# A Spatial-Temporal Approach Based on Antenna Array for GNSS Anti-Spoofing

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## Abstract

**:**

## 1. Introduction

- (1)
- We present a novel technique based on antenna array for GNSS anti-spoofing, which can not only distinguish low-power spoofing from multipath but also provides advanced signal processing methods for multipath and spoofing mitigation.
- (2)
- The DOA and power offered by the improved spatial spectrum estimation and enhanced power estimation can be used as support for the subsequent spoofing localization.
- (3)
- All operations are based on the baseband samples, without the need to perform despreading processing on the receiver, which avoids the acquisition and tracking of the receiver and thus does not bring additional computational complexity to the GNSS receivers.

## 2. Signal Model

## 3. Proposed Anti-Spoofing Scheme

#### 3.1. DOA Estimation

#### 3.1.1. Signal Preprocessing

#### 3.1.2. Eigen-Spatial Spectrum Construction

**T**is the propagator, ${\mathbf{A}}_{1}$ and ${\mathbf{A}}_{2}$ are composed of the first $L+1$ and $M-L+1$ rows of $\mathbf{A}$ respectively. Consequently, the preprocessed covariance matrixpreprocessed covariance matrix ${\mathbf{R}}_{fb}$ can be devided into

**T**is only limited by the sample covariance matrix [29]. Therefore, in order to reduce the influence of

**T**and improve the accuracy of subsequent DOA estimation algorithm, multiple data blocks are utilized to get a more accurate sample covariance matrix. Let ${\mathbf{U}}_{0}^{H}=\left(\right)open="["\; close="]">{\mathbf{T}}^{T},-{\mathbf{I}}_{M-L-1}$, it can be seen from Equation (14)

#### 3.2. GNSS Spoofing Detection and Mitigation

#### 3.2.1. Enhanced Power Estimation

#### 3.2.2. The Combined Spoofing Detection Technology

#### 3.2.3. Interference Mitigation

#### 3.3. Overall Spoofing Detection and Mitigation Scheme

Algorithm 1: GNSS Anti-Spoofing Scheme |

DOA Estimation |

Input: $x\left(n\right)$ |

1: Construct the covariance matrix by Equation (5) to suppress the noise component. |

2: Reduce the correlation between sources according to Equation (13). |

3: Estimate the DOAs for sources through Equation (18). |

Output: Estimated DOAs |

Spoofing Detection and Mitigation |

Input: Estimated DOAs |

1: The enhanced power estimation is performed by Equation (19). |

2: Separate the incident signals according to Equation (24). |

3: Obtain the cross-correlation results by Equation (25). |

4: Make decisions based on power comparison and cross-correlation results. |

5: Calculate the output signal according to the decision results. |

## 4. Simulation Results

#### 4.1. DOA and Power Estimation

#### 4.1.1. DOA Estimation Verification

#### 4.1.2. Power Estimation Performance

#### 4.2. Spoofing Detection and Mitigation

- Scenario 1:

- Scenario 2:

- Scenario 3:

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Conflicts of Interest

## References

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**Figure 5.**The cross-correlation results. (

**a**) 25${}^{\circ}$ and 30${}^{\circ}$; (

**b**) 25${}^{\circ}$ and 38${}^{\circ}$; (

**c**) 25${}^{\circ}$ and 54${}^{\circ}$; (

**d**) 25${}^{\circ}$ and 38${}^{\circ}$.

Detection Results | Decision |
---|---|

Power difference are insignificant; No cross-correlation peaks. | No interference |

Only one cross-correlation peaks between two certain signals | Only multipath |

Multiple correlation peaks between the signal with highest power and others | Only spoofing |

Multiple correlation peaks; One correlation peaks between two certain signals. | Spoofing and multipath |

SS-MUSIC | ES-MMUSIC | Proposed |
---|---|---|

0.742 | 0.450 | 0.442 |

#1 | #2 | #3 | #4 | #5 | |
---|---|---|---|---|---|

DOA (${}^{\circ}$) | 30 | 54 | 25 | 38 | 70 |

SNR (dB) | −14.48 | −19.96 | −20.06 | −20.18 | −20.33 |

DOA (${}^{\circ}$) | 25 | 30 | 38 | 54 | 70 |
---|---|---|---|---|---|

25 | ∼ | ✓ | × | × | × |

30 | ✓ | ∼ | ✓ | ✓ | ✓ |

38 | × | ✓ | ∼ | × | × |

54 | × | ✓ | × | ∼ | × |

70 | × | ✓ | × | × | ∼ |

#1 | #2 | #3 | #4 | #5 | |
---|---|---|---|---|---|

DOA (${}^{\circ}$) | $-30$ | 20 | 0 | −50 | 50 |

SNR (dB) | −18.88 | −19.96 | −20.04 | −20.18 | −20.37 |

DOA (${}^{\circ}$) | −50 | −30 | 0 | 20 | 50 |
---|---|---|---|---|---|

−50 | ∼ | × | × | × | × |

−30 | × | ∼ | × | × | ✓ |

0 | × | × | ∼ | × | × |

20 | × | × | × | ∼ | × |

50 | × | ✓ | × | × | ∼ |

#1 | #2 | #3 | #4 | #5 | #6 | |
---|---|---|---|---|---|---|

DOA (${}^{\circ}$) | 50 | −40 | −20 | 20 | 0 | 30 |

SNR (dB) | −17.08 | −19.78 | −19.83 | −19.95 | −20.13 | −20.92 |

DOA (${}^{\circ}$) | −40 | −20 | 0 | 20 | 30 | 50 |
---|---|---|---|---|---|---|

−40 | ∼ | × | × | × | ✓ | ✓ |

−20 | × | ∼ | × | × | × | ✓ |

0 | × | × | ∼ | × | × | ✓ |

20 | × | × | × | ∼ | × | ✓ |

30 | ✓ | × | × | × | ∼ | ✓ |

50 | ✓ | ✓ | ✓ | ✓ | ✓ | ∼ |

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**MDPI and ACS Style**

Zhao, Y.; Shen, F.; Xu, G.; Wang, G.
A Spatial-Temporal Approach Based on Antenna Array for GNSS Anti-Spoofing. *Sensors* **2021**, *21*, 929.
https://doi.org/10.3390/s21030929

**AMA Style**

Zhao Y, Shen F, Xu G, Wang G.
A Spatial-Temporal Approach Based on Antenna Array for GNSS Anti-Spoofing. *Sensors*. 2021; 21(3):929.
https://doi.org/10.3390/s21030929

**Chicago/Turabian Style**

Zhao, Yuqing, Feng Shen, Guanghui Xu, and Guochen Wang.
2021. "A Spatial-Temporal Approach Based on Antenna Array for GNSS Anti-Spoofing" *Sensors* 21, no. 3: 929.
https://doi.org/10.3390/s21030929