Sensor deployment and target localization based on virtual forces
Summary (4 min read)
Introduction
- Sensor coverage, distributed sensor networks, sensor placement, virtual force, localization.
- During the execution of the force-directed VFA algorithm, sensors do not physically move but a sequence of virtual motion paths is determined for the randomly-placed sensors.
- The cluster head subsequently queries a subset of sensors that are in the vicinity of these likely target positions.
- In Section II, the authors review prior research on topics related to sensor deployment in DSNs.
A. Preliminaries
- For a cluster-based sensor network architecture, the authors make the following assumptions: After the initial random deployment, all sensor nodes are able to communicate with the cluster head.
- In addition to the positive and negative forces due to other sensors, a sensor si is also subjected to forces exerted by obstacles and areas of preferential coverage in the grid.
- When sensor detection areas overlap, the closer the sensors are to each other, the higher is the coverage probability for grid points in the overlapped areas.
- The coverage for the entire grid is calculated as the fraction of grid points that exceeds the threshold cth.
- Fig. 7 shows the data structure of the VFA algorithm and Fig. 8 shows the implementation details.
IV. TARGET LOCALIZATION
- In their two-step communication protocol, when a sensor detects a target, it sends an event notification to the cluster head.
- In order to conserve power and bandwidth, the message from the sensor to the cluster head is kept very small; in fact, the presence or absence of a target can be encoded in just one bit.
- Detailed information such as detection strength level, imagery and time series data are stored in the local memory and provided to the cluster head upon subsequent queries.
- Based on the information received from the sensors within the cluster, the cluster head executes a probabilistic localization algorithm to determine candidate target locations, and it then queries the sensor(s) in the vicinity of the target.
- The authors assume here that the sensor detection reports are time-labeled.
A. Detection Probability Table
- After the VFA algorithm is used to determine the final sensor locations, the cluster head generates a detection probability table for each grid point.
- The detection probability table contains entries for all possible detection reports from those sensors that can detect a target at this grid point.
- The probability table is built on the power set of Sxy since there are 2kxy possibilities for kxy sensors in reporting an event.
- The binary string 110 denotes the possibility that s1 and s2 report a target but s3 does not report a target.
- For each such possibility d1d2d3 (d1, d2, d3 ∈ {0, 1}) for a grid point, the authors calculate the conditional probabilities that the cluster head receives d1d2d3 given that a target is present at that grid point.
B. Score-based Ranking
- After the probability table is generated for all the grid points, localization is done by the cluster head if a target is detected by one or more sensors.
- Detailed target reporting involves sending large amount of data, which consumes more energy consumption and needs more bandwidth.
- There is also an inherent redundancy in sensor detection information so it is not necessary to query all sensors.
- The target starts to move at t = tstart from the grid point marked as “Start” and finishes at t = tend at the grid point marked as “End”.
- The parameter p tablexy(i(t)) corresponds to the conditional probability that the cluster head receives this event information given that there was a target at P (x, y).
C. Selection of Sensors to Query
- To select the sensor to query based on the event reports and the localization procedure, the authors first note that for time instant t, if kmax ≥ krep(t), then all reported sensors can be queried.
- Otherwise, the authors select sensors based on a score-based ranking.
- For the example of Fig. 10, Table II shows the selected sensor when the target is moving from “Start” to “End”.
- There are total of 24 locations for the target.
- The authors also assume the time instants are discrete, beginning with t = 1.
D. Evaluation of Energy Savings
- The authors next evaluate the energy saved by the proposed probabilistic localization approach.
- Assume the sensor node has three basic energy consumption types—sensing, transmitting and receiving, and these power values (energy per unit time) are Es, Et and Er, respectively.
- The parameters T1, T2 and T3 denote the lengths of time involved in the transmission and reception, which are directly proportional to the sizes of data for yes/no messages, control messages to query sensors, and the detailed sensor data transmitted to the cluster head.
- Fig. 12 shows the pseudocode of the procedure to generate the probability table for each grid point.
- Therefore, the computational complexity of the probabilistic localization algorithm is max{O, O(nm2k)} = O(nm2k).
V. SIMULATION RESULTS
- The authors first present simulation results obtained using the VFA algorithm.
- Then the simulation results of the probabilistic localization algorithm are presented using the sensor location data from the VFA algorithm as inputs.
- The deployment requirements include the maximum improvement of coverage over random deployment, the coverage for preferential areas and the avoidance of obstacles.
- For all simulation results presented in this section, distances are measured in units of grid points.
- Each sensor has a detection radius as 5 units (r = 5), and range detection error as 3 units (re = 3) for the probabilistic detection model.
A. Case Study 1: Binary Sensor Detection Model
- Figures 14-16 present simulation results based on the binary sensor detection model.
- The initial locations of the sensors are shown in Fig. 14.
- For the binary sensor detection model, an upper bound on the coverage is given by the ratio of the sum of the circle areas (corresponding to sensors) to the total area of the sensor field.
- For their example, this upper bound evaluates to 0.628 and it is achieved after 28 iterations of the VFA algorithm.
- Fig. 16 shows the improvement in coverage during the execution of the VFA algorithm.
B. Case Study 2: Probabilistic Sensor Detection Model
- Figures 17-19 present simulation results for the probabilistic sensor model.
- The initial sensor placements are shown in Fig. 17.
- Fig. 18 shows the final sensor positions determined by the VFA algorithm.
- Fig. 19 shows the virtual movement traces of all sensors during the execution of the VFA algorithm.
- The authors can see overlap areas are used to increase the number of grid points whose coverage exceeds the required threshold cth.
C. Case Study 3: Sensor Field with a Preferential Area and an Obstacle
- As discussed in Section III, VFA is also applicable with sensor field containing obstacles and preferential areas.
- Obstacles should be avoided, therefore they are modeled as repulsive force sources in the VFA algorithm.
- Fig. 20-22 present simulation results for a 50 by 50 sensor field that contains an obstacle and a preferential area.
- The initial sensor placements are shown in Fig. 20.
- Fig. 22 shows the improvement of coverage during the execution of the VFA algorithm.
D. Case Study 4: Probability-based Target Localization
- The authors evaluate the localization algorithm using the results produced by the VFA algorithm in the sensor deployment stage.
- At this stage, sensors are already moved to proper locations by the VFA algorithm.
- The target is assumed to move only 1 grid unit in one unit of time.
- There are total of 82 such moves in the simulated target movement trace.
- The set Srep(t) indicates sensors that have reported the detection at time instant t. The set Sq(t) includes sensors that are selected for querying by the cluster head at time t.
E. Discussion
- From the simulation results, the authors see that the VFA algorithm improves the sensor field coverage considerably compared to random sensor placement, and it does not require much computation time.
- For Case Study 2, the VFA algorithm took only 3 minutes to complete 50 iterations.
- Note that these computation time include the time needed for displaying the simulation results on the screen.
- The efficiency of the VFA algorithm depends on the values of the force parameters wA and wR.
- This need not always be true, so the authors are examining ways to choose appropriate values for wR and wA base on the initial configuration.
VI. CONCLUSION
- The authors have proposed the virtual force algorithm (VFA) as a practical approach for sensor deployment.
- The authors have also shown that the proposed probabilistic localization algorithm can significantly reduce the energy consumption for target detection and location.
- The VFA algorithm can be made more efficient if it is provided with the theoretical bounds on the number of sensors needed to achieve a given coverage threshold.
- Finally, the authors will examine continuous coordination systems instead of discrete coordination systems in this work.
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Cites methods or result from "Sensor deployment and target locali..."
...For example, the work in [ 24 ] assumes that a powerful cluster head is available to collect information and determine the target location of the mobile sensors....
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...This sensor relocation is different from existing work on mobile sensors which concentrate on sensor deployment; i.e., moving sensors to provide certain initial coverage [11], [12], [20], [21], [ 24 ]....
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523 citations
Cites background from "Sensor deployment and target locali..."
...The simulation result of Zou and Chakrabarty (2003) shows that a sensor deployment technique based on virtual forces can increase the area coverage after an initial random deployment....
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...Zou and Chakrabarty (2003) assumes that obstacles exert repulsive (negative) forces on a sensor....
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...The VFA algorithm combines the ideas of potential field [5] and disk packing [11]....
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...Sensor placement on two- and three-dimensional grids has been formulated as a combinatorial optimization problem, and solved using integer linear programming in [3], [4]....
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...Equation (1) shows the binary sensor model [3], [4] that expresses the coverage cxy(si) of a grid point P by sensor si....
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Frequently Asked Questions (10)
Q2. What are the future works mentioned in the paper "Sensor deployment and target localization based on virtual forces" ?
Their future work will be focused on overcoming the current limitations of the VFA algorithm. Since the current target localization algorithm considers only one target in the sensor field, it is necessary to extend the proposed approach to facilitate the localization of multiple objects. Extensions to non-mobile sensor nodes, and situations of sensor node failures will also be considered in future work. The VFA algorithm can be made more efficient if it is provided with the theoretical bounds on the number of sensors needed to achieve a given coverage threshold.
Q3. How is the message from the sensor to the cluster head kept small?
In order to conserve power and bandwidth, the message from the sensor to the cluster head is kept very small; in fact, the presence or absence of a target can be encoded in just one bit.
Q4. How can the VFA algorithm be used to ensure flexibility?
the desired sensor field coverage and model parameters can be provided as inputs to the VFA algorithm, thereby ensuring flexibility.
Q5. What is the role of the cluster head?
The cluster head is responsible for executing the VFA algorithm and managing the one-time movement of sensors to the desired locations.
Q6. How many units of detection error is the probabilistic detection model?
Each sensor has a detection radius as 5 units (r = 5), and range detection error as 3 units (re = 3) for the probabilistic detection model.
Q7. What is the way to cover a large grid?
This ensures that the detection regions of two sensors do not overlap, thereby minimizing “wasted overlap” and allowing us to cover a large grid with a small number of sensors.
Q8. What is the probability table for the detection of a target?
After the VFA algorithm is used to determine the final sensor locations, the cluster head generates a detection probability table for each grid point.
Q9. What is the probability that the grid point is not covered?
Since the term (1− cx,y(si))(1− cx,y(sj)) expresses the probability that neither si nor sj covers grid point at (x, y), the probability that the grid point (x, y) is covered is given by Equation (5).
Q10. What is the value of the set Srep(t)?
The set Srep(t) indicates sensors that have reported the detection at time instant t. The set Sq(t) includes sensors that are selected for querying by the cluster head at time t.