# Wind Profiling in the Lower Atmosphere from Wind-Induced Perturbations to Multirotor UAS

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Modeling Framework

#### 2.2. Aircraft System Identification

#### 2.2.1. Multirotor UAS Platform

#### 2.2.2. System Identification Flight Testing

#### 2.2.3. Model Structure Determination

#### 2.2.4. Parameter Estimation

#### 2.2.5. Model Validation

#### 2.3. Observer Synthesis

## 3. Experimental Validation of Wind Estimates

#### 3.1. Field Experiment Setup

#### 3.2. Comparison with Ground-Based Observations

## 4. Results

#### 4.1. System Identification

#### 4.1.1. Model Structure Determination

#### 4.1.2. Parameter Estimation

#### 4.1.3. Model Validation

#### 4.2. Comparison of Wind Velocity Measurements

#### 4.2.1. Sonic Anemometer and SoDAR Comparison

#### 4.2.2. SoDAR Comparison

#### 4.2.3. Validation of Quadrotor Wind Estimates

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

ABL | Atmospheric boundary layer |

AGL | Above ground level |

AHRS | Attitude and heading reference system |

Cov | Covariance |

LR | Long range |

MDE | Mean difference error |

Par. | Parameter |

PTH | Pressure, temperature, and relative humidity |

RMSE | Root mean squared error |

SA | Sonic Anemometer |

SNR | Signal-to-noise ratio |

SoDAR | Sound detection and ranging |

SR | Short range |

UAS | Unmanned aircraft system |

ctrl | Control |

ref | Reference |

## Appendix A. A Reliability Study of SoDAR Wind Measurements

**Figure A2.**Noise intensity values for

**u**and

**v**wind velocity observations from the LR-SoDAR at (

**a**) 110 m AGL, (

**b**) 70 m AGL, and (

**c**) 30 m AGL.

**Figure A3.**Singal-to-noise ratios for

**u**and

**v**wind velocity observations from the LR-SoDAR at (

**a**) 110 m AGL, (

**b**) 70 m AGL, and (

**c**) 30 m AGL.

**Figure A4.**Noise intensity for

**u**and

**v**wind velocity observations from the SR-SoDAR at (

**a**) 110 m AGL, (

**b**) 70 m AGL, and (

**c**) 30 m AGL.

**Figure A5.**Signal-to-noise ratios for

**u**and

**v**wind velocity observations from the SR-SoDAR at (

**a**) 110 m AGL, (

**b**) 70 m AGL, and (

**c**) 30 m AGL.

## Appendix B. Quadrotor Wind Velocity Profiles

**Figure A6.**Comparison of wind speed and wind direction profiles from the SoDAR and quadrotor ascending vertically at 1.0 m/s between 10 and 120 m AGL from (

**a**) 17:38 to 17:40 EDT, (

**b**) 17:41 to 17:42 EDT, and (

**c**) 17:43 to 17:45 EDT.

**Figure A7.**Comparison of wind speed and wind direction profiles from the SoDAR and quadrotor ascending vertically at 1.5 m/s between 10 and 120 m AGL from (

**a**) 18:45 to 18:46 EDT, (

**b**) 18:47 to 18:48 EDT, (

**c**) 18:49 to 18:51 EDT, and (

**d**) 18:52 to 18:53 EDT.

**Figure A8.**Comparison of wind speed and wind direction profiles from the SoDAR and quadrotor ascending vertically at 2.0 m/s between 10 and 120 m AGL from (

**a**) 19:07 to 19:08 EDT, (

**b**) 19:09 to 19:10 EDT, (

**c**) 19:11 to 19:12 EDT, and (

**d**) 19:13 to 19:14 EDT.

## Appendix C. Sensitivity of Wind Estimates to Parameter Variations

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**Figure 3.**(

**a**) The multirotor UAS employed for validation of model-based wind estimation along with (

**b**) dimensions.

**Figure 4.**(

**a**) The Gill MaxiMet sonic anemometer used to measure wind velocity 10 m AGL. (

**b**) The Remtech PA-0 sensor (SR SoDAR) used to measure wind velocity from 10 to 120 m AGL. (

**c**) The ASC 4000i sensor (LR SoDAR) used to measure wind velocity from 30 to 120 m AGL. (

**d**) The experiment setup used to validate quadrotor wind estimates from 10 to 120 m AGL.

**Figure 5.**Roll and pitch model parameter estimates corresponding to vertical constant ascent rates ${{V}_{z}}_{\mathrm{eq}}=\{0.0,0.5,1.0,1.5,2.0\}$ m/s.

**Figure 6.**Validation of the (

**a**) plunge, (

**b**) yaw, (

**c**) roll, and (

**d**) pitch models identified for quadrotor hovering flight.

**Figure 7.**Comparison of wind observations collected from the quadrotor and independent sensors at (

**a**) 10 m AGL, (

**b**) 60 m AGL, and (

**c**) 110 m AGL from 15:00 to 20:30 EDT on 5 June 2018.

**Figure 8.**Comparison of wind speed and wind direction profiles from SoDAR and the quadrotor ascending vertically from 10 to 120 m AGL at (

**a**) 0.5 m/s, (

**b**) 1 m/s, (

**c**) 1.5 m/s, and (

**d**) 2 m/s.

State Measurement | Sate Variables | Sensor Type and Sampling Rate | |||
---|---|---|---|---|---|

Direct | Indirect | ||||

Position | $\{x,y,z\}$ | GPS | 5 Hz | Barometer | 8 Hz |

Extended Kalman Filter | 8 Hz | ||||

Attitude | $\{\varphi ,\theta ,\psi \}$ | — | — | Gyroscope | 18 Hz |

Accelerometer | 18 Hz | ||||

Extended Kalman Filter | 8 Hz | ||||

Translational | $\{u,v,w\}$ | GPS | 5 Hz | Accelerometer | 18 Hz |

Velocity | Extended Kalman Filter | 8 Hz | |||

Angular Velocity | $\{p,q,r\}$ | Gyroscope | 18 Hz | — | — |

Make/Model | Descriptor | Range | Resolution | Accuracy | ||
---|---|---|---|---|---|---|

Spatial | Temporal | Wind Speed | Wind Direction | |||

ASC 4000i | LR-SoDAR | 30–410 m | 5 m | 30 s | <0.5 m/s above 2 m/s | ${2}^{\circ}$ above 2 m/s |

Remtech PA-0 | SR-SoDAR | 10–200 m | 10 m | 300 s | <0.2 m/s above 6 m/s | ${3}^{\circ}$ above 2 m/s |

Gill MaxiMet GMX541 | SA | N/A | N/A | 1 s | $3\%$ at 12 m/s | ${3}^{\circ}$ at 12 m/s |

**Table 3.**The plunge, yaw, roll and pitch model structures of the quadrotor determined from system identification flight experiments and step-wise regression algorithm presented in [51].

Model | Parameter Structure |
---|---|

Plunge | $\left(\begin{array}{c}\dot{z}\\ \dot{w}\end{array}\right)=\left(\begin{array}{cc}0& 1\\ 0& {Z}_{w}\end{array}\right)\left(\begin{array}{c}z\\ w\end{array}\right)+\left(\begin{array}{c}0\\ {Z}_{\delta}\end{array}\right){\delta}_{\mathrm{plunge}}$ |

Yaw | $\left(\begin{array}{c}\dot{\psi}\\ \dot{r}\end{array}\right)=\left(\begin{array}{cc}0& 1\\ {N}_{\psi}& {N}_{r}\end{array}\right)\left(\begin{array}{c}\psi \\ r\end{array}\right)+\left(\begin{array}{c}0\\ {N}_{\delta}\end{array}\right){\delta}_{\mathrm{yaw}}$ |

Roll | $\left(\begin{array}{c}\dot{y}\\ \dot{\varphi}\\ \dot{v}\\ \dot{p}\end{array}\right)=\left(\begin{array}{cccc}0& 0& 1& 0\\ 0& 0& 0& 1\\ 0& {Y}_{\varphi}& {Y}_{v}& 0\\ 0& {L}_{\varphi}& 0& {L}_{p}\end{array}\right)\left(\begin{array}{c}y\\ \varphi \\ v\\ p\end{array}\right)+\left(\begin{array}{c}0\\ 0\\ 0\\ {L}_{\delta}\end{array}\right){\delta}_{\mathrm{roll}}$ |

Pitch | $\left(\begin{array}{c}\dot{x}\\ \dot{\theta}\\ \dot{u}\\ \dot{q}\end{array}\right)=\left(\begin{array}{cccc}0& 0& 1& 0\\ 0& 0& 0& 1\\ 0& {X}_{\theta}& {X}_{u}& 0\\ 0& {M}_{\theta}& 0& {M}_{q}\end{array}\right)\left(\begin{array}{c}x\\ \theta \\ u\\ q\end{array}\right)+\left(\begin{array}{c}0\\ 0\\ 0\\ {M}_{\delta}\end{array}\right){\delta}_{\mathrm{pitch}}$ |

Speed | Plunge Model | Yaw Model | ||||||
---|---|---|---|---|---|---|---|---|

Parameter | Value | SE | Units | Parameter | Value | SE | Units | |

0–2 m/s | ${Z}_{w}$ | −0.55 | 0.28 | 1/s | ${N}_{\psi}$ | −1.71 | 0.41 | $1/{\mathrm{s}}^{2}$ |

${Z}_{\delta}$ | −1.71 | 0.79 | 1/kg | ${N}_{r}$ | −0.84 | 0.53 | 1/s | |

– | – | – | – | ${N}_{\delta}$ | 2.41 | 1.18 | 1/($\mathrm{kg}\xb7{\mathrm{m}}^{2}$) |

Pitch Model | 0.0 m/s | 0.5 m/s | 1.0 m/s | 1.5 m/s | 2.0 m/s | Units | |||||
---|---|---|---|---|---|---|---|---|---|---|---|

Parameters | Value | SE | Value | SE | Value | SE | Value | SE | Value | SE | |

${Y}_{\varphi}$ | 3.28 | 0.37 | 2.91 | 0.34 | 4.73 | 0.87 | 4.68 | 0.21 | 6.62 | 0.63 | $\mathrm{m}/{\mathrm{s}}^{2}$ |

${Y}_{v}$ | −0.49 | 0.68 | −0.31 | 0.04 | −0.70 | 2.33 | −0.62 | 0.14 | −1.06 | 0.25 | 1/s |

${L}_{\varphi}$ | −4.54 | 4.17 | −3.95 | 0.12 | −5.87 | 2.55 | −4.07 | 0.26 | −5.92 | 0.10 | $1/{\mathrm{s}}^{2}$ |

${L}_{p}$ | −1.09 | 2.62 | −1.15 | 0.22 | −1.62 | 1.99 | −0.82 | 0.23 | −1.80 | 1.17 | 1/s |

${L}_{\delta}$ | 4.62 | 3.55 | 5.76 | 0.32 | 8.52 | 2.28 | 6.27 | 0.31 | 9.68 | 0.65 | 1/($\mathrm{kg}\xb7{\mathrm{m}}^{2}$) |

Pitch Model | 0.0 m/s | 0.5 m/s | 1.0 m/s | 1.5 m/s | 2.0 m/s | Units | |||||
---|---|---|---|---|---|---|---|---|---|---|---|

Parameters | Value | SE | Value | SE | Value | SE | Value | SE | Value | SE | |

${X}_{\theta}$ | −4.03 | 0.10 | −3.94 | 0.12 | −6.27 | 0.78 | −5.48 | 0.14 | −8.02 | 0.68 | $\mathrm{m}/{\mathrm{s}}^{2}$ |

${X}_{u}$ | −0.71 | 0.56 | −0.61 | 0.08 | −0.80 | 0.19 | −0.67 | 0.08 | −1.24 | 0.28 | 1/s |

${M}_{\theta}$ | −6.23 | 1.67 | −5.20 | 0.11 | −8.63 | 2.64 | −4.44 | 0.23 | −7.78 | 2.69 | $1/{\mathrm{s}}^{2}$ |

${M}_{q}$ | −1.46 | 0.87 | −1.42 | 0.35 | −2.63 | 0.65 | −1.27 | 0.50 | −2.09 | 0.84 | 1/s |

${M}_{\delta}$ | 6.61 | 0.36 | 6.32 | 0.28 | 10.80 | 1.98 | 6.81 | 0.40 | 10.70 | 0.64 | 1/($\mathrm{kg}\xb7{\mathrm{m}}^{2}$) |

Ascent Rate | Plunge Model | Yaw Model | Roll Model | Pitch Model | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Par. | RMSE | Units | Par. | RMSE | Units | Par. | RMSE | Units | Par. | RMSE | Units | |

0 m/s | w | 0.44 | m/s | r | 2.59 | rad/s | v | 0.23 | m/s | u | 0.12 | m/s |

p | 0.39 | rad/s | q | 0.19 | rad/s | |||||||

0.5 m/s | w | 0.44 | m/s | r | 2.59 | rad/s | v | 0.31 | m/s | u | 0.59 | m/s |

p | 0.21 | rad/s | q | 0.31 | rad/s | |||||||

1.0 m/s | w | 0.44 | m/s | r | 2.59 | rad/s | v | 0.73 | m/s | u | 0.38 | m/s |

p | 0.90 | rad/s | q | 0.37 | rad/s | |||||||

1.5 m/s | w | 0.44 | m/s | r | 2.59 | rad/s | v | 0.38 | m/s | u | 0.46 | m/s |

p | 0.48 | rad/s | q | 0.51 | rad/s | |||||||

2.0 m/s | w | 0.44 | m/s | r | 2.59 | rad/s | v | 0.48 | m/s | u | 0.37 | m/s |

p | 0.71 | rad/s | q | 0.28 | rad/s |

**Table 8.**Comparison of wind speed and wind direction observations collected from the sonic anemometer and SR-SoDAR at 10 m AGL from 15:30 to 20:30 EDT on 5 June 2018.

Sensor | Height | Wind Speed | Wind Direction | ||||
---|---|---|---|---|---|---|---|

Mean | MDE | RMSE | Mean | MDE | RMSE | ||

SA | 10 m | 2.0 m/s | 0.7 m/s | 1.0 m/s | 284${}^{\circ}$ | 32${}^{\circ}$ | 100${}^{\circ}$ |

SR-SoDAR | 2.7 m/s | 316${}^{\circ}$ |

**Table 9.**Results from the comparison of SoDAR wind speed and wind direction observations collected from 15:00 to 20:30 EDT on 5 June 2018.

Sensor | Height | Wind Speed | Wind Direction | ||||
---|---|---|---|---|---|---|---|

Mean | MDE | RMSE | Mean | MDE | RMSE | ||

SR-SoDAR | 60 m | 4.5 m/s | −0.9 m/s | 1.3 m/s | 321${}^{\circ}$ | −1${}^{\circ}$ | 25${}^{\circ}$ |

LR-SoDAR | 3.6 m/s | 320${}^{\circ}$ | |||||

SR-SoDAR | 110 m | 4.8 m/s | −0.9 m/s | 1.4 m/s | 321${}^{\circ}$ | 0${}^{\circ}$ | 26${}^{\circ}$ |

LR-SoDAR | 3.9 m/s | 321${}^{\circ}$ |

**Table 10.**Comparison of wind speed and wind direction observations from the quadrotor, sonic anemometer, and SR-SoDAR collected at 10 m AGL between 18:05 to 20:17 EDT on 5 June 2018.

Flight Mode | Flight Time | Height | Wind Speed Mean Difference | Wind Direction Mean Difference | ||
---|---|---|---|---|---|---|

SA | SR-SoDAR | SA | SR-SoDAR | |||

Hovering | 18:05–18:15 EDT | 10 m | 0.9 m/s | 0.5 m/s | $-{8}^{\circ}$ | $-{12}^{\circ}$ |

0.9 m/s | 0.1 m/s | ${12}^{\circ}$ | ${1}^{\circ}$ | |||

Hovering | 18:19–18:27 EDT | 10 m | −0.4 m/s | 1.0 m/s | ${25}^{\circ}$ | ${17}^{\circ}$ |

Hovering | 20:08–20:17 EDT | 10 m | −0.1 m/s | – | $-{9}^{\circ}$ | – |

Absolute Mean Difference | 0.6 m/s | 0.5 m/s | ${14}^{\circ}$ | ${10}^{\circ}$ |

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**MDPI and ACS Style**

González-Rocha, J.; De Wekker, S.F.J.; Ross, S.D.; Woolsey, C.A. Wind Profiling in the Lower Atmosphere from Wind-Induced Perturbations to Multirotor UAS. *Sensors* **2020**, *20*, 1341.
https://doi.org/10.3390/s20051341

**AMA Style**

González-Rocha J, De Wekker SFJ, Ross SD, Woolsey CA. Wind Profiling in the Lower Atmosphere from Wind-Induced Perturbations to Multirotor UAS. *Sensors*. 2020; 20(5):1341.
https://doi.org/10.3390/s20051341

**Chicago/Turabian Style**

González-Rocha, Javier, Stephan F. J. De Wekker, Shane D. Ross, and Craig A. Woolsey. 2020. "Wind Profiling in the Lower Atmosphere from Wind-Induced Perturbations to Multirotor UAS" *Sensors* 20, no. 5: 1341.
https://doi.org/10.3390/s20051341