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This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

Severe natural conditions and complex terrain make it difficult to apply precise localization in underground mines. In this paper, an anchor-free localization method for mobile targets is proposed based on non-metric multi-dimensional scaling (Multi-dimensional Scaling: MDS) and rank sequence. Firstly, a coal mine wireless sensor network is constructed in underground mines based on the ZigBee technology. Then a non-metric MDS algorithm is imported to estimate the reference nodes’ location. Finally, an improved sequence-based localization algorithm is presented to complete precise localization for mobile targets. The proposed method is tested through simulations with 100 nodes, outdoor experiments with 15 ZigBee physical nodes, and the experiments in the mine gas explosion laboratory with 12 ZigBee nodes. Experimental results show that our method has better localization accuracy and is more robust in underground mines.

Over the past decade, there has been a surge of accidents in coal mines all over the world. Realization of environment monitoring and miner localization in underground mines plays an important role in mining safety. Wireless sensor networks (Wireless Sensor Networks: WSN) have attracted more and more research interest in coal mine applications for their advantages of self-organization, low cost and high reliability. Supported by the British Department of Trade and Industry, the Exeter College Camborne Mining Institution has constructed a high reliable wireless mesh network in mines [

Localization algorithms in WSN can be divided into two classes: anchor-based algorithms and anchor-free algorithms [

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 [

Complete precise localization for mobile targets based on reference nodes. Oh-Heum

The above algorithms have respectively achieved certain goals under ideal environments. However, in underground mines, localization will face the following challenges.

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.

To solve the above problems, an anchor-free localization method in coal mine WSN (Coal Mine Wireless Sensor Networks: C-WSN) is proposed. The main contributions of this paper are as follows:

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,

The remainder of the paper is organized as follows. In Section 2, we describe the MDS and SBL method briefly. In Section 3, our anchor-free localization method in C-WSN is studied. In Section 4, we analyze our experimental results. Finally, we conclude the paper.

MDS algorithms are widely used in multivariate statistics. There are two types of MDS algorithms: metric MDS and non-metric MDS. The input in the metric MDS approach is a rigid distance matrix that specifies distances between every pair of nodes, and the output is a coordinate set of all the nodes. The metric MDS approach has been introduced into WSN localization in previous work [

Without loss of generality, let’s assume that _{i}_{i, 1}, _{i, 2}, …, _{i, p}_{i}_{i, 1}, _{i, 2}, …, _{i, p}

Step 1: Initialize the node’s coordinate _{i}

Step 2: For all node pairs, compute their Euclidean distances:

Step 3: For

Step 4: Compute the stress defined by the ^{−4}), then finish; Otherwise continue to Step 5.

Step 5: Update

As the iterative algorithm grows, the stress will decrease monotonically. It can be shown that _{i,j}_{u,v}_{i,j}_{i,j}

The sequence-based localization method is a novel and high-accuracy anchor-based WSN localization technique, which was recently proposed by Kiran and Bhaskar [

The process to calculate the localization of mobile targets based on SBL is as follows [

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.

However, based on our detailed observation, we find that it is not optimal in terms of average localization errors if only one “nearest” sequence is searched in the sequence table.

In addition, we also notice that the localization errors for nodes near the border of the region are possibly rather large. For example, in

To reduce the average localization errors and improve the localization accuracy for marginal nodes, a new sequence-based localization method:

To execute our localization algorithm, first a C-WSN was constructed in underground mines based on the ZigBee technology. We deployed the sensor nodes, called Cicada, as end devices in the C-WSN. There are six types of nodes including methane sensors, oxygen sensors, carbon monoxide sensors, smoke sensors, temperature-humidity sensors and voice sensors, just as shown in

Based on the non-metric MDS algorithm and the

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

The details of the anchor-free localization algorithm are discussed as follows.

Most of existing WSN localization methods based on the MDS algorithm adopt metric MDS. However, it is hard to obtain precise distance matrix of the nodes in underground mines. Here, non-metric MDS algorithm is used to estimate the coordinates of reference nodes. Under the condition that more than three anchor nodes’ absolute coordinates are known, the reference nodes’ coordinates can be calculated in the following steps:

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.

The detailed computation process of this step is given as follows:

For convenience, assume the previous

Here _{1} and _{2} as:

By simple deductions, we have:

If

After all the reference nodes have obtained their own absolute coordinates based on non-metric MDS, the mobile targets start up the

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

Return to step (1), repeat the localization process with different reference nodes.

In what follows, the _{R}_{T}_{0}) is the path loss for a reference distance of _{0}. ^{2} variance _{σ}^{2}).

Specific procedure of the

Step 1: Estimate the parameters

Step 2: Construct the location sequence table _{1}, _{2}, …, _{|T|}} from reference nodes.

Step 3: Estimate the optimal

Step 3.1: Generate a number of virtual nodes

Step 3.2: Loop for each ^{val}

Step 3.2.1: Loop for each node (

Step 3.2.1.1: RSS values with reference nodes are simulated by

Step 3.2.1.2: Calculate correlation coefficients, _{i}_{i}_{c}_{d}_{ts}_{tt}_{i}

Step 3.2.1.3: Sort ^{N}

Step 3.2.1.4: Estimate the coordinates by ^{N}_{i}_{i}

Step 3.3: Calculate the average location errors for virtual nodes by

Step 3.4: The optimal

Step 4: For any mobile target, measure RSS values with reference nodes and obtain a corresponding rank sequence

The practical significance of the

The following three steps are used to validate the performance of our algorithm:

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

Finally, the experiments in the mine gas explosion laboratory with our anchor-free localization algorithm were executed to test the whole localization performance.

The outdoor experiments were realized in a vacant environment within an area of 60 m × 40 m, where 15 nodes of the Cicada series were randomly distributed. Cicada nodes are designed based on the CC2430 ZigBee chip with a radio frequency power amplifier. The point to point communication distance reaches to 200 m. The experimental process is as follows:

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

Compute localization errors of the non-metric MDS algorithm according to

To verify the performance of the

Since the explosive-proof certification of our mine products was in process, the whole performance study of anchor-free localization method was executed in the mine gas explosion laboratory, which simulates the real environment of underground mines. The average temperature in the laboratory of mine gas explosion is about 24.5 °C and the average relative humidity is about 56.8%. The length of the tunnel is about 160 meters and the width is about 2 meters. Our ZigBee network comprises one gateway node, 10 static router nodes, 16 static sensor nodes and a mobile node. Sensor nodes are not involved in the localization process. Router nodes are deployed in fixed location every 15 meters. They completed location estimation based on the non-metric MDS algorithm with four anchor nodes firstly. Then the mobile node conducted the localization process with the

An anchor-free localization method for mobile targets is implemented in C-WSN based on non-metric MDS and

This work was supported in part by the National High Technology Research and Development Program of China under Grant No. 2006AA04Z208.

Example of rank sequences for four anchor nodes.

Localization errors due to

Localization for marginal nodes.

Circuit boards of Cicada sensor nodes.

Distributed system architecture for C-WSN.

Pictures of Cicada physical nodes.

Comparison between true location and estimated location due to non-metric MDS.

Non-metric MDS performance.

Outdoor experiments.

The average localization errors as a function of standard deviation

When

The performance comparison of SBL method and

Experiments in the mine gas explosion laboratory.

Performance comparison of anchor-free localization method.