# Flight Data-Based Wind Disturbance and Air Data Estimation

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## Abstract

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## 1. Introduction

## 2. Method

#### 2.1. Preprocessing of Flight Data

#### 2.2. Wind Field Modeling

#### 2.2.1. Modeling of Horizontal Prevailing Wind

#### 2.2.2. Turbulence Modeling

#### 2.3. Design of Forward–Backward Filter

#### 2.3.1. Building the Filtering System

#### 2.3.2. Design of the Forward–Backward Filtering Algorithm

## 3. Experiments and Discussion

#### 3.1. Simulation Analysis

#### 3.1.1. Simulation Settings

#### 3.1.2. Performance Comparison of Three Filters

#### 3.2. Experiments with Flight Data

#### 3.2.1. In-Turbulence Air Data and Wind Field Estimation

#### 3.2.2. Effects of Uncertain Disturbance on Filtering

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Appendix A

Parameter Type | Parameter Assignment | Symbol (Unit) | Sampling Rate/Hz | Out Resolution | Out Range | Accuracy |
---|---|---|---|---|---|---|

Inertial measurements | Longitudinal acceleration | ${a}_{x}(\mathrm{g})$ | 4 | 0.000976563 | −1~+1 | 0.01 |

Lateral acceleration | ${a}_{y}(\mathrm{g})$ | 4 | 0.00203649 | −1~+1 | 0.01 | |

Vertical acceleration | ${a}_{z}(\mathrm{g})$ | 8 | 0.001953125 | −3~6 | 0.046 | |

Roll angle | $\varphi {(}^{\circ})$ | 4 | 0.005493164 | −90~90 | 0.05 | |

Pitch angle | $\theta {(}^{\circ})$ | 4 | 0.005493164 | −90~90 | 0.05 | |

Yaw angle | $\psi {(}^{\circ})$ | 2 | 0.005493164 | −180~180 | 0.05 | |

Roll angular rate | $p({}^{\circ}/\mathrm{s})$ | 8 | 0.00390625 | −45~45 | 0.1 | |

Pitch angular rate | $q({}^{\circ}/\mathrm{s})$ | 8 | 0.00390625 | −45~45 | 0.1 | |

Yaw angular rate | $r({}^{\circ}/\mathrm{s})$ | 8 | 0.00390625 | −45~45 | 0.1 | |

Ground speed | ${V}_{G}(knot)$ | 4 | 0.1 | 0~1024 | N/A | |

Air data | Mach number | $M$ | 1 | 0.001 | 0~1.024 | N/A |

Angle of attack | $\overline{\alpha}{(}^{\circ})$ | 1 | 0.17578125 | −90~90 | N/A | |

Total temperature | $t{(}^{\xb0}\mathrm{C})$ | 1 | 0.5 | −512~512 | N/A |

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**Figure 7.**Spectrum analysis of theoretical model and estimated turbulence. (

**a**) Estimated and theoretical spectra of Wx. (

**b**) Estimated and theoretical spectra of Wy. (

**c**) Estimated and theoretical spectra of Wz.

Simulation Condition | Prevailing Wind | Turbulence Intensity | Flight State |
---|---|---|---|

SC-1 | $W=5\mathrm{m}/\mathrm{s}$,$\gamma ={0}^{\circ},\phi ={0}^{\circ}$ | Light, $\sigma =0.5\mathrm{m}/\mathrm{s}$ | Level flight, $h=8000\mathrm{m}$, $M=0.74$ |

SC-2 | $W=10\mathrm{m}/\mathrm{s}$,$\gamma ={30}^{\circ},\phi ={30}^{\circ}$ | Moderate, $\sigma =2\mathrm{m}/\mathrm{s}$ | Level flight, $h=\mathrm{10,000}\mathrm{m}$,$M=0.76$ |

SC-3 | $W=10\mathrm{m}/\mathrm{s}$,$\gamma ={30}^{\circ},\phi ={30}^{\circ}$ | Moderate, $\sigma =1.5\mathrm{m}/\mathrm{s}$ | Turn flight, $h=\mathrm{10,000}\mathrm{m}$, $M=0.76,r={1.2}^{\circ}/\mathrm{s}$ |

SC-4 | $W=20\mathrm{m}/\mathrm{s}$,$\gamma ={30}^{\circ},\phi ={60}^{\circ}$ | Severe, $\sigma =5\mathrm{m}/\mathrm{s}$ | Level flight, $h=\mathrm{12,000}\mathrm{m}$,$M=0.78$ |

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**MDPI and ACS Style**

Gao, Z.; Wang, H.; Xiang, Z.; Wang, D.
Flight Data-Based Wind Disturbance and Air Data Estimation. *Atmosphere* **2021**, *12*, 470.
https://doi.org/10.3390/atmos12040470

**AMA Style**

Gao Z, Wang H, Xiang Z, Wang D.
Flight Data-Based Wind Disturbance and Air Data Estimation. *Atmosphere*. 2021; 12(4):470.
https://doi.org/10.3390/atmos12040470

**Chicago/Turabian Style**

Gao, Zhenxing, Haofeng Wang, Zhiwei Xiang, and Debao Wang.
2021. "Flight Data-Based Wind Disturbance and Air Data Estimation" *Atmosphere* 12, no. 4: 470.
https://doi.org/10.3390/atmos12040470