# Hybrid Particle Swarm Optimization for Multi-Sensor Data Fusion

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Data Fusion Model Using Neural Network and PSO

**t**and

**a**are the target and actual output vectors of length c (e.g., c is 2 in this experiment), the batch size is m and

**θ**represents all weights and biases.

## 3. A Hybrid PSO Model for Multi-Sensor Data Fusion

#### 3.1. Improved Exploitation of Neural Network Using Ordinary PSO

_{k}(≈ 10 + 2 × (the dimension of the weights and biases)

^{0.5}) and the inertia weight is ω, which dynamically adjusts the velocity. Moreover, the cognitive component c

_{1}and the social component c

_{2}change the particles’ velocity toward the previous best and global best position, respectively. The PSO uses random numbers determined from a uniform distribution rand

_{1}and rand

_{2}to avoid unfortunate states in which all particles quickly settle into an unchanging direction. Consequently, the parameters are updated in accordance with the found global best position.

#### 3.2. Exploration Toward Ultimate Goals for the Use of Enhanced PSO

_{P}is the proportional term, K

_{I}is integral term, and K

_{D}is the derivative term, and they are selected through trial and error operations, as shown in Table 2.

#### 3.3. Three-Phase Hybrid PSO Method Balancing between Exploration and Exploitation

## 4. Performance Analysis

_{P}, K

_{I}, and K

_{D}) which are fixed to 0.5, 0.4, and 0.3, respectively to verify the reliability of performance evaluation of the proposed methodology in different exemplar datasets. Other parameters were used in the same manner with the generic PSO and the PSOpid approach. Figure 9 shows the enhancement of hybridizations among PSOpid-LM-PSO and the other algorithms. The results are summarized with the best, median, and worst results (out of 100 independent runs) reported. In the case of PSO and PSOpid, the range of each particle position becomes unstable or explodes; therefore, neither algorithm alone can be used to exploit the old certainty optimum as well as explore new possibilities. Through all evaluative processes, the proposed PSOpid-LM-PSO showed enhanced performance by using a hybrid scheme of ordinary PSO, LM, and PSOpid.

## 5. Conclusions

## Author Contributions

## Acknowledgments

## Conflicts of Interest

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**Figure 3.**PSO alone: (

**a**) Initial position of the particles within a hypercube using a uniform random distribution; and (

**b**) converged position of the particles.

**Figure 4.**A hybridization of PSOpid, LM and PSO, namely PSOpid-LM-PSO: (

**a**) initial position of particles within a shrunk hypercube; and (

**b**) convergence position of the particles.

**Figure 6.**Exploration of a new possibility. Each (x,y) coordinate indicates the minimum and maximum of all parameters such as weights and biases, and the outcomes are from each independent trial.

**Figure 8.**Enhancement graph of each algorithm as compared to the classic LM-based backpropagation algorithm.

Parameters | Value |
---|---|

Swarm size (Z_{k}) | 28 |

Initial Position of Particles | Spread within a hypercube using a uniform random distribution |

Minimum velocity norm | 0.05 |

Inertial weight (ω) | 1 |

Minimum position (min_pos) | −100 |

Maximum position (max_pos) | 100 |

Parameters | Value |
---|---|

Minimum position (min_pos) | 1.2 × min (LM-PSO) |

Maximum position (max_pos) | 1.2 × max (LM-PSO) |

Proportional term (K_{P}) | 0.5 (fixed) |

Integral term (K_{I}) | 0.5 (fixed) |

Derivative term (K_{D}) | 0.6 (fixed) |

Single-Subject Evaluation: Mean Distance Error [mm] | |||||
---|---|---|---|---|---|

Weight | Trilateration | LM alone | LM-PSO | PSOpid-LM-PSO | PSOpid-LM-PSO Error Reduction |

58 kg | 546.07 | 26.28 | 24.85 | 23.18 | 95.76% |

64 kg | 213.54 | 30.39 | 27.01 | 25.14 | 88.23% |

72 kg | 637.15 | 31.34 | 30.07 | 24.76 | 96.11% |

85 kg | 160.16 | 50.14 | 44.02 | 41.48 | 74.10% |

90 kg | 196.56 | 27.32 | 24.96 | 20.35 | 89.65% |

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Kim, H.; Suh, D.
Hybrid Particle Swarm Optimization for Multi-Sensor Data Fusion. *Sensors* **2018**, *18*, 2792.
https://doi.org/10.3390/s18092792

**AMA Style**

Kim H, Suh D.
Hybrid Particle Swarm Optimization for Multi-Sensor Data Fusion. *Sensors*. 2018; 18(9):2792.
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**Chicago/Turabian Style**

Kim, Hyunseok, and Dongjun Suh.
2018. "Hybrid Particle Swarm Optimization for Multi-Sensor Data Fusion" *Sensors* 18, no. 9: 2792.
https://doi.org/10.3390/s18092792