Research of node localization algorithm based on wireless sensor networks in marine environment monitoring

Abstract

Focusing on the applications of wireless sensor networks in marine environment monitoring, a localization algorithm in underwater wireless sensor networks with self-healing (SHLA) was proposed.The algorithm adopt the k-node overlay algorithm to elect some nodes as anchors, so as to make maximum common sensor nodes covered by four anchor nodes. The normal nodes adopt the location coordinate of the anchor node to locate the position, and then the nodes transmit the monitored environmental information and their coordinate information to the surface buoy. In order to avoid reducing the localization coverage and localization accuracy due to anchor nodes failure in underwater wireless sensor network, the node remedial positioning measures is adopted to reduce the effects of nodes failure in the localization algorithm, and locating the covered common nodes by locating other nodes instead of low-energy or ineffective anchor nodes. According to the simulation, this algorithm can effectively improve the localization coverage, relieve the impact caused by anchor nodes failure and prolong the network life at the time.

Keywords

Underwater wireless sensor networks node localization localization accuracy localization coverage self-healing reference nodes

1. Introduction

Underwater Wireless Sensor Network (UWSN) is a kind of Wireless Sensor Network (WSN), which consists of a variety of underwater sensor nodes, underwater autonomous aircraft and base stations, these nodes can sense certain signals within their coverage and pass the signals locally to the desired user [1]. According to the different types of sensor nodes, we can collect the hydrological data such as temperature of water environment, pressure, salinity and PH and so on, so as to complete many tasks such as environmental management, resource protection, disaster monitoring, military intelligence and so on, and the implementation of these applications need to grasp the location information of nodes in advance [2]. When the sensor nodes are deployed in water, they are moved due to the influence of factors such as water flow, underwater disturbance or collision of water animals and so on, so it is difficult to determine the location of nodes in real time. Moreover, it is necessary to the Coordinate information of the reference nodes when the normal nodes are positioned, when a few ordinary nodes in UWSN move to outside the communication scope of all the reference nodes because of external interference, these nodes can not be positioned, and they become isolated nodes. Therefore, how to overcome the movement problem of nodes in complex water environment, to locate isolated nodes from the scope of reference nodes communication, and to improve the location coverage of underwater wireless sensor network nodes are the focus of the study [3].

Figure 1.

Trilateral positioning method.

In the study of static underwater sensor networks, in view of nodes localization, the researchers turn three-dimensional positioning into two-dimensional positioning, and the traditional node positioning algorithms such as Time of Arrival (TOA), Received Signal Strength Indication (RSSI) and Angle of Arrival are used to calculate node coordinates in XOY firstly, then the $z$ -axis coordinates are determined according to the relationship between the underwater depth and the pressure value [4]. In addition, the researchers also take advantage of the characteristics of underwater sensor network voice transmission signal, and put forward the problem of time synchronization [4], the positioning accuracy is improved by controlling error propagation. For the underwater sensor network of nodes movement, the researchers mainly studied them under the premise of the hypothesis that nodes have a self-positioning function or sensor nodes have a positioning device with global positioning system (GPS) [5, 7]. However, in practical applications, the technical and cost issues are taken into account, it is impossible to equip positioning devices with GPS for each sensor node, and it is impossible to maintain a fixed position for each sensor node. Due to the mobility of the seawater, the sensor nodes will move along it, which leads to frequent changes in the topology of the network. Using the positioning mechanism in the static positioning algorithm, it is necessary to frequently update location information of nodes, which will not only consume the amount of resources, but also reduce the network response capability and positioning accuracy [6]. Therefore, for the wireless sensor network in marine monitoring, some of nodes are fixed by underwater anchored buoys or latent targets, and the location is known, the remaining nodes move freely with the sea water, in that case, a kind of underwater wireless sensor network location algorithm with self-healing is presented in this paper. When nodes are deployed, the anchor nodes and ordinary nodes are not distinguished in the algorithm, the anchor nodes are selected by the k-node coverage, and the normal nodes in the network are covered by four anchor nodes. At the same time, the algorithm replace low energy or failed anchor nodes with finding other nodes to locate the covered ordinary nodes, so as to avoid repeating election anchor nodes, and the positioning error that caused by energy depletion or failure of the anchor nodes can be reduced, the nodes positioning accuracy and positioning coverage can be improved, the algorithm is suitable for the underwater environment of slow flow velocity.

2. Mathematical model of positioning algorithm

2.1 Trilateral ranging algorithm model

Trilateral measurement method is a more extensive positioning method in practical applications, the principle has shown in Fig. 1. The distances $d_{1}$ , $d_{2}$ and $d_{3}$ between the unknown node P and anchor nodes A, B and C are obtained by the distance measurement technology respectively. Three circles are painted and they intersect at one point P, they take A, B and C as the center, take $d_{1}$ , $d_{2}$ and $d_{3}$ as the radius respectively. The coordinates of A, B, C and P are $({x_{1},y_{1}})$ , $({x_{2},y_{2}})$ , $({x_{3},y_{3}})$ , $({x,y})$ respectively. According to the distance formula between the point and the point, we can get the Eq. (1), it is given by

$\begin{cases}{({x-x_{1}})^{2}+({y-y_{1}})^{2}=d_{1}^{2}}\\ {({x-x_{2}})^{2}+({y-y_{2}})^{2}=d_{2}^{2}}\\ {({x-x_{3}})^{2}+({y-y_{3}})^{2}=d_{3}^{2}}\\ \end{cases}$ (1)

Figure 2.

Quadrilateral positioning model.

The coordinates $(x,y)$ of unknown node P can be calculated according to Eq. (1), it is given by

$\left[\begin{array}[]{*{20}c}x\\ y\\ \end{array}\right]=\left[\begin{array}[]{*{20}c}{2({x_{1}-x_{3}})}&{2({y_{1}-y% _{3}})}\\ {2({x_{2}-x_{3}})}&{2({y_{2}-y_{3}})}\\ \end{array}\right]^{-1}\left[{{\begin{array}[]{*{20}c}{x_{1}^{2}-x_{3}^{2}+y_{% 1}^{2}-y_{3}^{2}+d_{3}^{2}-d_{1}^{2}}\\ {x_{2}^{2}-x_{3}^{2}+y_{2}^{2}-y_{3}^{2}+d_{3}^{2}-d_{2}^{2}}\\ \end{array}}}\right]$ (2)

However, when the measurement distances are not accurate by three-sided measurement method, and there are more than one intersection or there are no intersection between the three circles, so it is impossible to achieve accurate positioning of unknown nodes. In order to further improve the accuracy of the algorithm based on distance measurement, the quadrilateral ranging algorithm is adopted.

2.2 Quadrilateral ranging algorithm model for three dimensional space

In order to further improve the positioning accuracy, the four-edge ranging positioning algorithm is adopted, that is, on the basis of the three sides ranging, then a anchor node is added to participate in positioning, it has shown in Fig. 2. At the same time, we know that three points in the space can determine a plane. If we know the coordinates of the three anchor nodes and the distance to the unknown nodes, we can determine the coordinates of two unknown points, which are symmetrical on both sides of the plane. If we know the coordinate of a point and the distance to the unknown nodes, we can determine the coordinates of unknown nodes. Therefore, we can determine the coordinate of an unknown node in the three-dimensional space, and the location information of the four anchor nodes and the distance from the unknown nodes to their distance should be known, so this positioning method is called the quadrilateral measurement method.

Assuming that the coordinate of the unknown node P is $({x,y,z})$ , the four anchor nodes A, B, C and D monitor the target at a time, Their coordinates are $({x_{1},y_{1},z_{1}})$ , $({x_{2},y_{2},z_{2}})$ , $({x_{3},y_{3},z_{3}})$ and $({x_{4},y_{4},z_{4}})$ respectively, and their distance to the unknown node P is $d_{1}$ , $d_{2}$ , $d_{3}$ and $d_{4}$ . Then

$({x-x_{i}})^{2}+({y-y_{i}})^{2}+({z-z_{i}})^{2}=d_{i}^{2}\quad(i=1,2,3,4)$ (3)

According to Eq. (3), the coordinate of the unknown node P can be calculated as follows:

$\left[{{\begin{array}[]{*{20}c}x\\ y\\ z\\ \end{array}}}\right]=\frac{1}{2}\left[{{\begin{array}[]{*{20}c}{({x_{2}-x_{1}}% )}&{({y_{2}-y_{1}})}&{({z_{2}-z_{1}})}\\ {({x_{3}-x_{1}})}&{({y_{3}-y_{1}})}&{({z_{3}-z_{1}})}\\ {({x_{4}-x_{1}})}&{({y_{4}-y_{1}})}&{({z_{4}-z_{1}})}\\ \end{array}}}\right]^{-1}\left[{{\begin{array}[]{*{20}c}{x_{2}^{2}-x_{1}^{2}+y% _{2}^{2}-y_{1}^{2}+z_{2}^{2}-z_{1}^{2}+d_{1}^{2}-d_{2}^{2}}\\ {x_{3}^{2}-x_{1}^{2}+y_{3}^{2}-y_{1}^{2}+z_{3}^{2}-z_{1}^{2}+d_{1}^{2}-d_{3}^{% 2}}\\ {x_{4}^{2}-x_{1}^{2}+y_{4}^{2}-y_{1}^{2}+z_{4}^{2}-z_{1}^{2}+d_{1}^{2}-d_{4}^{% 2}}\\ \end{array}}}\right]$ (4)

3. Underwater environmental structure model

Underwater environmental structure model has shown in Fig. 3, there are two different types nodes that they are sensor nodes and surface buoys in the model. Sensor nodes are randomly distributed in the target area, all nodes are the same, anchor nodes and ordinary nodes are not differentiated too, and then a part of nodes are selected to anchor nodes through the K-node coverage algorithm. Assume that the nodes are randomly distributed in different depths of the water according to the density situation, so that the nodes are randomly distributed in the three-dimensional underwater environment. The water buoy is randomly anchored in the target area of water surface, and its own position can be obtained by GPS device. Because of the sufficient energy, the information transmitted by sensor nodes can be collected and processed in the algorithm.

The algorithm of underwater wireless sensor network localization with self-repair capability is proposed, which mainly includes the underwater positioning algorithm of electing anchor nodes and the self-repairing localization algorithm based on anchor nodes failure. The positioning algorithm of selecting anchor nodes mainly includes positioning anchor nodes, positioning common sensor nodes and information transmission. When anchor nodes fail or drift to the sparse area of nodes, and can not be located due to the lack of location information, Nodes broadcast a signal that can not be positioned. When located nodes receive the signal that can not be located, whether it has the qualification to be converted into reference node or not, it is forced to be converted to reference node, in order to help nodes location, and each of the located nodes in the network will calculate their own accuracy, so no located nodes can select the nodes with higher accuracy from the received location information to improve the positioning accuracy. After a positioning cycle, located nodes that have been converted into reference nodes, which have been converted into common location nodes, so as to avoid the proliferation of information. In addition, most nodes will move with the influence of ocean currents and tides, and it is difficult to get the law of their movement. Therefore, it is necessary to re-position nodes periodically. Therefore, this paper sets a positioning error threshold, when the positioning error exceeds the set threshold, and the network has failed, the positioning is no longer done.

Figure 3.

Structure model in underwater environment.

4. Node location algorithm

4.1 Anchor node election and location algorithm

Each sensor node can perceive and collect the surrounding environment information, and the nodes exchange information through the underwater acoustic signal with each other, $s_{i}$ not only represents sensor node, but also represents its position coordinates. If the node $s_{0}$ is in a circle, and the circle is centered on $s_{i}$ and $R({s_{i}})$ is radius, that is, $D({s_{0},s_{i}})\prec R({s_{i}})$ , $s_{0}\neq s_{i}$ , then the node $s_{0}$ is called the neighbor of $s_{i}$ . If the two nodes have the same communication range, they are neighbors. the node $s_{0}$ is in a circle, and the circle is centered on $s_{i}$ and $R({s_{i}})$ is radius, then node $s_{0}$ is covered by node $s_{i}$ . $N$ nodes form a collection $I=\{{s_{1},s_{2},\ldots s_{i},\ldots s_{n}}\}({n\geqslant K})$ , if the distance between nodes $s_{0}$ and $s_{i}$ is less than the communication radius of $s_{i}$ , that is, $D({s_{0},s_{i}})\prec R({s_{i}})({i=1,2,\ldots n})$ , then the set $I$ is k-coverage for the node $s_{0}$ . The K-coverage relationship indicates that the node $s_{0}$ is within the communication range of not less than $K$ nodes in the set $I$ . In this paper, $K=4$ , that is, each node in the network is covered by four anchor nodes. $\forall\textit{SN}∼{}s_{i}\in\textit{SN}∼{}\exists\textit{at}∼{}\textit{least}% ∼{}4\textit{AN}s∼{}b_{j}∼{}s.t.∼{}D(s_{i},b_{j})\leqslant\min(C({s_{i}}),C({b_% {j}}))$ , SN denotes a normal sensor node, and AN denotes an anchor node. $D({s_{i},b_{j}})$ represents the Euclidean distance between nodes $s_{i}$ and $b_{j}$ , $C({s_{i}})$ and $C({b_{j}})$ represent the communication radius of nodes $s_{i}$ and $b_{j}$ , respectively.

Figure 4.

The importance graphic of 4 anchors to localize a node in a 3D environment.

In an $k-1$ -dimensional space, a node location must be at least covered by $K$ nodes ( $K\succ 1$ ). The importance graphic of 4 anchors to localize a node in a 3D environment is shown in Fig. 4. Anchor nodes A, B and C can determine the coordinates of two points $S$ and $S^{\prime}$ , the two points are symmetrical about the plane ABC, then an anchor node D is added, and the anchor nodes is not in the same plane with A, B and C, the point $S$ coordinates can be determined.

Thus, in a three-dimensional environment, a common sensor node is located through four anchor nodes that are not in the same plane. The coverage algorithm can achieve 4-nodes coverage, which means that the common nodes in each sensor network are within the communication radius of four anchor nodes. The four anchor nodes can know their own position, the solution of the four equations can be solved according to the three-dimensional Euclidean distance estimation method, and three unknown $x$ , $y$ and $z$ are obtained, $(x,y,z)$ is the absolute position that the ordinary node is in the three-dimensional underwater environment. Moreover, in the proposed K-covering algorithm, the coplanar probability of four anchor nodes that have been elected to cover a node is zero. The K-node coverage algorithm is as follows:

Step4 Step1

After nodes are randomly distributed in the target area, each common node $s_{i}$ broadcasts information to neighbor nodes, which contains its own ID number and energy value.

Step2

After the waiting time $\tau$ , each node $s_{i}$ receives the information of all neighbor nodes, and the neighbor nodes table $N({s_{i}})$ (including the ID number and energy value of all neighbor nodes) is set, then the table is sent to the neighbor nodes.

Step3

Ordinary nodes $s_{i}$ know their own neighbor nodes $s_{j}$ and their neighbor nodes table $N({s_{j}})$ . If the number of neighbor nodes $N({s_{j}})$ in a neighbor node is equal to 4, then the node $s_{i}$ is elected as the anchor node. If the number of neighbor nodes table $N({s_{j}})$ in all neighbor nodes is greater than 4, the four nodes that have the larger energy are taken as anchored nodes in neighbor nodes of the election node $s_{i}$ .

Step4

If the number of anchor nodes around a common node is greater than 4, the anchor nodes with smaller energy are marked as ordinary nodes without affecting the coverage of other nodes. After the above three steps, There may be a situation in K-node coverage algorithm, namely, the number of anchor nodes around some common nodes is greater than 4. It has shown in Fig. 5, the neighbor nodes of node P are A, B, C, D, E, F and G, the number of neighbor nodes of these seven nodes is greater than 4, then the nodes with large energy A, B, C and D are taken as anchor nodes. The number of neighbor nodes of neighbor node Q of the node E is equal to 4, and the node E is elected as the anchor node. Therefore, the node P will be covered by five anchor nodes A, B, C, D and E, in order to reduce energy consumption and avoid data redundancy, the redundant anchor nodes need to be marked as ordinary nodes by the step 4 of the algorithm.

Figure 5.

There are more than four anchor nodes in one node’s communication radius.

So the flow chart of the K-node coverage algorithm has shown in Fig. 6. $|{N({s_{j}})}|$ indicates the number of nodes in the neighbor node table of the node $s_{j}$ .

After the anchor nodes are selected, and they need to be positioned. The communication capacity, storage capacity and computing power for underwater anchor nodes are relatively stronger, and they can directly communicate with the surface buoy nodes, can locate themselves by taking use of information received. Water buoys are those nodes that have GPS and can obtain their own location information, and they exist as satellite nodes in underwater positioning.

4.2 Ordinary node localization algorithm

There are two cases for ordinary nodes location, one has no fewer than four neighbor nodes, the other has three neighbor nodes, and the number of neighbor nodes of these three nodes is not less than 4. If a common node has not less than four neighbor nodes, it can be covered by four anchor nodes through the K-node coverage algorithm. the distance can be obtained between the ordinary node and the surrounding anchor nodes through the distance measurement technique, and the itself coordinates are estimated by the quadrilateral measurement method. If a common node has three neighbor nodes, and the neighbor nodes of the three nodes are not less than 4. Because nodes are randomly deployed in the underwater environment, at the beginning, there may be cases where some nodes have fewer than four neighbor nodes, and even if all of their neighbor nodes become anchor nodes, the positioning can not be completed, and the situation can be processed in the K-node coverage algorithm. However, at the beginning, this paper considers that a node has three neighbor nodes, and the number of neighbor nodes of three nodes is not less than four. Assuming that node A has three neighbor nodes B, C and D at the beginning, nodes B, C and D may be anchor nodes or normal nodes, but due to the neighbor nodes of node B, C and D are not less than 4, Node B, C and D will get their own position after the above steps.

Figure 6.

The flowchart of K-node covering algorithm.

Now the unknown node A is located by the nodes B, C and D whose position are known, the nodes B, C and D will determine the two points $S$ and $S^{\prime}$ by Euclidean distance estimation method in the three-dimensional environment, and the two points are about plane BCD symmetry. Node B searches whether the distance between the neighbor nodes (except nodes A, C, D) and the two points $S$ and $S^{\prime}$ is less than the communication radius. Assuming that the distance between the neighbor nodes and the points $S^{\prime}$ is less than the radius of the communication, and the point $S^{\prime}$ is abandoned, then the obtained point $S$ is the node A. the distance between the neighbor nodes and the two points $S$ and $S^{\prime}$ is less than the communication radius for node B, and so on, the nodes C, D search whether the distance between the neighbor nodes and the two points $S$ and $S^{\prime}$ is less than the communication radius in turn.

4.3 Information transfer

After the common node is located, the node starts to monitor the information in the environment of the communication radius. When the information is monitored, the node transmits the information and its own location to the water buoy through the routing protocol algorithm. the source position of the information is processed and calculated by water buoy. the nodes that monitor the information are more, and the location is more accurate, it has shown in Fig. 7. Nodes A, B, C and D monitor the same event Z, nodes A, B, C and D send their own position and Euclidean distance $d_{\textit{AZ}}$ , $d_{\textit{BZ}}$ , $d_{\textit{CZ}}$ and $d_{\textit{DZ}}$ from the event to the surface buoy respectively. Based on this information, the surface buoy can determines that the occurrence of the event is the shaded area in Fig. 7.

Figure 7.

Several nodes detecting the same event and giving the localization of this event.

5. Self-repairing method based on anchor node failure

The anchor nodes communicate with the water buoy through the GPS system, in order to complete its own location and send its own location information to the ordinary nodes and so on. Compared with ordinary nodes, the energy consumption is more larger and it is easy to die for anchor nodes. At the same time, due to underwater environment is poor, the anchor nodes are prone to accidental failure. Due to the importance of the anchor nodes in the positioning process, this paper proposed a self-repair algorithm based on the failure of anchor nodes, and other nodes are found to replace the anchor nodes that are about to die or fail, so as to avoid repeating the election of anchor nodes, and to reduce the positioning errors that cause due to energy depletion or failure of anchor nodes. When anchor nodes fail or drift to the sparse area, the positioning can not be done due to the lack of location information, and nodes broadcast the signal that can’t be located. When the located nodes receive the signal that can not be located, whether it has the qualification to be converted into reference node or not, it is forced to be converted to reference node, in order to help nodes location, and each of the located nodes in the network will calculate their own accuracy, so no located nodes can select the nodes with higher accuracy from the received location information to improve the positioning accuracy. After a positioning cycle, the located nodes that has been converted into reference nodes, which has been converted into common location nodes, so as to avoid the proliferation of information. The specific positioning method is as follows:

Step4 Step1
The buoy nodes float in the water, equip with GPS system, and can directly get their own coordinates.
Step2
The anchor nodes communicate with the buoy nodes, and locate their coordinates through the quadrilateral measurement method, then broadcast their own position information to help the common nodes location.
Step3
Within a positioning period, if unknown nodes have not less than four neighbor nodes (the location information of the reference nodes may be contained), or there are three neighbor nodes and the number of neighbor nodes is not less than 4 ordinary nodes, and the quadrilateral measurement method is adopted to calculate their own coordinates. their own accuracy are calculated according to Eq. (5) after calculating their own coordinates. In Eq. (5), $({u,v,w})$ is the its own position coordinates that calculate by the positioning node, $({x_{i},y_{i},z_{i}})$ is the coordinates of the reference node, $\eta_{i}$ is the accuracy of the corresponding reference node, $l_{i}$ is the distance between the nodes and the corresponding reference nodes, and $l$ is the average value of $l_{i}$ . The accuracy of the anchor nodes in the network is 1, and the normal nodes are positioned according to the Eq. (5). Accuracy changes with the positioning cycle, the accuracy will be recalculated after each re-positioning. After the calculation is completed, their own qualified that converted into a reference node can be determined according to the threshold set. If the node satisfies the transformation condition, it is converted to a reference node to help locate the unreserved node.

$\eta=\frac{\sum\limits_{i=1}^{3}{\eta_{i}}}{3}\left({1-\frac{\sum\limits_{i=1}% ^{3}{|{({u-x_{i}})^{2}+({v-y_{i}})^{2}+({w-z_{i}})^{2}-l_{i}^{2}}|}}{\sum% \limits_{i=1}^{3}{({({u-x_{i}})^{2}+({v-y_{i}})^{2}+({w-z_{i}})^{2}})}}-\frac{% \sum\limits_{i=1}^{3}{({l_{i}-l})^{2}}}{\sum\limits_{i=1}^{3}{l_{i}^{2}}}}\right)$ (5)

Figure 8.
The located nodes operation flow.

Figure 9.
Not located nodes operation flow.

Accuracy can help the node to determine whether it is qualified to be converted into a reference node, and in the subsequent positioning, can help the unidentified nodes to filter out more accurate location information, thereby the accuracy of the entire network positioning is improved.
Step4
In the failure area of anchor nodes, or in the sparse area of anchor nodes, the unknown nodes are able to receive enough location information. Therefore, in a positioning period, if the unknown node does not receive four or more position information, then broadcast their own signal that can not be located.
Step5
If the located nodes have received the signal that can not be located, and have not been translated into reference nodes, they will be converted into the reference nodes directly, so the constraints that are converted to reference nodes are no longer executed. Their own location information that have been broadcast, which can help positioning of nodes that can not be located after the located nodes are converted to reference nodes.
Step6
When the unknown nodes receive location information, if the location information is greater than 4, which is sorted according to the accuracy, and the four position information with higher accuracy are selected for positioning.
Step7
The located nodes that have converted into reference nodes, which will be changed into normal nodes after one cycle, and broadcast their own location information no longer.

In short, the type of information will be judged when the nodes receive the broadcast information, and the relevant operations are done according to their own state. The operational flow of the located nodes has shown in Fig. 8 and The operational flow of the unreserved has shown in Fig. 9.
6. Simulation experiment and results analysis

6.1 Simulation environment model

Underwater environment is complex and changeable, the propagation path of acoustic signal is mainly multi-path propagation, it is impossible to establish a model which can accurately simulate the underwater acoustic channel. After comparing the existing typical underwater acoustic channel model, the Rayleigh fading channels model is adopted, that is, the attenuation model of the underwater acoustic signal is given by:

$A({d,f})=A_{\textit{norm}}d^{k}a(f)^{d}$ (6)

where $f$ is the signal frequency, $d$ is the transmission distance, $A_{\textit{norm}}$ is the normalization constant, $a(f)$ is the absorption coefficient, $k$ is the diffusion factor. The diffusion factor is related to the structure of the underwater medium, $k=1.5$ in normal conditions [8, 11]. The absorption coefficient increases with the increase of the carrier frequency. For the frequency that is more than several hundred hertz, the empirical expression of the absorption coefficient is given [5, 10]:

$a(f)=0.003+\frac{0.11f^{2}}{1+f^{2}}+\frac{44f^{2}}{4100+f^{2}}+2.75\times 10^% {-4}\times f^{2}$ (7)

where the unit of $f$ is kHz, the unit of $a(f)$ is dB/km. For a lower frequency, Eq. (7) can be simplified to the following representation:

$a(f)=0.002+\frac{0.11f^{2}}{1+f^{2}}+0.011\times f^{2}$ (8)

When underwater temperature, salinity or pressure (depth) changes, the transmission velocity of the underwater acoustic signal will also change, in this paper, so the sound velocity model is as follows [10]:

$\displaystyle V_{P}=1449.05+45.7P-5.21P^{2}+0.23P^{3}+(1.333-0.126P+0.009P^{2})$ $\displaystyle\quad∼{}(S-35)+163H+0.18H^{2}$ (9)

where P is the temperature ( $P={T_{\textit{temperatyre}}}/{10}$ ), $S$ indicates salinity, $H$ indicates the depth, the calculation accuracy of the above formula can get to $0.07$ s/m.

6.2 Simulation results analysis

In order to test the performance of the algorithm, the SHLA algorithm and the large-scale positioning method (LSL) are simulated and analyzed with MATLAB from the aspects of positioning coverage, average positioning error and average communication cost. There are three kinds of nodes such as water buoy, anchor node and common node in large-scale positioning method (LSL) [9, 10]. The water buoy can obtain its own position information by GPS system, and the anchor node completes the location and broadcasts its position information to the network after it obtains the surface buoy position information, then the unknown node receives the location information of the anchor node to complete the positioning. This algorithm adopts the TOA ranging technique to calculate the distance between nodes, and selects some nodes with high positioning accuracy as the reference nodes, so as to participate in the positioning process of the next ordinary node. In the region of 100 m $\times$ 100 m $\times$ 100 m, 500 sensor nodes are randomly distributed, the ratio of anchor nodes is 10% in large-scale positioning method. This paper does not change the number of nodes and the area of them, but the node density is controlled by changing the node’s communication radius. In order to obtain effective statistical results, this paper takes the mean of ten simulation results, and the confidence rate is 95%. The nodes coverage of the different positioning algorithm have shown in Fig. 10. Since the node density is less than 8, the SHLA algorithm selects the ratio of the anchor nodes that is zero or too high, so the two algorithms are compared when the node density is 8. It can be seen that the nodes density increase and the positioning coverage increase gradually, as long as the nodes density are sufficient, all unknown nodes can be positioned. If the nodes density are larger, the nodes whose neighborhood number are greater than or equal to 4 are more, and the nodes that can be located are more, so the node coverage is relatively large. Compared with the large-scale positioning method LSL, because the SHLA algorithm selects a part of the nodes as the anchor nodes through the K-node coverage algorithm, so as to ensure that the ordinary nodes are most covered by four anchor nodes. SHLA algorithm positioning coverage is slightly better than the LSL algorithm, the two positioning coverage tends to be the same as the nodes density increase.

Figure 10.

Node coverage of different localization algorithm.

Figure 11.

Localization error of different algorithm in static environment (nodes density is equal to 9).

The positioning errors of the two positioning algorithms in static environment have shown in Fig. 11. When the node density is equal to 8, the positioning error of SHLA algorithm is larger because the nodes of the network are not covered by four anchor nodes. When the node density is greater than 8, the positioning error will gradually be smaller than the LSL algorithm, and does not change after a certain value. The reason why the SHLA algorithm is superior to the LSL algorithm is that the anchor nodes in the network override the ordinary nodes optimally, and do not need to select the reference nodes to help the other unknown location nodes to complete the positioning, so the errors will not be accumulated. When the self-healing algorithm is started, the errors can be accumulated in the self-healing algorithm, and the expected error will be increased, but this is not seen in the simulation results.

The positioning errors of the two positioning algorithms in dynamic environment have shown in Fig. 12. Most nodes will move with the influence of ocean currents and tidal effects, and it is difficult to get the law of its movement, so it is necessary to the periodic re-positioning of nodes. The simulation experiment is carried out in a slow underwater environment. For the LSL algorithm, the anchor nodes are better distributed at the beginning, but due to the nodes have different moving speed in the different depth, the relative position between the nodes will be changed greatly, the better distribution will be broken, and some anchor nodes will die or fail, so the errors will be increased. The SHLA algorithm will re-elect the anchor nodes, the optimal coverage of ordinary nodes will be done, and the self-repair algorithm can find other nodes to replace the anchor nodes that they are energy depletion or failure, so as to locate the coverage ordinary nodes, so the error of the SHLA algorithm is lower than LSL algorithm.

Figure 12.

Localization error of different algorithm in dynamic environment.

Figure 13.

Average communication cost of different algorithm.

The average communication overhead for the different positioning algorithms has shown in Fig. 13. Compared with LSL algorithm, The SHLA algorithm has the election of anchor nodes and self-repair algorithm, so the average communication overhead is larger. In the stage of self-repair, the communication cost of SHLA algorithm is related to the number of hops, The larger the hop count is, and the higher the communication cost is. The nodes density are larger in the SHLA algorithm, the common nodes are more covered by four anchor nodes, the number of self-repair algorithms is reduced, and the average communication overhead is smaller.

In conclusion, the simulation results have shown that the SHLA algorithm has improved the positioning coverage and positioning accuracy at the expense of a small part of communication overhead, and it is suitable for underwater environment with slow flow rate.

7. Conclusion

In this paper, A Positioning algorithm with self-repair capability is proposed for underwater wireless sensor networks. First, some nodes are selected as anchor nodes by K-node coverage algorithm, so that the nodes in the network are most covered by four anchor nodes. Second, The nodes adopt the position coordinates of the anchor nodes to complete their positioning. then the nodes transmit the detected environmental information and their own coordinate information to surface buoy. In view of the failure of anchor nodes in the network, the self-repair algorithm can locate the common nodes that are covered by the failure anchor nodes well. Since most nodes move with ocean currents and tides, and it is difficult to get the laws of their movement, the nodes need to be re-positioned periodically. If nodes that monitor the same event are more, and the positioning results are more accurate. Through the simulation analysis, compared with LSL algorithm, the SHLA algorithm has improved the positioning coverage and positioning accuracy, and it is suitable for the underwater environment with slow flow rate.

Footnotes

Acknowledgments

This work was supported by Jiangsu Province Fifth “333 Project” Scientific Research Funding Project (BRA2016292), Six Talent Peaks Project in Jiangsu Province (DZXX-038) and Open Fund Project of Marine Resources Development Institute of Jiangsu (JSIMR201414).

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