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REVIEW 5 major objections 4 minor 27 references

Learning-based Airflow Inertial Odometry for MAVs using Thermal Anemometers in a GPS and vision denied environment

T0 review · 5 major / 4 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read A drone can estimate its own speed and position from airflow alone, with just 5.7 m drift over 203 s.

desk verdict A useful integrated airflow-inertial odometry system, but the central decoupling claim needs more than one flight and an identifiability argument. read the letter →

arxiv 2505.15044 v1 pith:IVO7YV54 submitted 2025-05-21 cs.RO cs.AIcs.LG

Ze Wang , Jingang Qu , Zhenyu Gao , Pascal Morin This is my paper · ORCID
classification cs.ROcs.AIcs.LG
keywords thermalanemometerairflowinertialodometryquadrotorstateestimationGRUneuralnetworksensorfusionGPS-deniednavigationbarometerbiasdownwashdecoupling
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper claims that a small quadrotor can navigate without GPS, vision, or any external reference by sensing the air it flies through. Thermal anemometers on the drone measure airflow, but the propellers' downwash and the ground's effect on that airflow corrupt the readings. The paper's central claim is that a recurrent neural network can learn to strip away the propeller-induced airflow and recover the drone's true airspeed, and that fusing this airspeed with an IMU, a barometer, and motor commands in a bias-estimating observer yields a full-flight odometry solution. On one 203-second manual random flight that includes takeoff and landing, the reported total position drift is 5.7 meters. If the result holds beyond that single flight, it offers a proprioceptive fallback for drones flying in places where satellite and visual navigation fail.

What carries the argument

The central machinery is a single CNN-GRU neural network architecture reused for three tasks: velocity estimation, acceleration estimation, and flight-status identification. For velocity, the network consumes a time window of raw anemometer measurements and gyroscope rates and outputs body-frame airspeed, supervised by motion-capture ground truth; the governing relation is $V_a^{\{B\}} = R_0 \bar{V}_C^a - \omega \times \delta$, meaning the body-frame airspeed equals the rotated anemometer measurement minus the rotational velocity at the sensor center, with the mounting rotation $R_0$ and lever arm $\delta$ left for the network to learn implicitly. This is what lets the network separate the propeller-induced downwash from the actual flight speed without ever receiving throttle or thrust inputs. Around the network outputs, an observer with bias states for the accelerometer, the velocity estimate, and the barometer fuses IMU, barometric altitude, and the learned acceleration, using the flight-status classifier to switch between a ground model and an in-air model.

What would settle it

During a flight with abrupt throttle changes at roughly constant velocity, compare the velocity estimator's output to motion-capture ground truth; if the airspeed estimate spuriously tracks the throttle commands, the network is fitting downwash rather than decoupling it.

Watch

Extended reading notes

Core claim

The paper's central claim is that airflow-inertial odometry can work with low-cost sensors in a wind-free indoor environment, provided a recurrent network learns to separate the propeller-induced downwash from the true airspeed. The velocity estimator takes raw anemometer readings in the sensor frame together with gyroscope measurements and outputs body-frame airspeed, implicitly learning the sensor mounting geometry and the induced downwash velocity; the reported velocity error stays within roughly 0.5 m/s of motion-capture ground truth across the full flight, including takeoff and landing. The acceleration estimator learns the quadrotor's aerodynamic force model from ESC commands, attitude, battery state, and airspeed, and a flight-status classifier tells the observer whether the drone is on the ground or in the air. The observer fuses these estimates with IMU acceleration and barometric altitude, treating the neural outputs as biased measurements, and estimates the accelerometer bias, the vertical velocity-estimator bias, and the barometer bias. The result is a trajectory whose total position drift is 5.7 meters over 203 seconds of manual random flight.

Load-bearing premise

The GRU velocity estimator must have learned a genuinely physical separation of propeller-induced downwash from true airspeed that generalizes beyond its two training flights, since it is never given throttle or thrust inputs to condition on.

Editorial extensions

If this is right

  • A quadrotor can run a continuous odometry solution from takeoff to landing without GPS or vision, since the flight-status classifier switches the observer between ground and in-air models.
  • The observer's explicit bias estimation for the accelerometer, the vertical velocity estimate, and the barometer removes the main sources of integration drift, cutting vertical position drift substantially.
  • The reported velocity error stays within about 0.5 m/s of ground truth across the validation flight, suggesting the learned downwash decoupling is stable within the training distribution.
  • The approach leaves horizontal drift uncorrected, so the authors position it for teleoperation and low-globality scenarios rather than as a standalone full navigation solution.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • A natural extension would be to expose the trained velocity estimator to a constant outdoor wind; because the network never sees throttle inputs, its ability to separate wind from flight speed is untested, and the claim is currently scoped to wind-free environments only.
  • The single 203-second test flight, with no error bars or repeated trials, is thin evidence for the 5.7 m drift figure; re-running the same protocol several times would reveal whether the reported accuracy is a typical outcome or a favorable one.
  • The acceleration estimator learns an aerodynamic model from ESC commands and battery state, which suggests the same architecture could be adapted to other multirotor platforms without hand-tuning a force model, but this cross-platform generalization is not demonstrated.
  • A stronger test of the downwash-decoupling claim would be an experiment with abrupt throttle changes at constant velocity; if the airspeed estimate tracks the throttle, the network would be fitting downwash rather than separating it.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

5 major / 4 minor

Summary. This paper proposes an airflow-inertial odometry system for small MAVs operating in GPS- and vision-denied, wind-free indoor environments. The system combines four orthogonal thermal anemometers, a 9-axis IMU, a barometer, ESC commands, and battery telemetry. Three GRU-based neural networks estimate body-frame airspeed, inertial-frame acceleration, and on-ground/in-air status, and a bias-augmented observer fuses these signals with IMU and barometer measurements. The headline result is a total position drift of 5.7 m over a 203 s manual random flight, together with the claim that the networks decouple propeller-induced downwash and ground effect from flight speed. Source code is made publicly available.

Significance. If validated, the proposed approach would be a meaningful contribution to proprioceptive MAV odometry for GPS- and vision-denied scenarios, using low-cost onboard sensors. The paper has several strengths: it addresses the full flight envelope including takeoff and landing, models barometer bias with a time-varying estimate, uses a symmetric anemometer configuration, and releases open-source code. The use of a learned acceleration estimator from ESC, battery, attitude, and anemometer inputs is also a useful idea. However, the evidence for the central decoupling claim is indirect and rests on very limited experimental support; the significance is therefore conditional on stronger validation of the identifiability and generalizability of the learned estimators.

major comments (5)
  1. [Section IV-A and Fig. 3a] The velocity estimator receives only raw anemometer readings and angular rate as inputs, yet it is claimed to output body-frame airspeed with the propeller-induced downwash and ground effect removed. In wind-free flight, the vertical anemometer signal is approximately the sum of the vehicle's vertical velocity and the downwash, which depends primarily on rotor speed, attitude, and ground proximity. Since neither ESC command nor altitude nor attitude is provided, two different states (different thrust and different vertical velocity) can produce identical anemometer time series, and the gyroscope alone does not resolve this ambiguity in quasi-steady flight. The paper's assertion in Section VI.D that the network can 'implicitly estimate and decouple the current induced wind speed based on a time-slice of data' needs an identifiability argument or a direct experiment, for example a hover test with varying thrust commands, to show that the estimator separates the two components rather than merely fitting the MoCap-derived targets in the training distribution.
  2. [Section V.C, Eq. (7)] The first line of Eq. (7), \dot{\hat P} = \hat V - k_2(\hat P - h + \hat b_b), mixes a 3D position vector with a scalar barometric altitude and a scalar bias. The barometer observes only the vertical channel, so the equation as written is dimensionally inconsistent and cannot be the actual filter implementation. Please specify the projected vertical formulation, clarify how horizontal position is updated, and state explicitly whether the horizontal position is simply integrated from velocity without corrective terms. This matters because the headline 5.7 m drift figure depends on the exact integration algorithm.
  3. [Section V.C and Table I] With the reported gain \alpha = 0 in Eq. (7), the fused acceleration is \hat A = a_p, so the term g + R a_m - \hat b_a is not used at all. Nevertheless, Section VI.E and Fig. 5c report estimates of the accelerometer bias \hat b_a. This is internally inconsistent: if \alpha = 0, \hat b_a does not appear in the observer dynamics and its estimate cannot influence the state estimate. Please clarify whether the gain value is misreported, or whether Fig. 5c comes from a different setting, and provide the actual gains used for the 203 s flight.
  4. [Section VI.C-E] The experimental evidence for the central claim is thin. Only one 203 s manual random flight underlies the reported 5.7 m drift, and no repeated trials, error bars, or cross-platform tests are provided. Fig. 4 is explicitly labeled as the validation set, but Fig. 5 and Fig. 6 are not labeled as test or validation, so it is unclear whether the data-fusion results are from the held-out test set. Because the neural networks are trained on MoCap ground truth collected in the same arena with the same manual piloting style, the authors should report per-axis RMSE and position drift statistics on the test set, over multiple flights, to support the generalization claims in the Abstract and Section VI.D.
  5. [Abstract and Section VI.D] The abstract claims that the system 'accurately estimate[s] the flight speed', but the only quantitative accuracy metric reported is the position drift of 5.7 m. No test-set speed RMSE, per-axis error, or comparison against the velocity estimator alone is quantified. Please provide explicit numerical speed-estimation errors on the held-out test flight, as well as a breakdown of the reported position drift by horizontal and vertical components, since the observer only corrects the vertical channel with the barometer.
minor comments (4)
  1. [Abstract] The open-source URL is typeset as 'onhttps://github.com/...' without a space; please fix the formatting.
  2. [Section IV.B] The text says 'the trust perpendicular to the rotor plane' where 'thrust' is intended.
  3. [Section VI.E] The captions of Fig. 5 contain 'verse' instead of 'versus', and in Fig. 5d it is unclear which curve corresponds to the velocity bias and which to the altitude bias; please label the curves directly.
  4. [Section VI.B] The description of obtaining ground-truth velocity and acceleration by polynomial fitting and smoothing of the MoCap position should state the polynomial order and window length, since these choices directly affect the training targets of the neural networks.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the learned estimators are supervised regressions with a described train/validation/test split, and self-citations are contextual rather than load-bearing.

full rationale

The paper's derivation chain is not circular. The velocity and acceleration estimators are supervised neural networks trained on MoCap-derived ground truth, which is standard practice for learned odometry; the paper states four manual random flights were split into training, validation, and test sets (Section VI.C). The final odometry is a fusion of these learned outputs with IMU, barometer, and ESC data in an observer (Eq. 7), and no equation reduces to its own input by construction. The claimed ability to 'implicitly estimate and decouple the current induced wind speed' is an empirical claim supported by validation-set plots, not a definitional identity; the absence of an identifiability argument or repeated cross-platform trials is a correctness/robustness concern, not circularity. Self-citations [4], [6], and [7] provide background and motivation (noise homoscedasticity, a Newton equation, and a prior neural approach) but are not used to forbid alternatives or to inject an unverified ansatz. The paper also explicitly acknowledges remaining limitations (horizontal drift due to lack of horizontal landmark observations, no learning-based attitude estimation), which further indicates the claims are empirical rather than self-referential.

Assumptions & free parameters 4 free parameters · 6 assumptions · 0 invented entities

The central claim rests on a learned separation of downwash from flight speed (supported only by supervised training), a hand-tuned observer with several gains, and a single test flight. No new physical entity is introduced.

free parameters (4)
  • Observer gains k0..k6, alpha, beta = k0=0.001, k1=0.9, k2=0.01 (z only), k3=0.01, k4=0.001, k5=0.005 (z only), k6=0.005 (z only), alpha=0, beta=0.4
    Table I lists non-negative gains used in the ground and air observers (Eq.6 and Eq.7). No tuning procedure or sensitivity analysis is given; the values are selected by hand for the reported flight.
  • Trained weights of velocity, acceleration, and flight-status networks = Not reported (trained on two 3-min flights with Adam + cyclic learning rate)
    The GRU/CNN weights are fitted to MoCap-derived ground truth; they are the core of the learned decoupling and are free parameters of the method.
  • MoCap polynomial fitting and sliding-window parameters = Unspecified
    Ground-truth velocity and acceleration are obtained by 'sliding average polynomial interpolation fitting' (Section VI.B); the window length and polynomial order are not reported, and the derived labels depend on them.
  • Neural network time windows and batch size = 1s/0.5s/0.5s windows, batch 512
    Chosen for the three networks; these hyperparameters affect what temporal context the networks can use for downwash decoupling.
assumptions (6)
  • domain assumption The flight environment is wind-free, so V_w = 0 and airspeed equals ground speed.
    Stated in Section I and IV-A; the entire velocity estimation chain relies on this.
  • domain assumption The MAV is a rigid body with constant sensor-to-body rotation R_0 and lever arm delta, which the networks sense implicitly.
    Section III-B and IV-A; no calibration procedure or uncertainty for R_0 and delta is provided.
  • ad hoc to paper The propeller-induced downwash velocity is a deterministic function of the recent anemometer and gyro time series, so a GRU can separate it from flight speed without ESC/thrust inputs.
    Section IV-A and Fig.3a; no physical model or identifiability argument supports this separation.
  • domain assumption Motor response time is small relative to the network input window, so rotor dynamics delays can be ignored in the acceleration estimator.
    Section IV-B.
  • standard math Standard atmosphere pressure-altitude equation (Eq.5) holds indoors.
    Section V-B; barometric altitude from a low-cost barometer is treated as a reliable vertical reference with a slowly varying bias.
  • domain assumption Aerodynamic drag is proportional to |V_a| V_a (quadratic drag model).
    Section IV-B, based on prior work [4]; used as the structure underlying the learned acceleration mapping.

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Cite this review

Pith. "Pith review of Learning-based Airflow Inertial Odometry for MAVs using Thermal Anemometers in a GPS and vision denied environment." pith.science (2026). https://pith.science/paper/IVO7YV54

@misc{pith2026250515044,
  author       = {Pith},
  title        = {Pith review of: Learning-based Airflow Inertial Odometry for MAVs using Thermal Anemometers in a GPS and vision denied environment},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/IVO7YV54}},
  note         = {Machine review of arXiv:2505.15044}
}
read the original abstract

This work demonstrates an airflow inertial based odometry system with multi-sensor data fusion, including thermal anemometer, IMU, ESC, and barometer. This goal is challenging because low-cost IMUs and barometers have significant bias, and anemometer measurements are very susceptible to interference from spinning propellers and ground effects. We employ a GRU-based deep neural network to estimate relative air speed from noisy and disturbed anemometer measurements, and an observer with bias model to fuse the sensor data and thus estimate the state of aerial vehicle. A complete flight data, including takeoff and landing on the ground, shows that the approach is able to decouple the downwash induced wind speed caused by propellers and the ground effect, and accurately estimate the flight speed in a wind-free indoor environment. IMU, and barometer bias are effectively estimated, which significantly reduces the position integration drift, which is only 5.7m for 203s manual random flight. The open source is available on https://github.com/SyRoCo-ISIR/Flight-Speed-Estimation-Airflow.

Figures

Figures reproduced from arXiv: 2505.15044 by the authors.

Figure 1
Figure 1. MAV equipped with four thermal anemometers or [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. System diagram of the proposed approach. The purple [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. Neural network architecture of the proposed approach. [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: Neural network predictions. The sub-figure Fig.5b illustrates the position from integration of neural network only velocity prediction and the position estimated by the observe verse the ground truth in inertial frame. The integration drift of the vertical velocity fro…
Figure 5
Figure 5. Figure 5: Data fusion results [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]
Figure 6
Figure 6. Figure 6: Full flight odometry trajectory (blue) vs. the ground [PITH_FULL_IMAGE:figures/full_fig_p008_6.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

27 extracted references · 24 canonical work pages

  1. [1]

    ”A survey on odometry for autonomous navigation systems.” IEEE Access 7 (2019): 97466-97486

    Mohamed, Sherif AS, et al. ”A survey on odometry for autonomous navigation systems.” IEEE Access 7 (2019): 97466-97486

    work page 2019

  2. [2]

    ”Ronin: Robust neural inertial navigation in the wild: Benchmark, evaluations, & new methods.” 2020 IEEE International Conference on Robotics and Automation (ICRA)

    Herath, Sachini, Hang Yan, and Yasutaka Furukawa. ”Ronin: Robust neural inertial navigation in the wild: Benchmark, evaluations, & new methods.” 2020 IEEE International Conference on Robotics and Automation (ICRA). IEEE, 2020

    work page 2020

  3. [3]

    ”Tlio: Tight learned inertial odometry.” IEEE Robotics and Automation Letters 5.4 (2020): 5653-5660

    Liu, Wenxin, et al. ”Tlio: Tight learned inertial odometry.” IEEE Robotics and Automation Letters 5.4 (2020): 5653-5660

    work page 2020

  4. [4]

    (2020, May)

    Letalenet, A., & Morin, P. (2020, May). Identification and evaluation of a force model for multirotor UA Vs. In 2020 IEEE International Conference on Robotics and Automation (ICRA) (pp. 4280-4286). IEEE

    work page 2020

  5. [5]

    ”Probabilistic ve- locity estimation for autonomous miniature airships using thermal air flow sensors.” 2012 IEEE International Conference on Robotics and Automation

    M ¨uller, J ¨org, Oliver Paul, and Wolfram Burgard. ”Probabilistic ve- locity estimation for autonomous miniature airships using thermal air flow sensors.” 2012 IEEE International Conference on Robotics and Automation. IEEE, 2012. 1https://github.com/amov-lab/Prometheus

    work page 2012

  6. [6]

    Deep learning flight speed estimation using thermal anemometers

    Wang, Z., Qu, J., & Morin, P. Deep learning flight speed estimation using thermal anemometers. In 2022 International Micro Air Vehicle Conference (IMA V)

    work page 2022

  7. [7]

    ”Airflow-based Odometry for MA Vs using Thermal Anemometers.” International Journal of Micro Air Vehicles

    Wang, Z., Qu, J., & Morin, P. ”Airflow-based Odometry for MA Vs using Thermal Anemometers.” International Journal of Micro Air Vehicles

    work page

  8. [8]

    Tagliabue, A., & How, J. P. (2021, May). Airflow-Inertial Odometry for Resilient State Estimation on Multirotors. In 2021 IEEE International Conference on Robotics and Automation (ICRA) (pp. 5736-5743). IEEE

    work page 2021

Show all 27 references
  1. [9]

    & El- Sheimy, N

    Li, Y ., Zahran, S., Zhuang, Y ., Gao, Z., Luo, Y ., He, Z., ... & El- Sheimy, N. (2019). IMU/magnetometer/barometer/mass-flow sensor integrated indoor quadrotor UA V localization with robust velocity updates. Remote Sensing, 11(7), 838

    2019

  2. [10]

    Mur-Artal, R., Montiel, J. M. M., & Tardos, J. D. (2015). ORB-SLAM: a versatile and accurate monocular SLAM system. IEEE transactions on robotics, 31(5), 1147-1163

    2015

  3. [11]

    ”Contact inertial odometry: collisions are your friends.” The International Symposium of Robotics Research

    Lew, Thomas, et al. ”Contact inertial odometry: collisions are your friends.” The International Symposium of Robotics Research. Springer, Cham, 2019

    2019

  4. [13]

    ”FlowDrone: Wind Estimation and Gust Rejection on UA Vs Using Fast-Response Hot-Wire Flow Sensors.” arXiv preprint arXiv:2210.05857 (2022)

    Simon, Nathaniel, et al. ”FlowDrone: Wind Estimation and Gust Rejection on UA Vs Using Fast-Response Hot-Wire Flow Sensors.” arXiv preprint arXiv:2210.05857 (2022)

    2022 arXiv

  5. [14]

    ”Fast-response hot-wire flow sensors for wind and gust estimation on UA Vs.” Measurement Science and Technology (2022)

    Simon, Nathaniel, et al. ”Fast-response hot-wire flow sensors for wind and gust estimation on UA Vs.” Measurement Science and Technology (2022)

    2022

  6. [15]

    E., & Chen, Y

    Hollenbeck, D., Nunez, G., Christensen, L. E., & Chen, Y . (2018, June). Wind measurement and estimation with small unmanned aerial systems (suas) using on-board mini ultrasonic anemometers. In 2018 International Conference on Unmanned Aircraft Systems (ICUAS) (pp. 285-292). IEEE

    2018

  7. [16]

    ”A magnetically transduced whisker for angular displacement and moment sensing.” 2019 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)

    Kim, Suhan, et al. ”A magnetically transduced whisker for angular displacement and moment sensing.” 2019 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS). IEEE, 2019

    2019

  8. [17]

    ”A whisker-inspired fin sensor for multi-directional airflow sensing.” 2020 IEEE/RSJ International Conference on Intelli- gent Robots and Systems (IROS)

    Kim, Suhan, et al. ”A whisker-inspired fin sensor for multi-directional airflow sensing.” 2020 IEEE/RSJ International Conference on Intelli- gent Robots and Systems (IROS). IEEE, 2020

    2020

  9. [18]

    ”Bat wing sensors support flight control.” Proceedings of the National Academy of Sciences 108.27 (2011): 11291-11296

    Sterbing-D’Angelo, Susanne, et al. ”Bat wing sensors support flight control.” Proceedings of the National Academy of Sciences 108.27 (2011): 11291-11296

    2011

  10. [19]

    ”A new velocity meter based on hall effect sensors for UA V indoor navigation.” IEEE Sensors Journal 19.8 (2018): 3067-3076

    Zahran, Shady, et al. ”A new velocity meter based on hall effect sensors for UA V indoor navigation.” IEEE Sensors Journal 19.8 (2018): 3067-3076

    2018

  11. [20]

    Tagliabue, A., Paris, A., Kim, S., Kubicek, R., Bergbreiter, S., & How, J. P. (2020, October). Touch the wind: Simultaneous airflow, drag and interaction sensing on a multirotor. In 2020 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) (pp. 1645- 1652). IEEE

    2020

  12. [21]

    ”Imu-based inertia estimation for a quadrotor using newton-euler dynamics.” IEEE Robotics and Automation Letters 5.3 (2020): 3861-3867

    Svacha, James, et al. ”Imu-based inertia estimation for a quadrotor using newton-euler dynamics.” IEEE Robotics and Automation Letters 5.3 (2020): 3861-3867

    2020

  13. [22]

    ”Neural-Fly enables rapid learning for agile flight in strong winds.” Science Robotics 7.66 (2022): eabm6597

    O’Connell, Michael, et al. ”Neural-Fly enables rapid learning for agile flight in strong winds.” Science Robotics 7.66 (2022): eabm6597

    2022

  14. [23]

    ”Wavenet: A generative model for raw audio.” arXiv preprint arXiv:1609.03499 (2016)

    Oord, Aaron van den, et al. ”Wavenet: A generative model for raw audio.” arXiv preprint arXiv:1609.03499 (2016)

    2016 arXiv

  15. [24]

    Cho, K., Van Merri ¨enboer, B., Gulcehre, C., Bahdanau, D., Bougares, F., Schwenk, H., & Bengio, Y . (2014). Learning phrase representations using RNN encoder-decoder for statistical machine translation. arXiv preprint arXiv:1406.1078

    2014 arXiv

  16. [25]

    Hochreiter, S., & Schmidhuber, J. (1997). Long short-term memory. Neural computation, 9(8), 1735-1780

    1997

  17. [26]

    Nair, V ., & Hinton, G. E. (2010, January). Rectified linear units improve restricted boltzmann machines. In Icml

    2010

  18. [27]

    Bramwell’s helicopter dynamics

    Bramwell, Anthony Robert Southey, David Balmford, and George Done. Bramwell’s helicopter dynamics. Elsevier, 2001

    2001

  19. [28]

    ”Multirotor aerial ve- hicles: Modeling, estimation, and control of quadrotor.” IEEE Robotics and Automation magazine 19.3 (2012): 20-32

    Mahony, Robert, Vijay Kumar, and Peter Corke. ”Multirotor aerial ve- hicles: Modeling, estimation, and control of quadrotor.” IEEE Robotics and Automation magazine 19.3 (2012): 20-32

    2012

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Reviewed August 7, 2026 · model on record in the stance chip above.