# Acoustic Detection of a Fixed-Wing UAV

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Experimental Methods

## 3. Data Analysis

#### 3.1. Signal Processing Overview

#### 3.2. Harmonic Spectral Transforms

^{th}signal. Expanding out the above form gives:

#### 3.3. Distribution-Free CFAR Detection

^{th}—largest value of $\stackrel{\rightharpoonup}{N}$), $G$ is the number of guard cells, and $I$ is the number of interfering targets.

#### 3.4. Kinematic Considerations

- Head perpendicularly away from the intruder path by making the minimum bearing change.
- Head perpendicularly away from the intruder path by making the maximum bearing change.
- Adjust course to perpendicularly cross the intruder path.

## 4. Results & Discussion

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**Depiction of the experimental setup where the aircrafts’ direction of flight is indicated by the arrows.

**Figure 2.**Google Earth image of the aircrafts’ GPS tracks with wind and direction of flight indicated by the relevant arrows.

**Figure 3.**Delta X-8 fitted with four DPA 4053 microphones with a close-up of the sensor in the top right sub image.

Delta X-8 | Giant Big Stik | |
---|---|---|

Wingspan (m) | 2.12 | 2.05 |

Length (m) | 0.82 | 1.89 |

Mass (kg) | 2.2 | 6.5 |

Payload Capacity (kg) | 2–3 | 4–5 |

Cruising Speed (knots) | 20–30 | 30–40 |

Sound Pressure Level (dBc @ 1 m) | NA | ≈110–115 |

Data Type | Sensor Accuracy |
---|---|

GPS Position | ±1.5 m |

Compass Orientation (3D) | ±2.5° |

Altitude | ±5 m |

Airspeed | ±1 m/s |

Harmonic | Geometric | Standard | RMS |
---|---|---|---|

$a=-1$ | $a=0$ | $a=1$ | $a=2$ |

${\left[\frac{1}{R}{\displaystyle \sum _{r=1}^{R}{\left|X(f\cdot r)\right|}^{-1}}\right]}^{-1}$ | ${\left[{\displaystyle \prod _{r=1}^{R}\left|X(f\cdot r)\right|}\right]}^{1/R}$ | $\left[\frac{1}{R}{\displaystyle \sum _{r=1}^{R}\left|X(f\cdot r)\right|}\right]$ | ${\left[\frac{1}{R}{\displaystyle \sum _{r=1}^{R}{\left|X(f\cdot r)\right|}^{2}}\right]}^{1/2}$ |

Harmonics ($\mathit{R}$) | Fractional Peaks ($\mathit{F}$) |
---|---|

2 | 2 |

3 | 5 |

4 | 8 |

5 | 14 |

6 | 17 |

7 | 26 |

8 | 32 |

Intruder Aircraft | Intruder Speed (knots) | ${\mathit{d}}_{\mathit{o}}$ (m) ($\mathit{\beta}\mathbf{=}\mathbf{180}$, $\mathit{\gamma}\mathbf{=}\mathbf{0}$) | ||
---|---|---|---|---|

$\mathit{\alpha}\mathbf{=}\mathbf{0}$ | $\mathit{\alpha}\mathbf{=}\mathbf{45}$ | $\mathit{\alpha}\mathbf{=}\mathbf{90}$ | ||

Giant Big Stik (UAV) | 35 | 218 | 185 | 178 |

Cessna 185 | 95 | 551 | 494 | 483 |

Bell 206 | 115 | 662 | 600 | 584 |

Sikorsky S-92 | 140 | 795 | 725 | 711 |

Boeing 737 | 250 * | 1402 | 1290 | 1270 |

Sampling Frequency (${f}_{s}$) | 48 kHz | Number of Signals | 2 |

Decimation Factor | 10 | FFT Window | 0.5 s |

IIR Step Size ($\mu $) | 5 × 10^{−4} | Window Overlap | 50% |

Notch Radius ($r$) | 0.995 | Padded Length (${L}_{fft}$) | 6000 pts |

Harmonics Removed ($H$) | 8 | Spectral Resolution (${f}_{r}$) | 0.5 Hz/bin |

Detector Type | OS-CFAR | Noise Samples (N) | 101 |

Forgetting Factor ($\xi $) | 0.2 | Order Statistic ($k$) | $0.75\times N$ |

Flooring Factor ($\delta $) | 0.5 | Guard Cell Band ($\stackrel{\rightharpoonup}{G}$) | 5.5 Hz |

Noise Band ($\stackrel{\rightharpoonup}{N}$) | 50 Hz | Guard Cells ($G$) | 12 |

${\overline{\mathbf{H}}}_{\mathbf{1}}\mathbf{\left[}\mathit{X}\mathbf{\right]}$ | $\overline{\mathit{X}}$ | ${\overline{\mathbf{H}}}_{\mathbf{1}}\mathbf{\left[}\mathit{X}\mathbf{\right]}$ | $\overline{\mathit{X}}$ | ||
---|---|---|---|---|---|

Noise Sample Band ($\stackrel{\rightharpoonup}{N}$) | 10–400 Hz | 10–492.5 Hz | Order Statistic ($\overline{k}$) | 3 | 3 |

Test Band ($\stackrel{\rightharpoonup}{B}$) | 100–200 Hz | 200–400 Hz | Consec. Trials ($T$) | 3 | 3 |

Guard Cell Band ($\stackrel{\rightharpoonup}{G}$) | 10 Hz | 10 Hz | Consec. Detections ($D$) | 3 | 3 |

Fract. Guard Band (${\stackrel{\rightharpoonup}{G}}_{F}$) | 1 Hz | 1 Hz | Cell Deviation ($\Delta $) | 1 | 1 |

Noise Samples ($N$) | 780 pts | 965 pts | Maxima Tested ($M$) | 3 | 3 |

Test Cells ($B$) | 201 pts | 401 pts | ${P}_{FA}^{SC}$ | 4.2 × 10^{−3} | 3.4 × 10^{−3} |

Guard Cells ($G$) | 22 pts | 22 pts | ${P}_{FA}^{ST}$ | 0.63 | 0.83 |

Fract. Guard Cells (${G}_{F}$) | 2 pts | 2 pts | ${P}_{FA}^{BI}$ | 1.5 × 10^{−5} | 1.5 × 10^{−5} |

Fractional Peaks ($F$) | 17 | 17 | ${P}_{FA}^{RBI}$ | 1.4 × 10^{−4} | 1.4 × 10^{−4} |

Detections (#) | Max Distance (m) | Mean Distance (m) | ||||
---|---|---|---|---|---|---|

$\overline{X}$ | ${\overline{\mathrm{H}}}_{\langle 11\rangle}^{\langle 6,2\rangle}\left[X\right]$ | $\overline{X}$ | ${\overline{\mathrm{H}}}_{\langle 11\rangle}^{\langle 6,2\rangle}\left[X\right]$ | $\overline{X}$ | ${\overline{\mathrm{H}}}_{\langle 11\rangle}^{\langle 6,2\rangle}\left[X\right]$ | |

Single Trial (ST) | 1077 | 1930 | 672 | 678 | 270 | 302 |

Binary Integration (BI) | 215 | 551 | 498 | 572 | 205 | 240 |

Robust Binary Integration (RBI) | 300 | 884 | 500 | 593 | 212 | 258 |

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**MDPI and ACS Style**

Harvey, B.; O’Young, S.
Acoustic Detection of a Fixed-Wing UAV. *Drones* **2018**, *2*, 4.
https://doi.org/10.3390/drones2010004

**AMA Style**

Harvey B, O’Young S.
Acoustic Detection of a Fixed-Wing UAV. *Drones*. 2018; 2(1):4.
https://doi.org/10.3390/drones2010004

**Chicago/Turabian Style**

Harvey, Brendan, and Siu O’Young.
2018. "Acoustic Detection of a Fixed-Wing UAV" *Drones* 2, no. 1: 4.
https://doi.org/10.3390/drones2010004