- freely available
Sensors 2010, 10(6), 5899-5926; doi:10.3390/s100605899
2. Related Work
3. Matrix Transform Based SPA
3.1. Assumptions and Scheme Overview
- All sensors are stationary. So the network topology is fixed.
- There are no landmarks in the network. That is to say, no sensor has absolute location information.
- All sensors are homogeneous, with the same technical characteristics, and especially the same transmission range.
- All sensors have enough energy to accomplish a node localization algorithm.
- All sensors use omnidirectional antennae.
- All the wireless links between sensors are bidirectional.
- There are no base stations to coordinate or supervise activities among sensors. Hence, the sensors must make all decisions without reference to a centralized controller.
3.2. Phase I: Construction of Local Coordinate Systems
|(1) Each sensor initializes a random waiting timer with a value WTi(0) ∈ (0, Tmax) and initial status Si = none (i = 1, 2, 3, …)|
|(2) Decrease all random waiting timer WTi(k)|
|(3) Master node check:|
|if the random waiting timer expires, that is, WTi(k) = 0|
|(a) Si = master node|
|(b) broadcast a message M1 with multiplication factor α|
|(c) delete the waiting timer|
|(4) Establish and update the neighbor identification:|
|if a sensor Sj receives a message M1 at time step k|
|(a) if Sj = slave node|
|Sj = border node|
|Sj = slave node|
|(b) transmit messages M2 to its neighbor nodes with the distance between node i and j|
|(c) WTj(k + 1) = α × WTj(k)|
|(d) if WTj(k + 1) > Tmax|
|delete the waiting timer|
|(5) Termination conditions check:|
|if the waiting timers of all sensors are deleted|
|algorithm is over|
|k = k + 1 and go to step (2)|
3.3. Phase II: Organizing a Global Coordinate System
3.4. More Discussion about the Transformation Matrix
4. Theoretical Analysis
4.1. Analysis of Energy Consumption
4.2. Parameter-setting Guidelines
- Conclusion 1. In the local coordinate system construction phase, except for the two slave nodes selected first, the coordinates of other slave nodes are determined by at least three neighbor nodes.
- Conclusion 2. In the global coordinate system organization phase, the coordinates of border nodes are determined by at least four neighbor nodes when no master-slave relationships exist between the master nodes of two local coordinate systems.
- Conclusion 3. In the global coordinate system organization phase, the coordinates of border nodes are determined by at least two neighbor nodes when there exists a master-slave relationship between the master nodes of two local coordinate systems.
5. Simulation Results
5.2. Typical Result
5.3. Effects of Different Parameters
5.4. Performance Comparison with Other Algorithms
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|Mean value||Standard deviation|
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