s18072075
Chicago/Turabian StyleZhai, Shuangjiao, Zhanyong Tang, Dajin Wang, Qingpei Li, Zhanglei Li, Xiaojiang Chen, Dingyi Fang, Feng Chen, and Zheng Wang. 2018. "Enhancing Received Signal StrengthBased Localization through Coverage Hole Detection and Recovery" Sensors 18, no. 7: 2075. https://doi.org/10.3390/s18072075