Sensor nodes in underwater wireless sensor networks (UWSNs) are in a three-dimensional space, and water fluidity continuously changes the positioning in water, the clock synchronization of underwater nodes is challenging, and ranging algorithms affected by water flow produce large errors. A three-dimensional UWSN positioning algorithm based on modified RSSI values is proposed to address the problem of UWSN positioning algorithms being susceptible to water influence and prone to unstable positioning and large positioning errors. An unlocated node screens the received anchor node signal strength and then makes a weighted correction to reduce the influence of the water environment and improve the ranging accuracy. A position estimation model is proposed and combined with a three-dimensional underwater model and least squares method to deduce the unlocated node’s position on the basis of the distance between the unlocated node and the anchor node. The proposed algorithm effectively reduces the influence of the water environment on the ranging algorithm’s accuracy and improves the performance of three-dimensional underwater positioning algorithms. Simulation results show that the proposed algorithm can effectively reduce the influence of the underwater environment on positioning algorithms.

Sensor node positioning is a key technology in wireless sensor networks. With the development of terrestrial wireless sensor network applications, underwater wireless sensor network applications have attracted increasing attention. However, the complex underwater environment hinders the location of underwater wireless sensor networks (UWSNs) [

In sum, underwater positioning algorithms in UWSNs are prone to large errors, and they are susceptible to water fluidity. Moreover, the nodes comprising UWSNs are difficult to synchronize. A received signal strength ranging algorithm is low cost and requires simple technology and minimal hardware. However, underwater sensor nodes are difficult to replace, they are susceptible to the underwater environment, their energy is limited, and their cost is relatively high. Therefore, a three-dimensional UWSN positioning algorithm based on modified RSSI values is proposed in this work. Weighted and modified RSSI values reduce ranging errors. Combined with a three-dimensional underwater positioning model, the proposed algorithm can estimate the unlocated node position in a three-dimensional space by using the least squares method. The proposed algorithm shows improved robustness, reduces the impact of underwater fluidity on ranging, and enhances the accuracy of network node positioning.

A ranging algorithm based on received signal strength can convert the signal strength received by an unlocated node and sent by an anchor node in a certain distance. Specifically, a mobile anchor node sends the signal. During the transmission process, certain loss occurs because of the influence of the external environment. The longer the transmission distance is, the greater the signal loss will be and the smaller the RSSI value received by the unlocated node. The loss during transmission can be converted into an RSSI value through the path loss model. In an actual ranging process, the loss model uses a log-normal distribution model. The parameters in the model can be calculated by the actual distance between anchor nodes and by the algorithm measurement distance [

In the current work, the signal transmission attenuation model uses a log-normal distribution model:

By simplifying formula (

The distance

The signal strength ranging algorithm is easily affected by the application environment, thereby resulting in ranging errors [

A mobile anchor node broadcasts signals regularly during its movement. Anchor nodes release signal

According to formula (

According to formula (

As the anchor node moves through the network and broadcasts signals to the surroundings, the ordinary node receives information from the anchor node and uses the distance conversion model to calculate the distance between nodes. In this section, a position estimation model is proposed to obtain the location information of unlocated nodes on the basis of the distance between nodes.

Wireless sensor networks on land generally require two-dimensional planar positioning, whereas UWSNs in special underwater environments require three-dimensional positioning [

The positioning requirements of wireless sensor networks on land are generally two-dimensional planar positioning, while the special underwater environment requires UWSN to adopt a three-dimensional positioning. The traditional positioning algorithm cannot meet the requirement of underwater sensor nodes positioning. It is necessary to consider how the anchor node and normal node send and receive signals in the three-dimensional underwater environment.

As shown in Figure

Sensor node sending and receiving signals.

In a three-dimensional underwater environment, unlocated nodes receive the information of

Sensor nodes sending and receiving signals.

Three sensor nodes form a plane. An unlocated node in underwater node positioning requires three anchor nodes, and four nodes form a polyhedron. Four nodes need to be projected to a horizontal plane to achieve relative positioning. Three anchor nodes are mapped to the same plane as that of the unlocated node. The coordinate

From formulas (

The coordinates of

Formula (

Formula (

Finally, the estimated position coordinate of the unlocated sensor node

Differences exist between water and terrestrial environments [

As shown in Figure

Algorithm model diagram.

The process of the proposed three-dimensional positioning algorithm is shown in Figure

Step 1: the mobile anchor node traverses the network according to the planned route, reaches the specified location, broadcasts signals for _{i}, _{i}, _{i}) of the location.

Step 2: the unlocated node receives the information of the mobile anchor node and records the information list and signal strength on its own information list. The ID number of the same position corresponds to

Step 3: the node processes the data in the obtained information list. A unique RSSI value is obtained by correcting the signal strength at the same position through the weighted modified RSSI value model. The information list is updated. An unknown ID corresponds to a signal strength.

Step 4: according to the distance conversion model, only the input RSSI value gets the distance between nodes.

Step 5: the unlocated nodes repeat Steps 2, 3, and 4 to obtain the corresponding distance of three position IDs and convert the three-dimensional space ID into a two-dimensional space ID by using the three-dimensional positioning model.

Step 6: the maximum likelihood estimation method is used to calculate the two-dimensional coordinates of the positioning node. With the node’s own depth information, the three-dimensional reverse conversion is carried out, and two-dimensional coordinates are converted into three-dimensional network coordinates. The estimated position of the unlocated node is obtained, thereby completing the network positioning.

Algorithm flowchart.

MATLAB 2016a simulation software is applied to test the proposed positioning algorithm. A total of 50 ordinary sensor nodes are randomly arranged; the proportion of anchor nodes is 20%, and the communication radius of ordinary nodes is 20 m. Ordinary sensor nodes cannot be removed after being randomly deployed. Each anchor node is aware of its own position information. The logarithmic attenuation model is used in the signal propagation attenuation model in the experiment. The proposed algorithm is compared with the traditional RSSI location algorithm, the median RSSI location algorithm, and the DV-Hop location algorithm based on RSSI value optimization [

Three-dimensional distribution diagram of UWSN nodes.

Top view of three-dimensional node distribution.

The evaluation indexes of the positioning algorithm in this work are as follows.

Average measuring distance: ^{th} unlocated node and the ^{th} anchor node. _{ij} represents the measuring distance between the ^{th} unlocated node and the ^{th} anchor node.

Node average positioning error: the difference between the estimated position and the actual position of unlocated sensor node _{i}.

The smaller the node average positioning error is, the higher the positioning accuracy is and the better the performance of the positioning algorithm will be, as shown in the followingformula:

Average maximum positioning error: in formula (_{i} represents the ^{th} maximum positioning error of the node and _{Meero} represents the average maximum positioning error of the node:

The experimental parameter settings are shown in Table

Experimental parameter settings.

Parameter | Value |
---|---|

Simulation area side length (m) | 100 |

Total number of sensor nodes (n) | 50 |

Anchor node ratio (%) | 20 |

Ordinary node communication radius (m) | 20 |

Anchor node communication radius (m) | 25, 30, 35, and 40 |

Signal transmission attenuation model | Logarithmic attenuation model |

Path loss index | 2 |

Given the 20 m communication radius of common nodes and the varying communication ranges of anchor nodes, the actual distance between nodes, traditional RSSI distance, median RSSI distance, and modified RSSI distance are compared in this work (Table

Average measured distance between nodes.

Anchor node communication radius (m) | Actual distance (m) | Traditional RSSI ranging (m) | Median RSSI ranging (m) | Modified RSSI ranging (m) |
---|---|---|---|---|

25 | 12.9948 | 9.918 | 11.1843 | 11.9665 |

30 | 9.75967 | 7.7065 | 8.6203 | 9.0692 |

35 | 17.5656 | 15.7956 | 16.8796 | 17.1693 |

40 | 11.4812 | 12.2875 | 11.0354 | 11.6564 |

Given the 20 m communication range of ordinary nodes and the varying communication ranges of anchor nodes, this work compares the average node positioning errors of the traditional RSSI positioning algorithm, DV-Hop-based positioning algorithm, and three-dimensional UWSN positioning algorithm based on revised RSSI values. The comparison is illustrated in Figure

The average positioning error of nodes.

Figure

Average maximum positioning error.

A three-dimensional UWSN positioning algorithm based on modified RSSI values is proposed to address the problem of UWSN positioning algorithms being susceptible to water influence and prone to unstable positioning and large positioning errors. The unlocated node screens the received signal strength of the anchor node and then performs weighted correction to reduce the influence of the water environment and improve ranging accuracy. Combined with a three-dimensional underwater environment, the accuracy and stability of the positioning algorithm are improved, and the error of the underwater positioning algorithm is reduced. The algorithm is simulated with other related positioning algorithms through experiments. The results show that the proposed three-dimensional UWSN positioning algorithm based on modified RSSI values remains stable, shows improved ranging accuracy, and reduces positioning error.

No data were used to support this study.

The authors declare that there are no conflicts of interest regarding the publication of this paper.

This work was supported by Natural Science Foundation of Guangxi (2019GXNSFAA245053), Guangxi Science and Technology Major Project (AA19254016/2019AA06002), Beihai Science and Technology Planning Project (202082023), and Beihai Science and Technology Planning Project (202082033).