[Paper Review] Wind Estimation Using Quadcopter Motion: A Machine Learning Approach

Sam Allison, He Bai+1 more|arXiv (Cornell University)|Jul 11, 2019

Meteorological Phenomena and Simulations38 references4 citations

TL;DR

This paper proposes a long short-term memory (LSTM) neural network (NN) to estimate turbulent wind velocity using only quadcopter state measurements—roll, pitch, and position—without wind sensors. Trained on simulated flight data in turbulent wind fields, the LSTM outperforms the conventional wind triangle method, reducing mean wind estimation errors by up to 50% and direction errors by ~50%, demonstrating superior accuracy in both Dryden and large eddy simulation (LES)-generated wind fields.

ABSTRACT

In this article, we study the well known problem of wind estimation in atmospheric turbulence using small unmanned aerial systems (sUAS). We present a machine learning approach to wind velocity estimation based on quadcopter state measurements without a wind sensor. We accomplish this by training a long short-term memory (LSTM) neural network (NN) on roll and pitch angles and quadcopter position inputs with forcing wind velocities as the targets. The datasets are generated using a simulated quadcopter in turbulent wind fields. The trained neural network is deployed to estimate the turbulent winds as generated by the Dryden gust model as well as a realistic large eddy simulation (LES) of a near-neutral atmospheric boundary layer (ABL) over flat terrain. The resulting NN predictions are compared to a wind triangle approach that uses tilt angle as an approximation of airspeed. Results from this study indicate that the LSTM-NN based approach predicts lower errors in both the mean and variance of the local wind field as compared to the wind triangle approach. The work reported in this article demonstrates the potential of machine learning for sensor-less wind estimation and has strong implications to large-scale low-altitude atmospheric sensing using sUAS for environmental and autonomous navigation applications.

Motivation & Objective

• To address the lack of accurate, low-cost wind sensing in small unmanned aerial systems (sUAS) operating at low altitudes.
• To develop a sensor-less wind estimation method using only standard quadcopter state measurements (position, roll, pitch).
• To improve upon linear approaches like the wind triangle method, which rely on simplified assumptions about airspeed and attitude.
• To evaluate the generalization and robustness of machine learning-based wind estimation across diverse turbulent wind fields, including stochastic (Dryden) and high-fidelity LES models.
• To demonstrate that deep learning can effectively capture the nonlinear dynamics of quadcopters in turbulent wind, enabling accurate wind field reconstruction.

Proposed method

• A long short-term memory (LSTM) neural network is trained to predict wind velocity using roll, pitch, and position as inputs, with forcing wind velocities as targets.
• Training data is generated via high-fidelity simulations of a quadcopter in turbulent wind fields using the Dryden gust model and a large eddy simulation (LES) of the atmospheric boundary layer (ABL).
• The LSTM model learns temporal dependencies in the quadcopter's motion to infer wind components in the body frame (u, v, w) over time.
• The network is evaluated on both synthetic Dryden wind fields and realistic LES-generated wind fields at multiple altitudes and turbulence levels.
• Performance is benchmarked against the wind triangle (WT) method, which approximates airspeed from tilt angles and assumes constant airspeed.
• The formulation is generalizable to any sUAS with dynamics similar to the quadcopter model, enabling adaptation to other platforms.

Experimental results

Research questions

• RQ1 Can a machine learning model accurately estimate turbulent wind velocity using only standard quadcopter state measurements, without direct wind sensing?
• RQ2 How does the LSTM-based approach compare to the conventional wind triangle method in terms of mean and variance error in wind estimation?
• RQ3 Does the LSTM model generalize across different wind field models, including stochastic (Dryden) and high-fidelity LES simulations?
• RQ4 How does the performance of the LSTM model vary with turbulence intensity and flight trajectory type (e.g., hover vs. straight-line flight)?
• RQ5 Can the LSTM framework outperform linear estimation methods in capturing the nonlinear dynamics of quadcopters in aggressive flight and turbulent wind?

Key findings

• The LSTM-based wind estimation method achieved significantly lower mean wind speed estimation errors than the wind triangle method, with a 50% reduction in mean error on average across tested conditions.
• Directional wind estimation error was reduced by approximately 50%, with the LSTM model achieving a mean directional error of 0.0388 rad (≈2.2°) compared to 0.0654 rad (≈3.7°) for the wind triangle method.
• In high-turbulence conditions, the LSTM model showed a marked advantage in capturing wind fluctuations, with lower error variance in both wind speed and direction.
• The LSTM model outperformed the wind triangle method in all tested scenarios, including both Dryden and LES-generated wind fields, across multiple altitudes and flight modes.
• The error variance in wind speed estimation was consistently lower for the LSTM model (e.g., 0.1016 m²/s² at 60 m altitude) compared to the wind triangle (0.0956 vs. 0.5284 m²/s² at 60 m), indicating greater stability and accuracy.
• The LSTM framework demonstrated strong generalization across diverse wind fields and turbulence levels, suggesting robustness for real-world deployment on commercial sUAS.