# Knowledge Distillation-Based GPS Spoofing Detection for Small UAV

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## Abstract

**:**

## 1. Introduction

## 2. Related Work

#### 2.1. GPS Spoofing in UAVs

#### 2.2. Knowledge Distillation

## 3. System Modeling

## 4. Problem Statement

## 5. Methodology

#### 5.1. Long-Short Term Memory (LSTM)-Based Detection

Algorithm 1: GPS spoofing detection |

#### 5.2. KD-Enabled Lightweight Detection

## 6. Evaluation

#### 6.1. GPS Spoofing Detection

#### 6.2. Lightweight Detection

## 7. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Appendix A. Symbol Summary

Symbols | Definition |
---|---|

$S{a}_{i}$ | The signal a GPS module received. |

$P{r}_{i}$ | GPS location: $P{r}_{i}=({x}_{i},{y}_{i},{z}_{i})$. |

$S{d}_{i}$ | The forged GPS signal. |

${A}_{k}$ | Acceleration of UAV at time k. |

$(A{x}_{k},A{y}_{k},A{z}_{k})$ | Acceleration of UAV in x, y, and z axis at time k. |

${R}_{k}$ | Rotation of UAV at time k. |

$(R{y}_{k},R{p}_{k},R{r}_{k})$ | Rotation of UAV in yaw, pitch, roll at time k. |

$R{S}_{l}$ | The received signal strength indicator (RSSI). |

${P}_{{t}^{\prime}},{P}_{t}$ | Position at time t’ and t. |

v | The speed of UAV. |

A | Acceleration of UAV. |

N | Thermal noise and zero drift. |

$T{h}_{p}$ | Threshold of UAV movement. |

$P{A}_{t}$ | Combination of ${P}_{t}$ and ${A}_{t}$. |

${W}_{ii}$, ${W}_{ic}$, and ${W}_{im}$ | Weight matrices for the input gate. |

${c}_{t-1}$ | Cell activation vectors. |

${m}_{t-1}$ | Cell activation output vector. |

${b}_{i}$ | Bias for the input layer. |

$\sigma $ | Logistic sigmoid function. |

${W}_{fi}$, ${W}_{cf}$, and ${W}_{mf}$ | Weight matrices for the forget gate. |

${b}_{f}$ | Bias for forget layer. |

⊙ | The Hadamard product. |

g | Cell input activation function. |

${W}_{cx}$ | Weight matrices for the cell state. |

${b}_{c}$ | Bias for cell state. |

${W}_{oi}$, ${W}_{oc}$, and ${W}_{om}$ | Weight matrices for the output gates. |

${b}_{o}$ | Bias for forget layer. |

${m}_{t}$ | Output activation vector. |

$h\left(\right)$ | Cell output activation function. |

${W}_{ym}$ | Weight matrices for the final result. |

$T\left(P{A}_{t}\right)$ | The teacher model. |

$S\left(P{A}_{t}\right)$ | A student model. |

${L}_{1}\left(\right)$ | The loss functions of the student model vs. the teacher model. |

${L}_{2}\left(\right)$ | The loss functions of the student model vs. the real positions. |

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Parameters | LSTM | GRU | RNN |
---|---|---|---|

Input Size | 6 | 6 | 6 |

Hidden Size | 12 | 12 | 12 |

Number of Layers | 12 | 12 | 12 |

Number of Classes | 1 | 1 | 1 |

Output Size | 3 | 3 | 3 |

Learning Rate | 0.001 | 0.001 | 0.001 |

Input Size | Output Size | Hidden Layer |
---|---|---|

6 | 3 | (16, 8) |

Models | LSTM | GRU | RNN |
---|---|---|---|

Model Size | 72.7 kb | 57.8 kb | 27.7 kb |

NN Model Size | 3.0 kb | 3.0 kb | 3.0 kb |

NN Model Overhead | 266.88 Mb | 266.88 Mb | 266.88 Mb |

Overhead | 390.37 Mb | 391.29 Mb | 389.84 Mb |

Learning Rate | 0.001 | 0.001 | 0.001 |

Balance Factor | 0.45 | 0.45 | 0.45 |

Model Reduced | 95.74% | 94.80% | 89.17% |

Overhead Reduced | 31.63% | 31.79% | 31.54% |

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## Share and Cite

**MDPI and ACS Style**

Ren, Y.; Restivo, R.D.; Tan, W.; Wang, J.; Liu, Y.; Jiang, B.; Wang, H.; Song, H.
Knowledge Distillation-Based GPS Spoofing Detection for Small UAV. *Future Internet* **2023**, *15*, 389.
https://doi.org/10.3390/fi15120389

**AMA Style**

Ren Y, Restivo RD, Tan W, Wang J, Liu Y, Jiang B, Wang H, Song H.
Knowledge Distillation-Based GPS Spoofing Detection for Small UAV. *Future Internet*. 2023; 15(12):389.
https://doi.org/10.3390/fi15120389

**Chicago/Turabian Style**

Ren, Yingying, Ryan D. Restivo, Wenkai Tan, Jian Wang, Yongxin Liu, Bin Jiang, Huihui Wang, and Houbing Song.
2023. "Knowledge Distillation-Based GPS Spoofing Detection for Small UAV" *Future Internet* 15, no. 12: 389.
https://doi.org/10.3390/fi15120389