# MNCE: Multi-Hop Node Localization Algorithm for Wireless Sensor Network Based on Error Correction

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## Abstract

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## 1. Introduction

- Range-based localization algorithms require additional physical measurement techniques to complete the localization calculation. Physical measurement techniques, such as RSSI, TOA and AOA, are often used in the localization process of range-based localization algorithms [8];
- Range-free localization algorithms usually use multi-hop routing information directly obtained by sensor nodes in the network to achieve node localization [9].

## 2. Range-Free Localization Algorithms

## 3. MNCE Algorithm

- Distance estimation: We can get the estimated distance between nodes by the information that can be directly obtained by sensor nodes such as arrival time, hop number information and connected information;
- Initial localization: According to the estimated distance of the previous stage, the corresponding estimation algorithm is selected to complete the initial localization of the target node;
- Calibration localization: According to the information of the first two stages, the redundant information is eliminated, and the corresponding optimization algorithm is selected to optimize and calibrate the estimated location of target nodes.

#### 3.1. Distance Estimation

_{ij}represents the Euclidean distance between the two nodes. The general idea of this type of localization algorithms is to propose a measure which is positively correlated with the distance between nodes according to the node distribution and node connectivity information, and then to represent the measure as accurately as possible according to the locality of the node distribution. As an example of DV-hop algorithm: The estimated distance is calculated by the minimum hop count and the single hop correction.

_{ij}is obtained by geometric calculation:

_{ij}in Formula (2) is the distance between the two nodes, so we can get the area ratio between node communication overlap region and node communication region as shown in Formula (3):

_{ij}, so we cannot work out the d

_{ij}according to one formula. Formula (4) is the inverse function of Formula (3). We assume that there are a large number of sensor nodes in the WSN, and the nodes deployment characteristics in the local region of the node communication range are approximately the same. In addition, the ratio of the two regions is approximately equal to the ratio of the quantity of nodes in two regions. The MNCE algorithm does not require additional measurement techniques, as long as the neighbor nodes can communicate. Therefore, this type of localization algorithms has low power consumption and nodes can be deployed with the high density in such algorithms. The node distribution of local neighboring regions is approximately the same in WSNs with the node high density deployment. Therefore, we can approximate the area ratio of the two regions by the ratio of the quantity of nodes in the two local neighboring regions. Therefore, the distance d

_{ij}between neighbor nodes can be calculated using Formula (3):

_{i}, obviously the initial estimated distance is calculated using the above method:

_{ij}between the two hops is much less than d

_{ik}+ d

_{kj.}

_{ij}and area A

_{ij}must satisfy the Formula (2) if the distance between nodes is calculated by the method in this study. When the hop count is greater than 2, there is no overlapped area in the communication area between two nodes. Therefore, it is reasonable to divide the multi-hop distance into multiple accumulations in units of two hops. The node distance and area of two hops also apply to the function $\phi ({d}_{ij})$:

#### 3.2. Error-Correction Rate for the Estimated Distance

_{i}, y

_{i}) and d

_{ij}is the actual distance between the two anchor nodes.

#### 3.3. Node Location Method Based on Total Least Squares

_{A}and the error vector of the observation vector b is E

_{b}, the actual formula is shown in Formula (18):

## 4. Simulation Experiment

#### 4.1. Performance Indicators

#### 4.2. Impact of the Error Correction Rate on RADE

#### 4.3. Impact of Node Communication Radius on RADE

#### 4.4. Impact of the Total Number of Nodes on RAPE

#### 4.5. Impact of Node Communication Radius on RAPE

#### 4.6. Impact of the Proportion of Anchor Nodes on RAPE

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Hop count between the nodes connected by the three red lines is one hop, but the actual distance between them is quite different.

**Figure 3.**The two broken lines between node i and node j represent two communication paths, the red line represents the shortest path, and d1, d2 and d3 are the distance of each hop.

**Figure 8.**Impact of communication radius on RADE. (

**a**) broken line diagram of the experimental results; (

**b**) histogram of experimental significance values.

**Figure 9.**Impact of total number of nodes on localization error (RAPE). (

**a**) broken line diagram of the experimental results; (

**b**) histogram of experimental significance values.

**Figure 10.**Impact of communication radius on RAPE. (

**a**) broken line diagram of the experimental results; (

**b**) histogram of experimental significance values.

**Figure 11.**Impact of POA on RAPE. (

**a**) broken line diagram of the experimental results; (

**b**) histogram of experimental significance values.

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**MDPI and ACS Style**

Meng, Y.; Chen, Y.; Zhang, Q.; Zhang, W.
MNCE: Multi-Hop Node Localization Algorithm for Wireless Sensor Network Based on Error Correction. *Information* **2020**, *11*, 269.
https://doi.org/10.3390/info11050269

**AMA Style**

Meng Y, Chen Y, Zhang Q, Zhang W.
MNCE: Multi-Hop Node Localization Algorithm for Wireless Sensor Network Based on Error Correction. *Information*. 2020; 11(5):269.
https://doi.org/10.3390/info11050269

**Chicago/Turabian Style**

Meng, Yinghui, Yuewen Chen, Qiuwen Zhang, and Weiwei Zhang.
2020. "MNCE: Multi-Hop Node Localization Algorithm for Wireless Sensor Network Based on Error Correction" *Information* 11, no. 5: 269.
https://doi.org/10.3390/info11050269