# ECS-NL: An Enhanced Cuckoo Search Algorithm for Node Localisation in Wireless Sensor Networks

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## Abstract

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## 1. Introduction

## 2. System Model

#### 2.1. System Architecture

#### 2.2. Distance Calculation Model

#### 2.3. Operation Scenarios

- (i)
- Most Likely ScenarioThis scenario is most likely to happen during the testing phase. Here, M number of anchor nodes and N number of unknown nodes would be placed randomly and each unknown node would call the ECS algorithm to localise itself. In this way, all the nodes are likely to localise themselves using the ECS node localisation process. The ranging error between any two arbitrary nodes depends on the Euclidean distance between them and is independent of the ranging error between any other two nodes of the network.
- (ii)
- Diverse ScenarioThis scenario is infrequent to be implemented in a network, yet essential to consider. Any unknown node requires at least three or more anchor nodes within its transmission range to become localised. This scenario occurs when an unknown node gets deployed in a deserted area with no minimum anchor nodes around it, which prohibits the unknown node from getting localised. Figure 2 illustrates the diverse scenario of operation, which is also the limitation scenario of node deployment and is outside the control domain of node localisation. Consequently, the unknown nodes would remain unlocalised.

#### 2.4. Optimisation Problem Formulation

#### 2.5. ECS Algorithm

#### 2.6. Proposed Node Localisation Process in WSNs

- Deploy a finite M number of anchor nodes and N number of unknown nodes; each node is assumed to have a homogeneous transmission range equal to R.
- Establish the objective function using Equation (5).
- Each unknown node attempts to localise itself by running the ECS algorithm independently.
- ECS algorithm estimates the optimal positions for all the localisable nodes by minimising the ranging error. After getting localised, each unknown node starts acting as an anchor node and helps other localisable nodes get localised, indicating the increase in the number of anchor nodes as the iteration count progresses.
- Repeat steps 2–5 until all the localisable nodes become localised.
- The performance of the node localisation process is analysed in terms of ALE and Localisation Success Ratio (LSR). These parameters are discussed in the simulation analysis in Section 3.1.

Algorithm 1:ECS algorithm |

## 3. Simulation Experiment

#### 3.1. Simulation Analysis Parameters

- Average Localisation Error (ALE)ALE indicates how effectively the localisation technique estimates the position of the unknown nodes of the network. ALE is defined as the mean of the Euclidean distance between the estimated node location and the actual unknown node location of the sensor nodes, as shown by Equation (7)$$ALE=\frac{{\sum}_{i=1}^{{N}_{L}}\sqrt{{({X}_{i}-{x}_{i})}^{2}+{({Y}_{i}-{y}_{i})}^{2}}}{{N}_{L}}$$
- Localisation Success Ratio (LSR)LSR is defined as the ratio of the number of localised nodes to the total number of unknown nodes in the network and can be calculated by Equation (8):$$LSR=\frac{\mathrm{Number}\phantom{\rule{4.pt}{0ex}}\mathrm{of}\phantom{\rule{4.pt}{0ex}}\mathrm{unknown}\phantom{\rule{4.pt}{0ex}}\mathrm{nodes}\phantom{\rule{4.pt}{0ex}}\mathrm{localised}}{\mathrm{Total}\phantom{\rule{4.pt}{0ex}}\mathrm{number}\phantom{\rule{4.pt}{0ex}}\mathrm{of}\phantom{\rule{4.pt}{0ex}}\mathrm{unknown}\phantom{\rule{4.pt}{0ex}}\mathrm{nodes}}\times 100\%$$A higher value of LSR represents that the localisation algorithm performs better.

#### 3.2. Simulation Setup

## 4. Simulation Results and Analysis

#### 4.1. The Impact of the ES Criterion

#### 4.2. Comparison of Modified CS and ECS Algorithm

#### 4.3. Dependency of ECS Algorithm on Anchor Density

- ALEFigure 7a displays the variation effect of the anchor ratio on ALE. We found that the ALE decreases with an increase in the anchor ratio from $10\%$ to $50\%$. However, the value of ALE does not vary much with the anchor ratio, as it remains between 0.5 m and 2 m. Furthermore, the value of ALE decreases as the node density increases. This decrease owes to the network connectivity getting better with the increase in population density of the nodes.
- LSRFigure 7b shows the variation of the anchor density on LSR for different node densities in the network. We found that the ECS algorithm can localise all the localisable nodes with an anchor ratio of just $30\%$ and node density of 100 nodes. As the node density increases to 200 nodes, the ECS algorithm can localise all the unknown nodes present in the network with an anchor ratio of a mere $10\%$. A similar trend is observed when the node density is increased to 300. In Figure 7b, the observation points overlap each other for node density 200 and 300. Therefore, we can reduce the network cost using the ECS algorithm and make it less dependent on the GPS-assisted nodes.
- Number of Iterations (${N}_{iter}$)Figure 7c demonstrates that the number of iterations required to localise all the possibly localisable nodes decreases with increasing anchor ratio. This trend is observed because the number of unknown nodes to be localised reduces as the anchor ratio increases from $10\%$ to $50\%$. As we increase the node density, the required number of iteration also increases.

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**(

**a**) System architecture with M anchor (in black-filled circle) and N unknown nodes (in black-filled triangle) deployed in $X\times Y$ square units area. (

**b**) Sensor nodes with transmission range R distance units.

**Figure 4.**Comparison of modified Cuckoo Search (CS) algorithm and the proposed Enhanced Cuckoo Search (ECS) algorithm based on average time taken to localise one localisable node.

**Figure 5.**Variation of ALE with respect to the number of iterations for a transmission range of 15 m over a monitoring area of 100 m × 100 m.

**Figure 6.**Variation of total time taken with respect to the number of iterations for a transmission range of 15 m over a monitoring area of 100 m × 100 m.

**Figure 7.**Effect of anchor ratio variation on the performance of the proposed ECS algorithm. (

**a**) The effect of anchor ratio variation on ALE. (

**b**) The effect of anchor ratio variation on LSR. (

**c**) The effect of anchor ratio variation on the performance of the proposed ECS algorithm.

Simulation Parameter | Description | Value |
---|---|---|

Deployment Area (in m${}^{2}$) | The application area of the WSN where all the sensor nodes are deployed | 100 × 100 |

Node Density | It is defined as the total number of sensor nodes in the given test area | 100, 200, 300 |

Anchor Ratio (in %) | Percentage of anchor nodes out of the total nodes in the network | 10, 20, 30, 40, 50 |

Communication Range (in m) | The distance up to which a sensor node can communicate | 10, 20, 30, 40, 50 |

$\alpha $ | Step size | 0.9–1.0 |

${P}_{a}$ | Mutation probability | 0.05–0.25 |

${N}_{nest}$ | Number of candidate solutions | 25 |

${N}_{itertotal}$ | Maximum number of iterations allowed to localise each unknown node | 100 |

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**MDPI and ACS Style**

Kotiyal, V.; Singh, A.; Sharma, S.; Nagar, J.; Lee, C.-C.
ECS-NL: An Enhanced Cuckoo Search Algorithm for Node Localisation in Wireless Sensor Networks. *Sensors* **2021**, *21*, 3576.
https://doi.org/10.3390/s21113576

**AMA Style**

Kotiyal V, Singh A, Sharma S, Nagar J, Lee C-C.
ECS-NL: An Enhanced Cuckoo Search Algorithm for Node Localisation in Wireless Sensor Networks. *Sensors*. 2021; 21(11):3576.
https://doi.org/10.3390/s21113576

**Chicago/Turabian Style**

Kotiyal, Vaibhav, Abhilash Singh, Sandeep Sharma, Jaiprakash Nagar, and Cheng-Chi Lee.
2021. "ECS-NL: An Enhanced Cuckoo Search Algorithm for Node Localisation in Wireless Sensor Networks" *Sensors* 21, no. 11: 3576.
https://doi.org/10.3390/s21113576