Anchor-Free Localization Method for Mobile Targets in Coal Mine Wireless Sensor Networks
Abstract
:1. Introduction
- Estimate the coordinates of the reference nodes. Several methods for this process have been proposed. Meerens and Fitzpatrick use one-hop neighbors and multilateration to construct a global coordinate system [6]. Shang and Ruml use multi-dimensional scaling (Multi-dimensional Scaling: MDS) to realize localization, which has drawn much attention recently [7].
- Water-vapor and coal dust will potentially absorb the wireless signal in different ways and lead to large localization errors.
- The complex terrain and irregular network topology in underground mines make many localization algorithms do not work well.
- A coal mine wireless sensor network is constructed in underground mines based on the ZigBee technology.
- Non-metric MDS algorithm is introduced into the estimation of the reference nodes’ location, which provides higher fault-tolerance ability.
- An improved SBL algorithm, N-best SBL, is proposed to improve the localization accuracy.
2. Preliminaries
2.1. Non-metric MDS algorithms
- Step 1: Initialize the node’s coordinate Ri and the number of iterations k:
- Step 2: For all node pairs, compute their Euclidean distances:
- Step 3: For and RSS matrix W, calculate the matrix using step-wise monotone regression by Equation 2 and Equation 3, i.e. for ∀i, j, u, v,
- Step 4: Compute the stress defined by the Equation (4). If stress < ε (here ε = 10−4), then finish; Otherwise continue to Step 5.
- Step 5: Update k ← k + 1, and compute the new node coordinates as follows:
2.2. Sequence-based localization
- Determine all feasible location sequences in the localization space and store them in a location sequence table.
- Obtain the location sequence of the mobile node by measuring RSS.
- Search the location sequence table for the “nearest” sequence to the location sequence of the mobile node.
- Take the centroid of the region, which is presented by the “nearest” location sequence, as the position of the mobile node.
3. Anchor-Free Localization Method in C-WSN
3.1. Coal mine wireless sensor networks
3.2. Anchor-free localization algorithm in C-WSN
- After C-WSN was established, static ZigBee router nodes start up the non-metric MDS algorithm and then complete the estimation of coordinates with few anchor nodes.
- With the estimated coordinates of static router nodes, mobile nodes finish the precise localization process by executing the N-best SBL algorithm.
3.2.1. Non-metric MDS algorithm for static router nodes
- Step 1: After joining the network, all reference nodes broadcast one-hop RSS request message. The neighbor nodes measure the RSS value between them and report the response message to the sever through the gateway.
- Step 2: The sever starts up the Dijkstra's shortest path algorithm to construct the RSS relationship matrix for every pair of nodes, which is the input to the non-metric MDS.
- Step 3: Finish the non-metric MDS algorithm process to obtain the relative coordinates of all reference nodes.
- Step 4: Compute the absolute coordinates through shifting, translating, rotating and/or reversing with anchor nodes.
3.2.2. Precise localization for mobile targets based on N-best SBL algorithm
- Mobile targets broadcast one-hop RSS request messages at fixed time cycle. After receiving the messages, reference nodes calculate RSS values between them and report them to the server through gateway.
- The server reads the coordinates information of related reference nodes, starts up N-best SBL algorithm, and obtains the position coordinates of mobile node.
- Return to step (1), repeat the localization process with different reference nodes.
- Step 1: Estimate the parameters η and σ in Equation 11 by linear regression and maximum likelihood methods based on the RSS information of reference nodes.
- Step 2: Construct the location sequence table T = {S1, S2, …, S|T|} from reference nodes.
- Step 3: Estimate the optimal N value, denoted as N*.
- Step 3.1: Generate a number of virtual nodes DN randomly according to a uniform distribution in the area bounded by B.
- Step 3.2: Loop for each N in N val = {1, 2, …, 10}.
- Step 3.2.1: Loop for each node (x, y) ∈ DN.
- Step 3.2.1.1: RSS values with reference nodes are simulated by Equation 11, thus a corresponding rank sequence S is obtained.
- Step 3.2.1.2: Calculate correlation coefficients, τ (Si), i = 1, 2, …, |T |, between S and each rank sequence Si in T according to Equation 12:
- Step 3.2.1.3: Sort T by correlation coefficients in descending order, and then select top N rank sequences from T, denoted as TN.
- Step 3.2.1.4: Estimate the coordinates by Equation 13,
- Step 3.3: Calculate the average location errors for virtual nodes by Equation (14):
- Step 3.4: The optimal N value is denoted as follows:
- Step 4: For any mobile target, measure RSS values with reference nodes and obtain a corresponding rank sequence S firstly. Then complete one precise localization process based on Step 3.2.1.2 to Step 3.2.1.4.
4. Experimental Results
- Firstly, outdoor experiments with 15 real Cicada nodes were carried out to test the performance of the non-metric MDS algorithm..
- Secondly, 10,000 repeats of simulation experiments with 100 nodes were finished to compare the performance between the N-best SBL algorithm and the original SBL algorithm.
- Finally, the experiments in the mine gas explosion laboratory with our anchor-free localization algorithm were executed to test the whole localization performance.
4.1. Outdoor experiments for non-metric MDS
- Measure the real location coordinates of the 15 nodes after deployment.
- All the nodes broadcast one-hop RSS request message. The neighbor nodes report the response messages to the server.
- Construct the RSS relationship matrix for all the nodes in the server.
- Choose m reference nodes (m = 3, 4,…14) as anchor nodes randomly, run the non-metric MDS algorithm and estimate the location coordinates for all the nodes according to the RSS relationship matrix.
- Compute localization errors of the non-metric MDS algorithm according to Equation 14. For each m, 15 runs are conducted and then the total average localization errors are obtained.
4.2. Simulations for N-best SBL
4.3. Experiments in the laboratory of mine gas explosion for anchor-free localization algorithm
5. Conclusions
Acknowledgments
References and Notes
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Pei, Z.; Deng, Z.; Xu, S.; Xu, X. Anchor-Free Localization Method for Mobile Targets in Coal Mine Wireless Sensor Networks. Sensors 2009, 9, 2836-2850. https://doi.org/10.3390/s90402836
Pei Z, Deng Z, Xu S, Xu X. Anchor-Free Localization Method for Mobile Targets in Coal Mine Wireless Sensor Networks. Sensors. 2009; 9(4):2836-2850. https://doi.org/10.3390/s90402836
Chicago/Turabian StylePei, Zhongmin, Zhidong Deng, Shuo Xu, and Xiao Xu. 2009. "Anchor-Free Localization Method for Mobile Targets in Coal Mine Wireless Sensor Networks" Sensors 9, no. 4: 2836-2850. https://doi.org/10.3390/s90402836
APA StylePei, Z., Deng, Z., Xu, S., & Xu, X. (2009). Anchor-Free Localization Method for Mobile Targets in Coal Mine Wireless Sensor Networks. Sensors, 9(4), 2836-2850. https://doi.org/10.3390/s90402836