Wind-Aware Reinforcement Learning Control of a Small Quadrotor Using Learned Onboard Wind Estimation in Simulated Atmospheric Turbulence

# Wind-Aware Reinforcement Learning Control of a Small Quadrotor Using Learned Onboard Wind Estimation in Simulated Atmospheric Turbulence
Source: [https://arxiv.org/html/2607.01528](https://arxiv.org/html/2607.01528)
Abdullah Al Tasim111Graduate Research Assistant, School of Aerospace and Mechanical Engineering\.and Wei Sun222Corresponding Author, School of Aerospace and Mechanical Engineering; wsun@ou\.edu\.

###### Abstract

Small multirotor aircraft are increasingly tasked with operations in the atmospheric boundary layer, where turbulent winds comparable to the vehicle’s airspeed degrade trajectory tracking and can defeat conventional feedback control\. This work illustrates a two\-stage learning pipeline that first estimates the local wind from onboard kinematics and dynamics and then exploits that estimate inside a reinforcement learning \(RL\) flight controller\. The wind estimator, an attention\-augmented gated recurrent network trained on thousands of simulated flights through von Kármán turbulence with power\-law shear and veer, recovers the horizontal wind vector with a per\-flight root\-mean\-square error of0\.40ms−10\.40\\text\{\\,\}\\mathrm\{m\}\\text\{\\,\}\{\\mathrm\{s\}\}^\{\-1\}and a direction error of3\.2°3\.2\\text\{\\,\}\\mathrm\{\\SIUnitSymbolDegree\}on unseen wind regimes, an accuracy near the floor imposed by unresolved turbulence, and generalizes to vertical ascent profiles with a skill score of 0\.861 over a constant\-wind reference\. A proximal policy optimization controller receiving the frozen estimator’s output reduces horizontal trajectory tracking error by 48% relative to a wind\-blind proportional\-derivative baseline across mean winds of4ms−1to12ms−14\\text\{\\,\}\\mathrm\{m\}\\text\{\\,\}\{\\mathrm\{s\}\}^\{\-1\}12\\text\{\\,\}\\mathrm\{m\}\\text\{\\,\}\{\\mathrm\{s\}\}^\{\-1\}, winning on 100% of evaluation episodes\. A three\-way ablation decomposes this improvement into a kinematic component, available without wind information, and a wind\-perception component; the perception share rises with wind speed, from small in light winds toward roughly half the total benefit in strong winds, consistent with the quadratic scaling of aerodynamic drag\. The controller degrades gracefully on out\-of\-distribution winds of13ms−1to15ms−113\\text\{\\,\}\\mathrm\{m\}\\text\{\\,\}\{\\mathrm\{s\}\}^\{\-1\}15\\text\{\\,\}\\mathrm\{m\}\\text\{\\,\}\{\\mathrm\{s\}\}^\{\-1\}, where the baseline fails catastrophically\.

## Nomenclature

UmeanU\_\{\\mathrm\{mean\}\}=reference mean wind speed atzrefz\_\{\\mathrm\{ref\}\},ms−1\\mathrm\{m\}\\text\{\\,\}\{\\mathrm\{s\}\}^\{\-1\}zrefz\_\{\\mathrm\{ref\}\}=reference height for the wind profile,m\\mathrm\{m\}α\\alpha=power\-law wind\-shear exponentwN,wEw\_\{N\},w\_\{E\}=north and east components of the mean wind,ms−1\\mathrm\{m\}\\text\{\\,\}\{\\mathrm\{s\}\}^\{\-1\}w^N,w^E\\hat\{w\}\_\{N\},\\hat\{w\}\_\{E\}=estimated north and east mean\-wind components,ms−1\\mathrm\{m\}\\text\{\\,\}\{\\mathrm\{s\}\}^\{\-1\}τ\\tau=exponential\-moving\-average filter time constant,s\\mathrm\{s\}SS=skill score relative to a constant\-wind referenceRMSE\\mathrm\{RMSE\}=root\-mean\-square errorMAE\\mathrm\{MAE\}=mean absolute errorAcronymsGRU =gated recurrent unitMAE =mean absolute errorOOD =out\-of\-distributionPD =proportional\-derivativePPO =proximal policy optimizationRL =reinforcement learningRMSE =root\-mean\-square errorsUAS =small uncrewed aircraft system
## 1Introduction

Small uncrewed aircraft systems \(sUAS\) typically operate within the atmospheric boundary layer \(ABL\), where mean winds, vertical shear, and turbulent gusts routinely reach a substantial fraction of the vehicle’s own airspeed and at times exceed it\. For a multirotor with mass on the order of a few kilograms, the aerodynamic disturbance force scales approximately with the square of the relative wind speed, so the control burden grows sharply with wind: a disturbance that is negligible at 3 m s\-1becomes dominant at 12 m s\-1\. Conventional cascaded proportional\-derivative \(PD\) and related model\-based controllers treat wind purely as an unmeasured disturbance to be rejected reactively, after it has already produced a tracking error\. As wind strengthens, this reactive posture leads to growing position error and, beyond the actuation margin, to divergence\.

An attractive alternative is to give the controller direct knowledge of the wind\. Dedicated airflow sensors add mass, cost, and calibration burden that small platforms can rarely afford, but the vehicle itself is an aerodynamic body: the mismatch between commanded thrust, measured acceleration, and observed velocity carries information about the relative wind\. This motivates a two\-stage architecture in which \(i\) a learned estimator infers the ambient wind vector from onboard kinematics and dynamics, and \(ii\) a learned flight controller consumes that estimate as part of its observation, enabling anticipatory rather than purely reactive disturbance handling\.

This paper develops and evaluates such a pipeline in a six\-degree\-of\-freedom simulation of a 2\.59\-kg quadrotor flying through von Kármán turbulence with power\-law vertical shear and direction veer, physics\-based sensor noise, and a library of horizontal and vertical reference trajectories\. The contributions are threefold\. First, it shows that an attention\-augmented gated recurrent unit \(GRU\) network, trained on several thousand simulated flights, estimates the horizontal wind vector with a per\-flight vector root\-mean\-square error \(RMSE\) of 0\.40 m s\-1and a direction mean absolute error \(MAE\) of 3\.2∘on wind regimes never seen in training, an accuracy near the floor set by unresolved turbulent fluctuations, and that the same architecture extends to vertical ascent–descent flight with strong skill over a constant\-wind reference\. Second, it shows that a proximal policy optimization \(PPO\) controller conditioned on the frozen estimator’s output reduces horizontal tracking RMSE by 48% and vertical\-regime horizontal\-axis RMSE by 39\.5%, relative to a wind\-blind PD baseline, outperforming it in every matched evaluation episode, and that a three\-way ablation cleanly decomposes this improvement into a kinematic\-learning component and a wind\-perception component\. Third, it demonstrates that the value of wind perception is regime\-dependent rather than constant\. In the horizontal regime the wind\-perception share of the total improvement grows with mean wind speed to a mid\-range peak nearU=8U=8m s\-1before receding at the strongest winds; in the vertical regime this share rises with wind speed, from near zero in light winds toward roughly half the total benefit in strong winds\. The learned controller also degrades gracefully on out\-of\-distribution winds, where the baseline fails outright\. Together these results argue that learned wind perception is a high\-leverage, sensor\-free addition to small\-UAS autonomy in the demanding wind conditions where it is most needed\.

The remainder of the paper is organized as follows\. Section[2](https://arxiv.org/html/2607.01528#S2)reviews related work in multirotor wind estimation and learning\-based flight control\. Section[3](https://arxiv.org/html/2607.01528#S3)describes the simulation environment, turbulence model, and trajectory library\. Section[4](https://arxiv.org/html/2607.01528#S4)presents the wind estimation stage and its evaluation in horizontal and vertical regimes\. Section[5](https://arxiv.org/html/2607.01528#S5)describes the wind\-aware RL controller, baselines, and the ablation design\. Section[6](https://arxiv.org/html/2607.01528#S6)reports tracking results, the improvement decomposition, and the out\-of\-distribution probe\. Section[7](https://arxiv.org/html/2607.01528#S7)discusses mechanisms and limitations, and Section[8](https://arxiv.org/html/2607.01528#S8)concludes\.

## 2Literature Review

A hovering or slowly translating multirotor must tilt against the relative wind to hold its position, so its attitude and motor commands carry information about the wind\. Model\-based approaches treat the vehicle as a calibrated drag body and invert a parametric aerodynamic model, often within a Kalman\-filtering framework\. The inclination\-angle method of\[Neumann2015\]introduced this idea, relating quadrotor pitch and roll to the wind vector and achieving a wind\-speed RMSE near 0\.6 m s\-1after wind\-tunnel calibration, while\[Gonzalez2019\]compared a hierarchy of kinematic, dynamic\-particle, and rigid\-body models and found that the richer rigid\-body model yields the most accurate speed estimates\. Such platforms have been deployed as wind sensors in atmospheric field campaigns, where\[Palomaki2017\]recovered lower\-atmosphere wind profiles from a hovering multirotor\. A related line augments the vehicle with dedicated airflow sensing, for example the onboard flow sensors used by\[Yeo2018\]for multirotor pitch control in wind; the present work instead infers wind from existing state and control signals alone\. These model\-based methods are attractive for their transparency but degrade when the aerodynamic model is misspecified, in aggressive maneuvers, and in strong winds where quasi\-steady drag assumptions break down\.

Learning\-based estimators relax these assumptions by regressing wind from flight dynamics directly\. These span a range of methods, from nearest\-neighbor regression on flight data\[Wang2019\]to deep residual\-aerodynamics representations that capture wind effects accurately enough to support control, most prominently the Neural\-Fly line of work, in which a learned basis of wind\-dependent aerodynamic residuals enables rapid online adaptation\[OConnell2022\]\. The present work differs in explicitly reconstructing the wind vector itself as an interpretable intermediate quantity, which can serve mapping and forecasting applications in addition to control, and in quantifying estimation skill against the floor imposed by unresolved turbulence\.

Deep RL has produced quadrotor controllers that match or exceed classical cascades in tracking accuracy and robustness, beginning with demonstrations that neural policies can stabilize and recover a quadrotor from arbitrary initial states\[Hwangbo2017\], extending to policies that plan near\-time\-optimal racing trajectories\[Song2021\]and that outperform expert human pilots in drone racing\[Kaufmann2023\]\. Recent evidence indicates that the advantage of learned control over classical optimal control is most pronounced under unmodeled effects, where a policy can discover more robust responses than a decomposition\-based controller\[Song2023\]; wind is precisely such an effect\. Policy\-gradient methods, particularly PPO\[Schulman2017\]as implemented in libraries such as Stable\-Baselines3\[Raffin2021\], are the workhorse of this literature\. A growing line of work addresses flight under disturbances:\[Huang2023\]train a feedforward\-feedback policy in simulation that tracks aggressive trajectories in unsteady wind fields and augment it at deployment with an adaptive disturbance estimator\. Most such studies treat wind either as unmodeled noise to be overcome through domain randomization\[Tobin2017\]or as a lumped force disturbance to be rejected\. Comparatively little work conditions the deployed policy on an explicitly estimated wind state and then quantifies how much of the resulting performance is attributable to that perception channel as opposed to the policy’s general kinematic competence; this attribution question is a central focus of the present study\.

Classical adaptive and disturbance\-observer\-based control augments a nominal controller with an online estimate of lumped disturbances, withℒ1\\mathcal\{L\}\_\{1\}adaptive control a representative framework offering fast adaptation with bounded transients\[Hovakimyan2010\]\. Closer to the multirotor setting,\[Bisheban2021\]combine a geometric controller with neural\-network disturbance estimates to track trajectories in wind fields\. Such methods estimate the*force*disturbance rather than the wind*velocity*, and their authority is typically limited to slow, quasi\-constant disturbance components\. Hybrid approaches that combine learned aerodynamic models with adaptive control blur this line, including learned residual\-force models\[OConnell2022\]and hybrid blade\-element models such as NeuroBEM\[Bauersfeld2021\]\. The flatness\-based controller used as the classical baseline here is itself a standard high\-performance quadrotor comparator\[Sun2022\]\. The methodology introduced here, comparing a wind\-blind classical baseline, a wind\-blind learned policy, and a wind\-aware learned policy under identical replayed physics, offers a general template for attributing performance in any such disturbance\-aware architecture, independent of how the disturbance information is obtained\.

## 3Simulation Environment

All experiments are conducted in a custom six\-degree\-of\-freedom quadrotor simulator that integrates rigid\-body dynamics, a spectral turbulence field, calibrated sensor models, and a trajectory\-tracking controller\. The horizontal and vertical training datasets are produced from simulation that share identical vehicle dynamics, sensor models, wind model, and controller, differing only in their trajectory libraries and in how flight altitude is sampled; this shared physics guarantees that the two estimators and the two control regimes are compared on a common substrate\.

### 3\.1Vehicle and dynamics

The simulated platform is a 2\.59\-kg quadrotor with diagonal inertia tensorJ=diag​\(0\.078,0\.082,0\.14\)J=\\mathrm\{diag\}\(0\.078,0\.082,0\.14\)kg m2and an arm length of 0\.25 m\. Each rotor produces thrust and reaction torque through coefficientskT=1\.5×10−5k\_\{T\}=1\.5\\times 10^\{\-5\}andkM=0\.055​kTk\_\{M\}=0\.055\\,k\_\{T\}, and the four motor speeds map to collective thrust and body torques through a fixed mixing matrix; motor dynamics are modeled as a first\-order lag with time constant 0\.05 s and speeds bounded to\[0,1200\]\[0,1200\]rad s\-1, with per\-axis collective thrust limited to between 0\.3 and 2\.5 times hover\. Translational aerodynamic drag is modeled as a quadratic force in the body\-relative wind with effective drag coefficientsCd​Ax​y=0\.038C\_\{d\}A\_\{xy\}=0\.038m2in the horizontal plane andCd​Az=0\.10C\_\{d\}A\_\{z\}=0\.10m2along the vertical axis at air densityρ=1\.225\\rho=1\.225kg m\-3, so the disturbance force scales with the square of the relative wind speed\. Rigid\-body dynamics are integrated with a fixed step ofd​t=2dt=2ms; the flatness\-based controller \(described below\) runs at 100 Hz \(d​tctrl=10dt\_\{\\mathrm\{ctrl\}\}=10ms\) and all signals are logged at 10 Hz \(d​tlog=0\.10dt\_\{\\mathrm\{log\}\}=0\.10s\), which sets the time resolution of the estimator’s input sequences\.

The reference controller used during dataset generation is a flatness\-based cascade with pure PD outer position and inner attitude loops, with position gainsKp=\(5,5,7\)K\_\{p\}=\(5,5,7\),Kd=\(3\.5,3\.5,4\.5\)K\_\{d\}=\(3\.5,3\.5,4\.5\), attitude gainsKR=diag​\(10,10,5\)K\_\{R\}=\\mathrm\{diag\}\(10,10,5\)andKω=diag​\(3\.5,3\.5,2\)K\_\{\\omega\}=\\mathrm\{diag\}\(3\.5,3\.5,2\), a commanded\-tilt limit of 35∘, and a position\-error saturation of\(12,12,15\)\(12,12,15\)m\. This same wind\-blind PD controller is the classical baseline against which the reinforcement learning policies are compared in Sections[5](https://arxiv.org/html/2607.01528#S5)and[6](https://arxiv.org/html/2607.01528#S6)\.

### 3\.2Atmospheric wind and turbulence model

The ambient wind is the sum of a deterministic mean profile and a spatially correlated turbulent fluctuation\. The mean horizontal wind follows a power law in altitude,

U¯​\(z\)=Umean​\(max⁡\(z,zref\)zref\)α,\\bar\{U\}\(z\)=U\_\{\\mathrm\{mean\}\}\\left\(\\frac\{\\max\(z,z\_\{\\mathrm\{ref\}\}\)\}\{z\_\{\\mathrm\{ref\}\}\}\\right\)^\{\\alpha\},\(1\)with reference heightzref=10z\_\{\\mathrm\{ref\}\}=10m and shear exponentα\\alpha, and its direction veers linearly with altitude at a rate of 3–8∘per 100 m\. The reference mean speedUmeanU\_\{\\mathrm\{mean\}\}is defined atzrefz\_\{\\mathrm\{ref\}\}\. The turbulent fluctuation is synthesized from the von Kármán spectrum\[vonKarman1948\], the standard continuous\-turbulence model for atmospheric flight\[MILHDBK1797\], using the TurboGenPY spectral\-mode method\[TURBOGENPY\]with 300 Fourier modes on a64364^\{3\}grid spanning a1200×1200×12001200\\times 1200\\times 1200m domain, producing a frozen, divergence\-free turbulence cube that is sampled along the flight path\. Turbulence intensity is set per flight in the range 0\.08–0\.25 and scaled with the local mean speed, with mild altitude dependence and stability\-dependent anisotropy cycled through neutral, stable, and convective regimes\[Stull1988\]\. A configurable cap on the horizontal mean\-wind magnitude \(max\_horizontal\_wind, 20 m s\-1in the evaluation environment\) clips the upper tail of Eq\. \([1](https://arxiv.org/html/2607.01528#S3.E1)\); its consequence for the out\-of\-distribution analysis is disclosed in Section[7](https://arxiv.org/html/2607.01528#S7)\.

Wind regimes are drawn by Latin hypercube sampling \(LHS\) to spread coverage evenly over the regime parameters\. The vertical\-dataset sampler spans six dimensions \(UmeanU\_\{\\mathrm\{mean\}\}, direction, turbulence intensity, shear exponentα\\alpha, veer, and a turbulence period\) while the horizontal\-dataset sampler adds a seventh dimension, the fixed flight altitude of each flight\. In both cases the upper bound onUmeanU\_\{\\mathrm\{mean\}\}is set adaptively from the sampled shear so that the mean wind encountered at altitude does not exceed a physical ceiling of 20 m s\-1: the vertical sampler bounds the wind at the maximum training altitude \(zmax=600z\_\{\\max\}=600m\), whereas the horizontal sampler bounds it at each flight’s own fixed altitude, which lets low\-altitude horizontal flights experience strong winds without violating the ceiling\. Evaluation uses a disjoint LHS seed, so all reported estimation and control results are on wind regimes never seen during training\. The shear law in Eq\. \([1](https://arxiv.org/html/2607.01528#S3.E1)\) materially constrains the usable vertical evaluation range, an effect quantified in Section[7](https://arxiv.org/html/2607.01528#S7)\.

### 3\.3Sensors

Onboard measurements emulate a standard small\-UAS sensor suite with physics\-based sampling rate, noise, and slowly drifting bias for each instrument: a Global Positioning System \(GPS\) receiver reporting position and velocity at 10 Hz \(position noise 0\.7 m, velocity noise 0\.15 m s\-1, with random\-walk bias\), a barometric altimeter at 25 Hz \(0\.8 m noise\), an attitude estimate at 50 Hz \(0\.6∘roll/pitch, 1\.5∘yaw\), a rate gyro at 200 Hz \(0\.3∘s\-1noise with bias drift\), and a body\-frame accelerometer at 200 Hz \(0\.05 m s\-2noise with bias drift\)\. Sensor streams are down\-sampled to the 10 Hz logging grid by zero\-order hold\. Critically, the suite contains no airflow sensor of any kind: all wind information available to the estimator must be inferred from the vehicle’s kinematic and control response\.

The logged feature schema is the seventeen\-channel “sensor17” set used throughout this work\. Thirteen of its channels are controller\-agnostic kinematic signals: altitude, the three velocity components, the three body accelerations, the three Euler angles, and the three body rates\. The remaining four are controller\-aware channels, namely the commanded collective thrustuTu\_\{T\}and the three commanded body torques\(uτx,uτy,uτz\)\(u\_\{\\tau\_\{x\}\},u\_\{\\tau\_\{y\}\},u\_\{\\tau\_\{z\}\}\), which expose the control effort the vehicle is exerting to hold its trajectory against the wind\. The ground\-truth labels logged alongside the sensor channels are the north and east components of the mean wind,\(mean​\_​wind​\_​N,mean​\_​wind​\_​E\)\(\\mathrm\{mean\\\_wind\\\_N\},\\mathrm\{mean\\\_wind\\\_E\}\), evaluated from the turbulence\-free mean profile at the vehicle’s instantaneous altitude\. Because the labels exclude the turbulent fluctuation, whose magnitude is comparable to the estimator’s residual error, the unresolved turbulence sets an irreducible floor on achievable estimation accuracy, a point central to interpreting the results in Section[4](https://arxiv.org/html/2607.01528#S4)\.

### 3\.4Trajectory library

Two trajectory libraries are used, one per regime\. The*horizontal*library holds altitude fixed within a flight \(sampled per flight over 80–550 m\) and varies wind across flights through the seventh LHS dimension; it comprises five constant\-altitude patterns chosen to expose the vehicle to wind from all relative angles within a single flight: a loiter circle \(loiter\_circle\_h\), a racetrack with long straight legs and 180∘turns \(racetrack\_h\), a figure\-eight lemniscate \(figure8\_h\), a four\-lobed cloverleaf \(cloverleaf\_h\), and a lawnmower raster scan \(lawnmower\_h\)\. The straight legs of the racetrack and lawnmower give clean steady\-state airspeed signatures, while the curved patterns sweep heading continuously, providing dense coverage of wind\-relative angles for the estimator\.

The*vertical*library sweeps altitude continuously within each flight so that the altitude\-dependent mean\-wind label varies along the trajectory, training the estimator for altitude\-conditioned inference\. It comprises four ascent profiles reaching up to 600 m: a pure vertical climb \(vertical\_climb\), a helical spiral ascent \(spiral\_ascent\), a three\-dimensional figure\-eight that sweeps altitude while exciting horizontal motion \(figure8\_3d\), and a lawnmower scan with a slow altitude ramp \(lawnmower\_scan\)\. Thefigure8\_3dprofile, which combines the largest horizontal excitation with altitude sweep, is used for the qualitative trajectory\-overlay results in Section[6](https://arxiv.org/html/2607.01528#S6)\.

![Refer to caption](https://arxiv.org/html/2607.01528v1/x1.png)Figure 1:Overview of the two\-stage wind\-aware control pipeline\. A frozen attention\-GRU network estimates the ambient mean wind vector from the onboard kinematic and control features; the filtered estimate augments the observation of a PPO trajectory\-tracking policy\. The same wind\-blind PD cascade used to generate the training data serves as the classical baseline\.

## 4Wind Estimation

This section develops the first stage of the pipeline \(Fig\.[1](https://arxiv.org/html/2607.01528#S3.F1)\): a learned estimator that reconstructs the mean wind from onboard signals alone\. First the methodology common to both flight regimes is described \(Section[4\.1](https://arxiv.org/html/2607.01528#S4.SS1)\), then the horizontal estimator is presented in full \(Section[4\.2](https://arxiv.org/html/2607.01528#S4.SS2)\); the vertical estimator, which shares the same architecture and training recipe, is presented in Section[4\.3](https://arxiv.org/html/2607.01528#S4.SS3)as a focused description of what differs\.

### 4\.1Common methodology

#### 4\.1\.1Problem formulation

The estimation task is causal sequence regression\. At each logging instant the model receives the most recent window of onboard features and predicts the north and east components of the mean wind,\(mean​\_​wind​\_​N,mean​\_​wind​\_​E\)\(\\mathrm\{mean\\\_wind\\\_N\},\\mathrm\{mean\\\_wind\\\_E\}\), at the vehicle’s current position\. The window length is 60 samples, which at the 10 Hz logging rate \(Section[3](https://arxiv.org/html/2607.01528#S3)\) corresponds to 6 s of recent history\. Ground truth is the turbulence\-free mean wind from Eq\. \([1](https://arxiv.org/html/2607.01528#S3.E1)\); because the labels exclude the turbulent fluctuation, whose instantaneous magnitude is comparable to the estimator’s residual error, the unresolved turbulence imposes an irreducible floor on the achievable per\-sample accuracy\. This distinction between per\-sample \(per\-window\) and per\-flight accuracy is central to interpreting the results and is made explicit below\. The two regimes use*different*input feature representations, tailored to what is observable in each; these are described in their respective subsections \(Sections[4\.2](https://arxiv.org/html/2607.01528#S4.SS2)and[4\.3](https://arxiv.org/html/2607.01528#S4.SS3)\)\.

#### 4\.1\.2Architecture

The estimator is a recurrent network with temporal attention\. A single\-layer unidirectional gated recurrent unit \(GRU\)\[Cho2014\]with 128 hidden units encodes the input window into a sequence of hidden states\. A Bahdanau\-style additive attention module\[Bahdanau2015\]\(attention dimension 128\) then forms a context vector over the hidden\-state sequence, using the final hidden state as the query so that the mechanism remains causal and the prediction at the end of the window attends over, and only over, the samples within that window\. The attention context is concatenated with the final hidden state and passed through a three\-layer multilayer\-perceptron head \(Gaussian error linear unit \(GELU\) activations, layer normalization, dropout 0\.2\) that outputs the two wind components\. Predictions and labels are standardized; the training loss is a Huber \(smooth\-L1L\_\{1\}\) term on the standardized components augmented by two small physical auxiliary terms in unscaled space, a speed term \(weight 0\.03\) and a direction term \(weight 0\.05\) weighted toward higher wind speeds which improve speed calibration and directional accuracy without distorting the dominant component regression\.

#### 4\.1\.3Post\-processing filter

Because the deployment target is a slowly varying mean wind, the per\-sample network output is smoothed by a causal exponential moving average \(EMA\) before use\. The filter time constant is treated as a deployment hyperparameter; as reported per regime below, a short time constant outperforms both the raw output and heavier smoothing, because the network output is already accurate enough that aggressive filtering removes genuine signal rather than noise\.

#### 4\.1\.4Metrics

Three complementary error measures are reported, since they answer different questions and differ substantially in magnitude\. The*per\-window vector RMSE*is the root\-mean\-square magnitude of the two\-dimensional error vector, evaluated on every sliding window in the test set; it is the most conservative and most standard measure\. The*component\-mean RMSE*averages the separate north and east RMSEs and is correspondingly smaller\. The*per\-flight vector RMSE*first averages the estimate over a whole flight and then measures its error against the flight’s mean\-wind label; it is the relevant measure when the deployed quantity is a per\-flight steady wind, and it is much smaller than the per\-window value precisely because per\-flight averaging cancels the turbulence\-driven fluctuations that dominate the per\-window error\. Direction mean absolute error \(MAE\) and the per\-component Pearson correlation are also reported\. Train, validation, and test splits are held out by wind case \(70/15/15%\), so all reported test metrics are on wind regimes disjoint from training\.

### 4\.2Horizontal wind estimation

#### 4\.2\.1Input features

The horizontal estimator consumes a 48\-channel feature representation computed per flight from the logged sensor streams\. This rich representation is warranted because, in horizontal flight at fixed altitude, the mean\-wind label is nearly constant within a flight and must be read entirely off the vehicle’s body response, with no altitude sweep to provide additional leverage\. The representation nests three groups\. The first is the raw sensor17 set of Section[3](https://arxiv.org/html/2607.01528#S3)altitude, the three velocity and three acceleration components, the three Euler angles, the three body rates, and the four commanded control channels \(uTu\_\{T\},uτxu\_\{\\tau\_\{x\}\},uτyu\_\{\\tau\_\{y\}\},uτzu\_\{\\tau\_\{z\}\}\) together with the three body\-frame specific\-force components\. The second is a set of physically motivated aerodynamic proxies: the north, east, up, and horizontal components of the inferred aerodynamic force \(aero​\_​N\\mathrm\{aero\\\_N\},aero​\_​E\\mathrm\{aero\\\_E\},aero​\_​U\\mathrm\{aero\\\_U\},aero​\_​horiz\\mathrm\{aero\\\_horiz\}\), formed from the residual between commanded and realized specific force, together with the commanded\-tilt magnitude and a tilt\-saturation flag\. These encode the central physical cue: to hold its track against a steady wind, the vehicle must tilt to generate a counteracting horizontal force, so the aerodynamic residual is, to first order, a direct readout of the wind\-induced drag\.

The third group is the temporal core of the representation: causal trailing rolling means of the most informative kinematic, aerodynamic, and control signals over two windows 10 s \(100 samples, theavg100channels\) and 30 s \(300 samples, theavg300channels\) applied to the horizontal velocities and accelerations, all four aerodynamic\-force components, roll and pitch, and commanded thrust\. The motivation is direct: the instantaneous aerodynamic residual is dominated by turbulent gusts, whereas the*mean*wind is revealed by the low\-frequency component of the drag signature\. These trailing averages act as causal low\-pass filters that suppress the turbulent fluctuation while preserving the steady drag bias, and they were the decisive ingredient in lowering estimation error: earlier feature sets restricted to instantaneous signals plateaued well above the present accuracy\.

#### 4\.2\.2Training configuration

The horizontal estimator was trained on the merged 5\-trajectory horizontal dataset \(1000 wind cases across the five constant\-altitude trajectories of Section[3](https://arxiv.org/html/2607.01528#S3)\)\. Sequences were built with a 60\-sample window \(6 s\) at a training stride of 12 samples, after a climb\-aware crop that discards each flight’s initial ascent transient \(it removes samples beforemax⁡\(tmin,z/z˙climb\+tsafety\)\\max\(t\_\{\\min\},z/\\dot\{z\}\_\{\\mathrm\{climb\}\}\+t\_\{\\mathrm\{safety\}\}\)withtmin=8t\_\{\\min\}=8s\), so the estimator sees only cruise\-phase data where the mean\-wind label is physically meaningful\. Optimization used Adam \(learning rate3×10−43\\times 10^\{\-4\}, weight decay10−510^\{\-5\}\) with a warmup and cosine\-style decay over 25 epochs at batch size 256, with light input noise augmentation and a wind\-case\-balanced sampler\. Validation vector RMSE converged to approximately 1\.08 m s\-1with a validation direction MAE near 3\.0∘\.

#### 4\.2\.3Estimation accuracy

On the held\-out test wind cases the horizontal estimator attains a per\-window vector RMSE of 1\.05 m s\-1, a component\-mean RMSE of 0\.74 m s\-1, and a direction MAE of 3\.2∘, with per\-component correlations of 0\.996 \(north\) and 0\.996 \(east\)\. Averaged to the per\-flight level, the form in which the estimate is consumed by the controller, and the vector RMSE falls to 0\.40 m s\-1\. The gap between the 1\.05 m s\-1per\-window value and the 0\.40 m s\-1per\-flight value is not a discrepancy but the signature of the turbulence floor: the per\-window error is dominated by unresolved gusts that average to near zero over a flight, leaving a small residual mean\-wind bias\. Because the labels deliberately exclude turbulence, the per\-flight figure is the meaningful measure of how well the steady wind is recovered, and at 0\.40 m s\-1it approaches the floor set by the labeling convention itself\. Table[1](https://arxiv.org/html/2607.01528#S4.T1)collects these figures\.

Per\-trajectory results are consistent across the five patterns, with per\-flight vector RMSE ranging from 0\.34 m s\-1on the loiter circle to 0\.51 m s\-1on the racetrack, and per\-window direction MAE between 3\.0∘and 3\.3∘\(Table[2](https://arxiv.org/html/2607.01528#S4.T2)\)\. The loiter circle, whose sustained curvature continuously exposes the airframe to wind from all relative angles, yields the cleanest per\-flight estimate; the racetrack, dominated by straight legs at two headings, is modestly harder, consistent with richer heading coverage improving mean\-wind observability\.

Table 1:Horizontal wind estimation on held\-out test wind cases\. Three RMSE conventions are reported because they differ in magnitude and meaning \(see Section[4\.1\.4](https://arxiv.org/html/2607.01528#S4.SS1.SSS4)\); the per\-flight value is the form consumed by the controller\.Table 2:Per\-trajectory horizontal estimation\. Per\-flight vector RMSE and per\-window direction MAE on held\-out test wind cases\.
#### 4\.2\.4Dependence on wind speed

The error structure varies systematically with wind speed in a way that supports the use of the estimator for control\. As the true wind increases from the 0–4 m s\-1band to above 16 m s\-1, the per\-window vector RMSE grows in absolute terms \(from 0\.58 to 1\.24 m s\-1\), but the direction MAE*falls*monotonically \(from 5\.3∘to 2\.1∘\) and the per\-component correlation rises toward 0\.998 \(Fig\.[2](https://arxiv.org/html/2607.01528#S4.F2)\)\. In other words, the absolute error grows sublinearly with wind while the*relative*error shrinks: the estimator becomes directionally sharper and more strongly correlated with truth exactly in the strong\-wind regime where wind compensation matters most for control\. This behavior follows from the drag physics and the aerodynamic signature that the estimator reads scales with the square of the relative wind, so the signal\-to\-noise ratio of the mean\-wind cue improves as wind strengthens\. Figure[3](https://arxiv.org/html/2607.01528#S4.F3)shows an example held\-out low\-wind test case, the regime where the relative error is largest\.

![Refer to caption](https://arxiv.org/html/2607.01528v1/x2.png)Figure 2:Horizontal estimation error as a function of true wind speed\. Per\-window vector RMSE \(bars, left axis\) rises with wind, while direction MAE \(line, right axis\) falls and the per\-component correlation \(annotated\) increases toward 0\.998\. Relative accuracy therefore improves in the strong\-wind regime most relevant to control\.![Refer to caption](https://arxiv.org/html/2607.01528v1/fig_esth_timeseries.png)Figure 3:Example horizontal estimation on a held\-out low\-wind test case \(true speed≈\\approx3\.8 m s\-1\)\. For each of the five trajectories, the predicted north and east mean wind \(solid\) track the true mean \(dashed\) through the turbulent full\-wind signal \(faint\); the per\-flight vector RMSE ranges from 0\.50 to 0\.76 m s\-1across trajectories in this low\-wind case, the regime where relative error is largest\.

### 4\.3Vertical wind estimation

The vertical estimator shares the architecture, training loss, sequence length, optimizer, wind\-case\-held\-out split protocol, EMA post\-filter, and metric definitions of Section[4\.1](https://arxiv.org/html/2607.01528#S4.SS1); this subsection describes only what differs: the input representation, the training data, and the resulting accuracy and its altitude structure\.

#### 4\.3\.1Input features

In vertical flight the mean\-wind label varies continuously along the trajectory as the vehicle sweeps altitude through the shear and veer profile \(Section[3](https://arxiv.org/html/2607.01528#S3)\), so the estimation problem is altitude\-conditioned rather than steady\-within\-flight\. This changes what information is most useful, and the vertical estimator accordingly uses a leaner 22\-channel representation rather than the horizontal postproc set\. It comprises the same thirteen base kinematic channels described in Section[3](https://arxiv.org/html/2607.01528#S3)\(altitude, the three velocity and three acceleration components, the three Euler angles, and the three body rates\), augmented with nine reference\-tracking channels: the three position tracking errors \(dX,dY,dZ\\mathrm\{dX\},\\mathrm\{dY\},\\mathrm\{dZ\}between actual and commanded position\) and the reference velocity and acceleration \(vx​\_​ref,vy​\_​ref,vz​\_​ref\\mathrm\{vx\\\_ref\},\\mathrm\{vy\\\_ref\},\\mathrm\{vz\\\_ref\},ax​\_​ref,ay​\_​ref,az​\_​ref\\mathrm\{ax\\\_ref\},\\mathrm\{ay\\\_ref\},\\mathrm\{az\\\_ref\}\), the latter computed by finite differences of the known reference position along each flight\. The altitude channel itself is informative here in a way it is not for the horizontal model: because the mean wind is a function of altitude,zzprovides the network with a direct index into the shear profile, and the reference\-kinematic channels disambiguate commanded motion from wind\-induced deviation during the continuous climb\.

#### 4\.3\.2Training configuration and data

The vertical estimator was trained on the merged vertical\-profile dataset of 4000 flights spanning the four altitude\-sweeping trajectories of Section[3](https://arxiv.org/html/2607.01528#S3)\(figure8\_3d,lawnmower\_scan,spiral\_ascent,vertical\_climb\) across 1000 wind cases\. Sequences use the same 60\-sample \(6 s\) window at a training stride of 16\. Optimization ran for up to 150 epochs \(best validation at epoch 116\) with early\-stopping patience 25, otherwise matching the horizontal recipe \(Adam, learning rate3×10−43\\times 10^\{\-4\}, batch 256, wind\-case\-balanced sampler\), with slightly stronger regularization \(feature dropout 0\.1\)\. The model has 133,315 parameters\. The train/validation/test split is again held out by wind case in a 700/150/150\-flight \(70/15/15%\) partition\.

#### 4\.3\.3Estimation accuracy

On the held\-out test wind cases the vertical estimator attains a per\-window vector RMSE of 1\.56 m s\-1, a component\-mean RMSE of 1\.11 m s\-1, and a direction MAE of 4\.9∘, with per\-component correlations of 0\.991 \(north\) and 0\.991 \(east\) \(Table[3](https://arxiv.org/html/2607.01528#S4.T3)\)\. The absolute error is larger than in the horizontal regime, which is expected: the vertical trajectories climb to 600 m, where power\-law shear amplifies the mean wind to substantially higher magnitudes than the horizontal flights experience, so the same fractional accuracy corresponds to a larger absolute RMSE\. The appropriate measure of the estimator’s quality is therefore not the raw RMSE but its skill against a meaningful reference\.

This was quantified with a skill scoreS=1−RMSEmodel/RMSErefS=1\-\\mathrm\{RMSE\}\_\{\\text\{model\}\}/\\mathrm\{RMSE\}\_\{\\text\{ref\}\}, where the reference is a constant\-wind predictor that emits the single best constant wind for the entire test set\. Because the test set pools many wind cases spanning a wide range of speeds and directions, and because the mean wind additionally ramps with altitude along each ascent through the shear profile, no single constant can represent the wind well: this reference yields a vector RMSE of 11\.26 m s\-1\. Against it, the estimator’s 1\.56 m s\-1corresponds to a vector skill score of 0\.861 and a speed skill score of 0\.899\. In other words, the estimator removes roughly 86% of the error that a no\-altitude\-knowledge constant predictor would incur, confirming that it has learned the altitude\-conditioned wind structure rather than merely regressing to a mean\. Per\-trajectory results are tightly clustered \(vector RMSE 1\.44–1\.64 m s\-1, direction MAE 4\.8–4\.9∘across all four trajectories\), indicating that accuracy does not depend strongly on the specific maneuver\.

Table 3:Vertical wind estimation on held\-out test wind cases\. The skill score is computed against a constant\-wind oracle that knows the test\-set mean\.
#### 4\.3\.4Altitude structure and post\-filter

Error grows gently and monotonically with altitude: per\-window vector RMSE rises from 1\.29 m s\-1in the lowest band \(0–150 m\) to 1\.70 m s\-1above 450 m, while direction MAE is essentially flat near 4\.8–5\.2∘across all bands \(Fig\.[4](https://arxiv.org/html/2607.01528#S4.F4)\)\. The error growth tracks the shear\-amplified increase in wind magnitude with altitude rather than any degradation in fractional accuracy, consistent with correlation remaining near 0\.99 at every altitude\. The estimator also recovers the vertical gradient of the wind: the predicted and true altitude–speed slopes agree closely \(approximately6\.9×10−36\.9\\times 10^\{\-3\}vs\.7\.2×10−37\.2\\times 10^\{\-3\}m s\-1per meter\), showing that the network reproduces the shear profile itself, not just the pointwise wind\.

The deployed EMA filter uses a short time constant ofτ=3\\tau=3s\. On an independently generated set of unseen wind cases \(a disjoint Latin hypercube design\), the filter improves the per\-window vector RMSE from 1\.43 m s\-1raw to 1\.30 m s\-1filtered and the direction MAE from 5\.5∘to 4\.9∘; heavier smoothing was found to degrade these metrics, because the network output is already accurate enough that a longer time constant removes genuine signal\. These unseen\-case results, slightly better than the held\-out test set on raw RMSE, confirm that the estimator generalizes to wind regimes generated entirely independently of training \(Fig\.[5](https://arxiv.org/html/2607.01528#S4.F5)\)\.

![Refer to caption](https://arxiv.org/html/2607.01528v1/x3.png)Figure 4:Vertical estimation error by altitude band\. Per\-window vector RMSE \(bars, left axis\) rises with altitude as shear amplifies the wind magnitude, while direction MAE \(line, right axis\) stays near 5∘and the per\-component correlation \(annotated\) remains near 0\.99 throughout\. The constant directional accuracy and correlation across altitude indicate that the error growth reflects the larger wind magnitude at altitude rather than any loss of fractional accuracy\.![Refer to caption](https://arxiv.org/html/2607.01528v1/all_trajectories_mean_NE_time_overview.png)Figure 5:Example vertical\-regime estimation on an unseen wind case\. For each of the four ascent profiles, the true mean wind \(solid\) ramps with the shear profile as the vehicle climbs, while the raw network prediction \(dashed\) and the deployedτ=3\\tau=3s EMA\-filtered estimate \(dotted\) track both the altitude\-driven trend and the turbulent excursions about it for the north and east components\.

## 5Wind\-Aware Reinforcement Learning Control

The second stage of the pipeline is a reinforcement learning \(RL\) controller that consumes the frozen estimator’s output and acts to reduce trajectory\-tracking error\. A central design choice, which shapes both the controller and the analysis that follows, is that the learned policy does not replace the classical controller but*augments*it: the policy outputs a feedforward wrench correction that is added to the same flatness\-based PD controller used as the baseline \(Section[3](https://arxiv.org/html/2607.01528#S3)\)\. This residual\-control formulation makes the wind\-blind PD law the literal zero\-action limit of the wind\-aware policy, so the comparison between them is exact rather than a comparison of two unrelated controllers\.

### 5\.1Policy, observation, and action

The policy is trained with proximal policy optimization \(PPO\)\[Schulman2017\]as implemented in Stable\-Baselines3\[Raffin2021\], using a multilayer\-perceptron actor–critic with two hidden layers of 256 units each\. Optimization uses a learning rate of3×10−43\\times 10^\{\-4\}, a rollout length of 2048 steps per environment, a minibatch size of 512, 10 epochs per update, discountγ=0\.99\\gamma=0\.99, generalized advantage estimation withλ=0\.95\\lambda=0\.95, a clip range of 0\.2, an entropy coefficient of 0\.005, a value\-function coefficient of 0\.5, and gradient\-norm clipping at 0\.5\. Observations are normalized by a running mean and variance whose statistics are frozen at evaluation time\. Policies are trained for approximately 3 million environment steps across parallel rollout environments\.

#### 5\.1\.1Observation

The policy observes a 23\-dimensional vector composed of the vehicle state, the wind estimate, the tracking error, and the controller’s own recent output\. Concretely, the observation comprises altitude; the three velocity components; the three body\-frame accelerations; the three Euler angles; the three body rates; the two horizontal components of the estimated mean wind\(w^N,w^E\)\(\\hat\{w\}\_\{N\},\\hat\{w\}\_\{E\}\)from the frozen estimator; the three components of the position tracking error relative to the reference; the base PD thrust normalized by weight; and the four components of the previously applied feedforward correction\. Providing the previous feedforward and the tracking error gives the policy the local context needed to issue a smooth, stabilizing residual\.

The wind estimate enters the observation at a single, well\-defined location, the two channels\(w^N,w^E\)\(\\hat\{w\}\_\{N\},\\hat\{w\}\_\{E\}\)which is what makes the perception ablation below clean: these two channels, and only these, carry information the policy could not otherwise obtain\. The estimator is a frozen instance of the attention\-GRU of Section[4](https://arxiv.org/html/2607.01528#S4), loaded from its trained checkpoint and never updated during policy training; it is queried online at every control step and its output is passed through the deployment EMA filter \(time constantτ=3\\tau=3s, with spike gating that attenuates the filter step when an innovation exceeds three times its running scale\) before entering the observation\. This preserves the two\-stage separation and ensures the controller results reflect the estimator exactly as characterized in Section[4](https://arxiv.org/html/2607.01528#S4)\.

#### 5\.1\.2Action

The action is a four\-dimensional feedforward wrench correction,\(Δ​T,Δ​τx,Δ​τy,Δ​τz\)\(\\Delta T,\\Delta\\tau\_\{x\},\\Delta\\tau\_\{y\},\\Delta\\tau\_\{z\}\)a thrust increment and three body\-torque increments added to the base PD controller’s output at every control update\. The raw policy output on\[−1,1\]4\[\-1,1\]^\{4\}is scaled by a fixed action\-scale vector\(Δ​T,Δ​τx,Δ​τy,Δ​τz\)max=\(10​N,5,5,5​N​m\)\(\\Delta T,\\Delta\\tau\_\{x\},\\Delta\\tau\_\{y\},\\Delta\\tau\_\{z\}\)\_\{\\max\}=\(10~\\mathrm\{N\},5,5,5~\\mathrm\{N\\,m\}\), then passed through a first\-order smoother \(smoothing coefficient 0\.7\) and a slew\-rate limiter before being applied, which prevents the policy from issuing abrupt corrections that would excite the airframe\. Because the correction is additive on top of the PD law, a zero action recovers the baseline controller exactly\.

#### 5\.1\.3Reward

The per\-step reward penalizes tracking error and control effort and gives a small survival bonus:

r=−α​ex​y−β​\|ez\|−γ​∥𝐮ff∥−δ​∥Δ​𝐮ff∥\+ralive,r=\-\\,\\alpha\\,e\_\{xy\}\\;\-\\;\\beta\\,\|e\_\{z\}\|\\;\-\\;\\gamma\\,\\lVert\\mathbf\{u\}\_\{\\mathrm\{ff\}\}\\rVert\\;\-\\;\\delta\\,\\lVert\\Delta\\mathbf\{u\}\_\{\\mathrm\{ff\}\}\\rVert\\;\+\\;r\_\{\\mathrm\{alive\}\},\(2\)whereex​ye\_\{xy\}is the horizontal andeze\_\{z\}the vertical position error,𝐮ff\\mathbf\{u\}\_\{\\mathrm\{ff\}\}is the applied feedforward wrench, andΔ​𝐮ff\\Delta\\mathbf\{u\}\_\{\\mathrm\{ff\}\}its change since the previous step\. The horizontal\-tracking weight isα=1\.0\\alpha=1\.0; the vertical\-tracking weight isβ=1\.0\\beta=1\.0in the horizontal regime but is reduced toβ=0\.5\\beta=0\.5in the vertical regime, where trajectories span hundreds of meters of altitude and an equal weighting would let vertical error dominate the objective\. The effort penalties useγ=0\.01\\gamma=0\.01on feedforward magnitude andδ=0\.02\\delta=0\.02on feedforward slew, with a survival bonusralive=0\.05r\_\{\\mathrm\{alive\}\}=0\.05\. An episode that violates a safety limit \(ground contact, excessive tilt, or non\-finite state\) is terminated with a large penalty \(−100\-100\)\. All reward weights and the action scale are saved with each run and held identical between training and every evaluation mode\.

### 5\.2Training regimes

Each episode samples a fresh wind case and trajectory\. In the horizontal regime the policy trains on the five fixed\-altitude trajectories of Section[3](https://arxiv.org/html/2607.01528#S3)at a fixed flight altitude, with mean winds sampled overU∈\[3,12\]U\\in\[3,12\]m s\-1and turbulence intensity over\[0\.05,0\.25\]\[0\.05,0\.25\]\. In the vertical regime the policy trains on the four altitude\-sweeping trajectories with an arm\-then\-climb episode structure \(the vehicle is pinned at the origin, arms att=1t=1s, and flies the full climb to 600 m\), and each episode samples a mean windUmean∈\[2,10\]U\_\{\\mathrm\{mean\}\}\\in\[2,10\]m s\-1, a direction, turbulence intensity in\[0\.05,0\.25\]\[0\.05,0\.25\], a shear exponentα∈\[0\.08,0\.15\]\\alpha\\in\[0\.08,0\.15\], and a veer of±5∘\\pm 5^\{\\circ\}per 100 m; the sampledUmeanU\_\{\\mathrm\{mean\}\}andα\\alphaare coupled so that the shear\-amplified wind at the top of the climb stays within the estimator’s training envelope \(Section[3](https://arxiv.org/html/2607.01528#S3)\)\. The vertical policy additionally uses a four\-stage difficulty curriculum that introduces trajectories in order of increasing complexity \(vertical\_climbfirst, thenspiral\_ascent,figure8\_3d, andlawnmower\_scan\) as training progresses\.

### 5\.3Baseline and the perception ablation

#### 5\.3\.1Baseline

The classical baseline is the wind\-blind flatness\-based PD controller of Section[3](https://arxiv.org/html/2607.01528#S3), evaluated with zero feedforward correction\. It is representative of the disturbance\-rejection posture of standard sUAS autopilots: it receives no wind information and reacts to wind only through the tracking error the wind induces\. Because the RL action is additive on top of this controller, the baseline is exactly the wind\-aware policy with its action set to zero\.

#### 5\.3\.2Three\-way decomposition

To attribute the wind\-aware controller’s improvement three controllers under identical replayed physics, identical wind fields, turbulence realizations, sensor\-noise streams, trajectories, and seeds are compared via the saved environment configuration: \(i\) the wind\-blind PD baseline; \(ii\) the trained policy run with its wind\-estimate observation channels forced to zero \(*wind\-blind RL*\); and \(iii\) the same trained policy with the wind\-estimate channels active \(*wind\-aware RL*\)\. The improvement of \(ii\) over \(i\) measures what the learned residual policy contributes from vehicle state and tracking error alone, without any wind information, the*kinematic*component\. The further improvement of \(iii\) over \(ii\) measures what the policy gains from the wind\-estimate channels, the*wind\-perception*component\.

A methodological point deserves emphasis\. The wind\-blind RL controller in \(ii\) is not a separately retrained policy; it is the*same*trained network evaluated with its two wind channels zeroed\. The decomposition therefore measures the inference\-time value of the wind signal to the deployed policy, holding the learned weights fixed, rather than the value of training a policy with versus without wind\. This is the appropriate and conservative quantity for characterizing the deployed system: it isolates exactly the information delivered through the estimator, and it cannot benefit from any incidental differences between two separate training runs\. The decomposition characterizes the value of the estimator’s output as actually delivered, not the value of perfect wind knowledge; because no true\-wind oracle is run, no claim of estimator sufficiency is made \(Section[7](https://arxiv.org/html/2607.01528#S7)\)\.

### 5\.4Evaluation protocol

All controllers are evaluated on a fixed factorial sweep of held\-out wind cases generated with a sampling seed disjoint from training\. The horizontal regime comprisesN=225N=225episodes \(five trajectories×\\timesfive mean\-wind levels×\\timesthree turbulence intensities×\\timesthree seeds\) and the vertical regimeN=144N=144episodes \(four trajectories×\\timesfour mean\-wind levels×\\timesthree turbulence intensities×\\timesthree seeds\)\. Every learned\-policy episode is paired with a baseline episode generated under identical replayed wind, sensor\-noise, and seed realizations, so the controllers are compared on matched conditions and observed differences reflect the controllers alone rather than variation in the wind or noise\.

Position\-tracking RMSE is recorded per episode\. Aggregate improvement is reported as the reduction in mean RMSE,1−RMSE¯RL/RMSE¯PD1\-\\overline\{\\mathrm\{RMSE\}\}\_\{\\mathrm\{RL\}\}/\\overline\{\\mathrm\{RMSE\}\}\_\{\\mathrm\{PD\}\}, with a bootstrap 95% confidence interval, and per\-episode quantities are reported as mean±\\pmstandard deviation\. The*win rate*is defined as the fraction of matched episode pairs in which the wind\-aware controller achieves strictly lower RMSE than the baseline\. To probe generalization beyond the training envelope, an out\-of\-distribution \(OOD\) evaluation applies the horizontal policy, unmodified, to mean winds of 13–15 m s\-1, above its\[3,12\]\[3,12\]m s\-1training range\.

## 6Results

### 6\.1Horizontal trajectory tracking

Across the in\-distribution evaluation the wind\-aware RL controller reduces mean horizontal position\-tracking RMSE from1\.32±1\.221\.32\\pm 1\.22m to0\.68±0\.230\.68\\pm 0\.23m, an aggregate reduction of 48\.0% \(bootstrap 95% CI 43\.3–52\.4%\)\. The wind\-aware controller achieves lower error than the baseline in all 225 matched episode pairs, and the accompanying drop in standard deviation, from 1\.22 m to 0\.23 m, shows that the gain in accuracy comes with substantially more consistent tracking \(Table[4](https://arxiv.org/html/2607.01528#S6.T4)\)\. Evaluation spansU∈\{4,6,8,10,12\}U\\in\\\{4,6,8,10,12\\\}m s\-1and turbulence intensities\{0\.05,0\.15,0\.25\}\\\{0\.05,0\.15,0\.25\\\}on wind cases disjoint from training\.

Table 4:Tracking performance and paired statistics for both regimes\. RMSE values are mean±\\pmstandard deviation overNNmatched episode pairs\. Improvement is the reduction in mean RMSE with a bootstrap 95% confidence interval; win rate is the fraction of matched pairs in which the wind\-aware controller achieves lower RMSE\.This dominance is uniform across conditions: Figure[6](https://arxiv.org/html/2607.01528#S6.F6)\(a\) shows all 225 per\-condition points lying below the diagonal, and Figure[6](https://arxiv.org/html/2607.01528#S6.F6)\(b\) shows the relative improvement growing monotonically with wind speed, from roughly 22% atU=4U=4m s\-1to between 56% and 68% atU=12U=12m s\-1depending on turbulence intensity\.

![Refer to caption](https://arxiv.org/html/2607.01528v1/x4.png)Figure 6:Horizontal tracking performance across all 225 evaluation conditions\. \(a\) Per\-condition comparison of wind\-aware RL against the PD baseline under identical replayed physics; every condition lies below the diagonal, so the wind\-aware controller wins in all 225 cases, with the margin widening at the strongest winds \(rightmost points\)\. \(b\) Relative RMSE reduction as a function of mean wind speed for the three turbulence intensities\. The improvement grows monotonically with wind, from≈\\approx22% atU=4U=4m s\-1to 56–68% atU=12U=12m s\-1, and is nearly independent of turbulence intensity at low wind, separating only at high wind where the strongest, most turbulent cases benefit most\.Table[5](https://arxiv.org/html/2607.01528#S6.T5)reports the per\-wind\-level breakdown\. The advantage widens sharply with wind speed: the improvement over the baseline grows from 21\.8% atU=4U=4m s\-1to 62\.4% atU=12U=12m s\-1, because the baseline degrades steeply as the disturbance grows \(its mean RMSE rises from 0\.65 m to 2\.74 m\) while the wind\-aware controller degrades only gradually \(0\.51 m to 1\.03 m\)\. Improvement is consistent across all five trajectories, ranging from 33\.0% on the cloverleaf to 59\.0% on the lawnmower \(Table[6](https://arxiv.org/html/2607.01528#S6.T6)\); the largest gains occur on the trajectories with the longest sustained crosswind legs, where anticipatory compensation has the most room to act\.

The qualitative character of the improvement is shown in Fig\.[7](https://arxiv.org/html/2607.01528#S6.F7): atU=12U=12m s\-1on the lawnmower survey pattern, the PD baseline is blown persistently off\-track on the crosswind legs, while the wind\-aware policy holds the reference by issuing a feedforward correction that anticipates the steady wind\.

Table 5:Horizontal tracking by mean wind speed: mean position RMSE for the PD baseline, wind\-blind RL \(policy with wind channels zeroed\), and wind\-aware RL, with the improvement over baseline and the wind\-perception share of the total improvement\. Each row averages 45 episodes\.Table 6:Horizontal tracking by trajectory: mean PD\-baseline and wind\-aware RMSE and the improvement, aggregated over all wind levels, turbulence intensities, and seeds \(45 episodes each\)\.![Refer to caption](https://arxiv.org/html/2607.01528v1/fig04_trace_lawnmower_U6.png)Figure 7:Example horizontal tracking on the lawnmower survey pattern \(reference windUmean=6U\_\{\\mathrm\{mean\}\}=6m s\-1at 10 m; encountered wind≈\\approx9\.6 m s\-1after power\-law shear amplification at the flight altitude\), evaluated under identical replayed wind and noise\. \(a\) Top\-down view: the wind\-blind PD baseline and the wind\-aware RL controller both follow the reference \(dashed\), with the PD path bowing away on the long crosswind legs\. \(b\) Horizontal tracking error over time: the wind\-aware policy holds a lower error for most of the flight, reducing the mean from 0\.79 m to 0\.60 m and the episode RMSE from 0\.901 m to 0\.685 m \(a 23\.9% reduction\)\.
### 6\.2Decomposition of the improvement

The three\-way ablation attributes the 48\.0% aggregate improvement to two additive components under identical replayed physics\. Zeroing the wind channels of the trained policy \(wind\-blind RL\) recovers a mean RMSE of 0\.985 m, versus 1\.315 m for the PD baseline and 0\.684 m for the full wind\-aware policy\. The step from baseline to wind\-blind RL, a 25\.1% reduction, is the*kinematic*component: what the learned residual policy contributes from vehicle state and tracking error alone\. The further step from wind\-blind to wind\-aware RL, a 30\.5% reduction relative to wind\-blind RL, is the*wind\-perception*component: what the policy gains from the estimated wind\. In terms of shares of the total 0\.631 m improvement, kinematics accounts for 52\.4% and wind perception for 47\.6%, so nearly half of the benefit is attributable specifically to sensing the wind\.

The decomposition’s dependence on wind speed \(Fig\.[8](https://arxiv.org/html/2607.01528#S6.F8)\) is revealing\. The wind\-perception share is smallest at the extremes of the range and largest in the middle, rising from 38\.0% atU=4U=4m s\-1to a peak of 65\.9% atU=8U=8m s\-1before falling back to 37\.8% atU=12U=12m s\-1\. The rise is the expected effect: as wind strengthens, the quadratic growth of aerodynamic drag makes anticipatory compensation from the wind estimate increasingly valuable relative to purely reactive kinematic control\. The fall at the highest wind is also interpretable: atU=12U=12m s\-1the disturbance becomes large enough that even wind\-blind RL must devote most of its residual authority to gross disturbance rejection, and the largest single increment over the baseline comes from that kinematic correction, so the kinematic share grows again\. The wind\-perception contribution is thus substantial across the whole range and dominant in the mid\-range, while never being the sole source of improvement consistent with the additive residual\-control design\.

![Refer to caption](https://arxiv.org/html/2607.01528v1/ablation_v2_decomposition.png)Figure 8:Three\-way decomposition of the horizontal tracking improvement into kinematic and wind\-perception components, under identical replayed physics\. Top left: mean tracking RMSE for the PD baseline, the wind\-blind RL policy \(wind channels forced to zero\), and the wind\-aware RL policy versus mean wind speed; the shaded gap between PD and wind\-blind RL is the kinematic component, and the further gap to wind\-aware RL is the wind\-perception component, both widening sharply with wind\. Top right: the same improvement over PD expressed as stacked percentage contributions per wind level, with the wind\-input share growing from 8% atU=4U=4m s\-1to a mid\-range maximum of 29% atU=10U=10m s\-1\. Bottom left: wind\-perception share of the total RL improvement, which rises from 38% atU=4U=4m s\-1to a mid\-range peak of 66% nearU=8U=8m s\-1before receding to 38% atU=12U=12m s\-1, as gross reactive disturbance rejection \(available to the wind\-blind policy\) accounts for the largest single increment over the baseline at the strongest winds\. Bottom right: per\-trajectory RMSE atU=12U=12m s\-1for the three controllers, showing the ordering PD\>\>wind\-blind RL\>\>wind\-aware RL on every trajectory, most dramatically on the lawnmower pattern\.
### 6\.3Vertical trajectory tracking

In the vertical regime the policy was evaluated on 144 held\-out episodes \(four ascent trajectories×\\timesfour mean\-wind levelsUmean∈\{3,5,7,9\}U\_\{\\mathrm\{mean\}\}\\in\\\{3,5,7,9\\\}m s\-1×\\timesthree turbulence intensities×\\timesthree seeds\), with shear amplifying the wind at altitude\. Because the estimated wind is horizontal, horizontal \(x​yxy\) and vertical \(zz\) tracking error are reported separately\. The wind\-aware policy reduces mean horizontal RMSE from0\.726±0\.1870\.726\\pm 0\.187m to0\.440±0\.0680\.440\\pm 0\.068m \(39\.5% reduction, 95% CI 37\.2–41\.6%\) and mean vertical RMSE from0\.492±0\.2140\.492\\pm 0\.214m to0\.369±0\.2540\.369\\pm 0\.254m \(25\.1% reduction, 95% CI 22\.0–28\.6%\); the combined position RMSE \(RMSEx​y2\+RMSEz2\\sqrt\{\\mathrm\{RMSE\}\_\{xy\}^\{2\}\+\\mathrm\{RMSE\}\_\{z\}^\{2\}\}\) falls by 34\.2%, from0\.899±0\.2040\.899\\pm 0\.204m to0\.592±0\.2180\.592\\pm 0\.218m \(Fig\.[9](https://arxiv.org/html/2607.01528#S6.F9), Table[4](https://arxiv.org/html/2607.01528#S6.T4)\)\. The wind\-aware policy achieves lower horizontal RMSE than the baseline in all 144 matched episode pairs and lower combined RMSE in 143 of 144\. The improvement reflects both the reduced mean error and the markedly lower variance of the wind\-aware controller\. Table[7](https://arxiv.org/html/2607.01528#S6.T7)gives the per\-wind\-level breakdown of the horizontal error: improvement grows with wind from 28\.9% atUmean=3U\_\{\\mathrm\{mean\}\}=3m s\-1to 50\.6% at 9 m s\-1, mirroring the horizontal\-regime trend\.

The decomposition separates cleanly along the two axes and is the central result of this regime\. For horizontal tracking, where the estimated wind is informative, the wind\-perception share of the improvement rises monotonically with wind speed: it is−7\.0\-7\.0% atUmean=3U\_\{\\mathrm\{mean\}\}=3m s\-1, where at low wind the wind channels are very slightly counterproductive, acting as observation noise when the disturbance is negligible, then climbs through 13\.4% and 38\.0% to 48\.3% atUmean=9U\_\{\\mathrm\{mean\}\}=9m s\-1\(Fig\.[10](https://arxiv.org/html/2607.01528#S6.F10)\)\. This is a cleaner monotonic trend than the horizontal regime showed, and it directly supports the central hypothesis: wind perception becomes more valuable precisely as the wind\-induced disturbance grows\. For vertical\-axis tracking, by contrast, the decomposition attributes essentially all of the improvement to the kinematic component \(104\.7%, with a wind\-perception contribution of−4\.7\-4\.7%\): the estimated horizontal wind carries little information relevant to altitude control, so thezz\-axis advantage of the RL policy comes almost entirely from better thrust management, and supplying the wind estimate is marginally counterproductive there\. This double dissociation, in which wind perception helps horizontal tracking and only horizontal tracking, is strong internal evidence that the perception channel acts through the physically correct mechanism rather than as a generic capacity boost\.

Per\-trajectory, combined\-RMSE improvement ranges from 13\.2% onfigure8\_3dto 46\.4% onlawnmower\_scan; the figure\-eight, with the most aggressive simultaneous horizontal and vertical excitation, is the hardest to improve upon, while the scan and climb profiles, dominated by sustained translation through the shear, benefit most\. Figure[11](https://arxiv.org/html/2607.01528#S6.F11)overlays traces on thefigure8\_3dtrajectory atUmean=9U\_\{\\mathrm\{mean\}\}=9m s\-1, where the horizontal perception contribution peaks\.

Table 7:Vertical\-regime horizontal \(x​yxy\) tracking by mean wind speed: mean RMSE for the PD baseline, wind\-blind RL, and wind\-aware RL, with the improvement over baseline and the wind\-perception share of that improvement\. Each row averages 36 episodes\.![Refer to caption](https://arxiv.org/html/2607.01528v1/x5.png)Figure 9:Vertical\-regime tracking comparison between the wind\-blind PD baseline and the wind\-aware RL controller by mean wind speed\. \(a\) Horizontal \(x​yxy\) RMSE: the wind\-aware advantage widens with wind, as the estimated horizontal wind enables anticipatory compensation \(aggregate 0\.726 m versus 0\.440 m, a 39\.5% reduction\)\. \(b\) Vertical \(zz\) RMSE: the wind\-aware policy improves on the baseline by a roughly constant margin independent of horizontal wind speed \(aggregate 0\.492 m versus 0\.369 m, a 25\.1% reduction\), consistent with thezz\-axis benefit arising from kinematic thrust management rather than wind perception\.![Refer to caption](https://arxiv.org/html/2607.01528v1/x6.png)Figure 10:Decomposition of the vertical\-regime horizontal\-tracking improvement: wind\-perception share of the total improvement as a function of mean wind speed\. The share rises monotonically from−7\.0\-7\.0% atUmean=3U\_\{\\mathrm\{mean\}\}=3m s\-1, where the wind channels act as slight observation noise, through 13\.4% and 38\.0% to 48\.3% atUmean=9U\_\{\\mathrm\{mean\}\}=9m s\-1, crossing from counterproductive to beneficial between 3 and 5 m s\-1\.![Refer to caption](https://arxiv.org/html/2607.01528v1/x7.png)Figure 11:Three\-dimensional trajectory traces on thefigure8\_3dprofile \(reference windUmean=9U\_\{\\mathrm\{mean\}\}=9m s\-1; encountered wind≈\\approx12\.7 m s\-1after shear amplification over the climb to 600 m\), under identical replayed physics\. The wind\-aware RL controller \(blue\) tracks the reference \(dashed\) more closely than the wind\-blind PD baseline \(red\); per\-episode horizontal RMSE is 0\.93 m for PD versus 0\.48 m for the wind\-aware policy\.
### 6\.4Out\-of\-distribution winds

Evaluated unmodified atU∈\{13,14,15\}U\\in\\\{13,14,15\\\}m s\-1, beyond its\[3,12\]\[3,12\]m s\-1training range, the horizontal wind\-aware policy improves on the PD baseline by 74\.9% in aggregate \(mean RMSE 1\.30 m versus 5\.19 m\) while retaining a 100% win rate over all 90 out\-of\-distribution episodes\. The improvement grows with wind, from 68\.7% atU=13U=13m s\-1to 78\.5% atU=15U=15m s\-1\(Fig\.[12](https://arxiv.org/html/2607.01528#S6.F12)\)\.

The asymmetry in failure modes is the salient result\. The PD baseline fails catastrophically: its worst\-case episode RMSE reaches 47 m on the lawnmower pattern atU=15U=15m s\-1, as the disturbance exceeds its reactive authority and the vehicle is swept far off track\. The wind\-aware policy, by contrast, remains bounded and controlled, with a worst\-case RMSE of 3\.8 m across all out\-of\-distribution episodes\. The failure is outlier\-driven: the PD mean diverges sharply from its median \(Fig\.[12](https://arxiv.org/html/2607.01528#S6.F12), top left\), reflecting a small number of episodes in which the vehicle is lost entirely, and five of the ninety PD conditions exceed a 15 m offset while every wind\-aware RL condition stays below 4 m \(Fig\.[12](https://arxiv.org/html/2607.01528#S6.F12), bottom left\)\.

The mechanism behind this asymmetry follows from how each controller responds to the steady wind force\. The PD law is purely reactive, with no integral action: it generates a corrective tilt only after a position error has developed, and the steady\-state error it settles to is the displacement at which its bounded restoring force balances the wind disturbance\. Because the aerodynamic disturbance grows with the square of the wind speed while the restoring force is capped by the commanded\-tilt limit, beyond a critical wind the disturbance can no longer be balanced within that limit; the equilibrium error then grows without bound, and on the upwind legs of the lawnmower pattern the vehicle is carried far off track before the trajectory reverses, which is why the lawnmower is the worst\-affected pattern \(Fig\.[12](https://arxiv.org/html/2607.01528#S6.F12), bottom right\)\. The wind\-aware policy instead acts in feedforward: it reads the estimated wind directly from its observation and applies an anticipatory thrust\-and\-torque correction that opposes the disturbance before an error accumulates, rather than waiting for one to develop\. This correction does not depend on a large tracking error to activate, so it does not exhibit the same runaway growth; even when the encountered wind exceeds anything seen in training, the policy continues to oppose it and the error stays bounded\. Estimation accuracy is in fact highest in this strong\-wind regime \(Section[4](https://arxiv.org/html/2607.01528#S4)\), so the feedforward correction remains correctly directed, and the controller degrades gracefully rather than diverging\.

The large headline improvement at these wind levels is therefore driven substantially by baseline collapse rather than by the RL controller performing intrinsically better than it does in distribution; it is best read as evidence of graceful degradation, not of extrapolated mastery\. An important caveat regarding the simulation wind cap in this regime is given in Section[7](https://arxiv.org/html/2607.01528#S7)\.

![Refer to caption](https://arxiv.org/html/2607.01528v1/fig09_ood_probe.png)Figure 12:Out\-of\-distribution evaluation atU∈\{13,14,15\}U\\in\\\{13,14,15\\\}m s\-1, above theU≤12U\\leq 12m s\-1training range \(90 conditions, 100% win rate, 74\.9% aggregate improvement\)\. Top left: PD and wind\-aware RL tracking RMSE versus wind speed, mean and median; the PD mean rises far above its median \(4\.40 versus 2\.18 m at turbulence intensity 0\.1, pooled over the three OOD wind levels\), the signature of outlier episodes in which the vehicle is lost\. Top right: aggregate RMSE reduction continuing to grow with wind through the out\-of\-distribution regime, from 68\.7% atU=13U=13m s\-1to 78\.5% atU=15U=15m s\-1\. Bottom left: per\-condition comparison, with every condition below the diagonal \(wind\-aware RL wins all 90\); five PD conditions exceed a 15 m offset while no RL condition exceeds 4 m\. Bottom right: per\-trajectory mean RMSE, with the lawnmower pattern the worst\-affected for PD \(PD 13\.96 m versus 1\.70 m, an 88% reduction\)\.

## 7Discussion and Limitations

The growth of the perception share with wind speed follows from the disturbance physics\. The aerodynamic disturbance force scales approximately as the square of the relative wind speed, so the cost of reacting to wind, by waiting for a tracking error to develop before correcting, grows quadratically, while the cost of small observation noise from the wind channels is roughly constant\. At low winds the noise term can dominate, as the vertical decomposition shows with a−7\-7% perception contribution atUmean=3U\_\{\\mathrm\{mean\}\}=3m s\-1\. At high winds the anticipatory benefit dominates and the wind channels carry up to half of the total improvement\. The horizontal regime adds a wrinkle at the top of its range: the perception share peaks nearU=8U=8m s\-1and recedes atU=12U=12m s\-1, because once the disturbance is large enough, the gross reactive correction available to wind\-blind RL accounts for the single largest increment over the baseline, so the kinematic share grows again even as the absolute perception benefit keeps rising\. The implication is that learned wind perception is not a uniform upgrade but a capability concentrated in the stronger\-wind conditions that define the operational envelope of small UAS\.

The vertical\-axis result reinforces this picture\. Thezz\-axis improvement is essentially fully kinematic, a useful negative result that localizes the perception benefit to the horizontal plane, where the estimated horizontal wind acts\. The perception channel helps where the perceived quantity is dynamically relevant and nowhere else, which supports the validity of the decomposition methodology\.

Several caveats bound the scope of these results\. The simulation imposes a horizontal wind\-magnitude cap of 20 m s\-1\. At in\-distribution wind levels this cap is rarely active, but at the OOD levels \(U∈\[13,15\]U\\in\[13,15\]m s\-1\) shear and turbulent gusts can drive the instantaneous wind toward the cap, truncating the upper tail of the gust distribution\. The OOD results should therefore be read as established under a clipped gust distribution\. The qualitative finding of bounded RL degradation versus unbounded PD failure is expected to be robust, but the 74\.9% headline figure is specific to the capped environment and is reported with that qualification\.

The decomposition quantifies the value of the estimator’s output as deployed; it does not establish how much additional improvement perfect wind knowledge would yield\. The contribution is framed through the ablation rather than against a true\-wind oracle, because the ablation isolates exactly the information the deployed system delivers without positing a perfect\-knowledge baseline that no real vehicle could access\. The accuracy results bound the gap: in the horizontal regime, with per\-flight estimation residuals of 0\.40 m s\-1against turbulent fluctuations of comparable magnitude, the headroom between the deployed estimator and an oracle is small by construction\. In the vertical regime the larger 1\.56 m s\-1residual leaves more room, so the perception shares reported there are a lower bound on what an ideal horizontal\-wind input could contribute\.

Finally, all results are in simulation\. The sensor models, aerodynamics, and turbulence statistics, while physics\-based, are not flight data, and hardware transfer remains future work\. The vertical evaluation range is constrained by shear amplification: at representative shear exponents, winds encountered near 600 m altitude substantially exceedUmeanU\_\{\\mathrm\{mean\}\}, soUmeanU\_\{\\mathrm\{mean\}\}must be capped to keep the encountered wind within the estimator’s training distribution\. The estimator and policy are also trained on the trajectory families of Section[3](https://arxiv.org/html/2607.01528#S3), so generalization to qualitatively different maneuvers such as aggressive aerobatics is untested\.

## 8Conclusion

This work presented a two\-stage pipeline for wind\-aware flight of a small quadrotor in simulated atmospheric turbulence: a frozen attention\-GRU estimator that recovers the ambient wind vector from onboard kinematics at accuracies near the turbulence\-imposed floor, and a PPO controller that exploits the estimate as a feedforward correction to a classical proportional\-derivative law\. Relative to the wind\-blind baseline, the wind\-aware controller reduces horizontal tracking error by 48% and vertical horizontal\-axis error by 39\.5%, winning every in\-distribution evaluation episode\. A three\-way ablation decomposed these gains into kinematic and wind\-perception components and showed that the perception share increases with wind speed, from negligible or slightly negative in light winds to roughly half the total benefit in strong winds, mirroring the quadratic scaling of aerodynamic disturbance forces\. The same decomposition localized the perception benefit to the horizontal plane, where the estimated wind acts, and found it absent on the vertical axis, internal evidence that the channel operates through the physically correct mechanism rather than as a generic capacity gain\. On out\-of\-distribution winds the learned controller degraded gracefully while the classical baseline diverged, a contrast that follows directly from the difference between anticipatory feedforward and purely reactive control\.

The central finding of this is that learned wind perception is a high\-leverage, sensor\-free addition to small\-UAS autonomy whose value concentrates in the strong\-wind conditions where reliable flight is hardest\. Future work includes extending the vertical evaluation to higher reference winds with reduced shear exponents, treating vertical wind\-component estimation and tracking as a research thread in its own right, and ultimately validating the pipeline in hardware flight\.

## References