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REVIEW 3 major objections 5 minor 25 references

Disturbance Estimation and Rejection for High-Precision Multirotor Position Control

T0 review · 3 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read This paper claims that an EKF disturbance estimate plus a soft-constrained nonlinear MPC cuts maximum horizontal position drift in 10-12 m/s wind gusts by 71-78% versus a PID baseline, with the EKF matching a UKF at 2.5x lower cost.

desk verdict A useful experimental comparison whose headline wind-gust numbers need run-to-run statistics before you trust them. read the letter →

arxiv 1908.03166 v1 pith:4OP2QPJP submitted 2019-08-08 cs.RO

Daniel Hentzen , Thomas Stastny , Roland Siegwart , Roland Brockers This is my paper · ORCID
classification cs.RO
keywords multirotorpositioncontroldisturbanceestimationextendedKalmanfilterunscentedmodelpredictivewindgustrejectiongroundeffect
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 asks whether the extra computational complexity of model predictive control (MPC) over a classical PID controller is worth it for high-precision multirotor position control in strong disturbances. It claims that adding an online disturbance estimate to either controller dramatically improves wind-gust rejection, and that the best combination—a soft-constrained MPC with an Extended Kalman Filter (EKF) disturbance estimate—cuts maximum horizontal position deviation by 71-78% in 10-12 m/s gusts relative to the PID baseline. It further claims that the simpler EKF matches an Unscented Kalman Filter (UKF) in estimate quality while running 2.5 times faster, so the EKF is the practical choice on a computationally constrained small drone. If these results hold, precision tasks such as docking, package delivery, and landing can stay accurate in heavy wind without requiring a large onboard computer.

What carries the argument

The central object is the disturbance-augmented estimation loop. An EKF (and, for comparison, a UKF) appends the external force vector $f_{\mathrm{ext}}$ and external torque vector $\eta_{\mathrm{ext}}$ to the quadrotor state, models their time evolution as a Gaussian random walk, and corrects them with the onboard state estimator's position, velocity, and attitude measurements. The resulting force estimate enters the position controller as a feedforward acceleration term, while the MPC also uses the estimated disturbance inside its prediction model. The control law that carries the best results in the paper is the soft-constrained nonlinear MPC: a receding-horizon optimal control problem with a 2 s horizon, thrust and roll/pitch input constraints, a slack variable $\epsilon$ that relaxes the cross-track error bound, and path-following guidance that steers the vehicle to the closest point on the reference path.

What would settle it

Repeat the 10 and 12 m/s gust landing experiments many times with randomized entry states and a measured wind field, then compare the distributions of maximum horizontal deviation; if the confidence intervals for the soft-constrained MPC with compensation and the PID with compensation overlap, the claimed 71-78% improvement over the PID baseline does not hold.

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Extended reading notes

Core claim

On the paper's own terms, the central discovery is that disturbance rejection, not the controller class, dominates performance once wind gusts become strong. At 3 m/s, PID with disturbance compensation and MPC with disturbance compensation both nearly eliminate the position error and no clear difference appears between them. At 10 and 12 m/s, uncompensated MPC performs about the same as uncompensated PID (19 vs 17 cm and 39 vs 45 cm maximum horizontal deviation), while the EKF feedforward improves both; the soft-constrained MPC with the slack cross-track constraint and disturbance compensation reaches 5 cm and 10 cm, respectively, which is a 71% and 78% reduction from the PID baseline's 17 cm and 45 cm. The paper also reports that the EKF and UKF produce nearly identical disturbance estimates, with the EKF averaging 8 ms per iteration versus 20 ms for the UKF, and that the EKF remains usable outdoors with degraded GPS-based state estimation, though the torque estimate becomes noisier. In the ground-effect experiment, the PID with disturbance compensation stayed within 2.5 cm of the reference, whereas without compensation the vehicle overshot and undershot by 5-10 cm and showed integrator wind-up.

Load-bearing premise

The 71-78% improvement is computed from maximum deviations over repeated landings, but the paper reports no run count, variance, or statistical test and only a qualitative manual tuning rule for both controllers, so if wind or entry conditions differed between runs the ranking could change.

Editorial extensions

If this is right

  • Precision maneuvers such as docking, perching, and precision landing can tolerate 10-12 m/s gusts while holding horizontal deviation around 5-10 cm, instead of the 17-45 cm of an uncompensated PID controller.
  • On small, payload-limited drones, the EKF is a better choice than the UKF: it runs at 100 Hz versus 40 Hz and gives essentially the same force and torque estimates.
  • Even without MPC, a PID controller with a disturbance feedforward term gets most of the benefit in moderate gusts, so the added complexity of MPC pays off mainly in extreme conditions or when a hazard corridor must be respected.
  • The soft-constrained MPC's slack variable gives a practical way to enforce an accuracy bound on cross-track error without risking infeasible optimization problems.

Reading between the lines

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

  • A testable extension the authors do not run is to replace the single-gust protocol with many randomized passes through a measured wind field and report per-run maxima; this would show whether the 71-78% margin is stable under run-to-run variability.
  • Because the torque estimate is not used in control, the paper leaves implicit that feeding estimated disturbance torque into the attitude loop might further reduce the residual position error during gust onset; this is an empirical question the experiments do not answer.
  • The paper's explanation that estimator convergence time limits rejection suggests an adaptive process-noise schedule—raising the random-walk variance right after a detected gust—could shorten the 1.1 s rise time without inducing roll/pitch oscillations.
  • The MPC treats the disturbance as constant over its 2 s horizon; extending the estimator to a time-varying or learned disturbance model inside the horizon could shrink the remaining 5-10 cm residual, though it would add computation the paper is explicitly trying to avoid.
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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

3 major / 5 minor

Summary. The paper presents an experimental comparison of PID and nonlinear MPC position controllers for a small quadrotor, both augmented with an Extended or Unscented Kalman Filter disturbance estimator. The authors model rotor thrust and drag maps with a voltage dependence, formulate an EKF and a UKF for external force and torque estimation, and integrate the resulting disturbance estimate as feedforward compensation in both PID and MPC architectures. They evaluate the system in three ways: ground-effect rejection during horizontal flights over a table edge, wind-gust rejection during vertical landings under 3, 10, and 12 m/s fan-generated wind, and computational cost on an Odroid XU4 companion computer. The main reported results are that the EKF achieves nearly the same estimation quality as the UKF at about 2.5x lower computational cost, and that a soft-constrained MPC with disturbance compensation reduces maximum horizontal deviation during strong wind gusts by 71-78% relative to an uncompensated PID baseline. The paper also includes an outdoor GPS-based validation of the EKF disturbance estimator and reports timing measurements for all controllers.

Significance. If the reported numbers are statistically sound, the paper provides useful experimental evidence on a question that is often addressed only in simulation: whether the added complexity of MPC and of UKF over EKF pays off on a computationally constrained multirotor. The strengths of the paper include the repeated ground-effect experiments with mean and 2-sigma bounds, the computational benchmarking on real hardware, the extension of disturbance estimation to GPS-grade state estimation outdoors, and the inclusion of a conventional PID baseline rather than only an MPC-versus-MPC comparison. The EKF/UKF comparison is empirical rather than derivation-based, and I see no circularity in the claims. The main weakness is that the central wind-gust result is reported as point maxima from an unspecified number of runs, with no variance or inferential statistics, which currently leaves the headline improvement unsupported.

major comments (3)
  1. [Section V-F, Table I] The central quantitative claim, a 71-78% reduction in maximum horizontal deviation, is reported as a point maximum for each controller, with no run counts, per-run values, variance, or statistical test. Section V-F-a only says 'repeated vertical landings,' and the experiment is described as involving 'turbulent wind,' so the maximum deviation is a high-variance statistic. The ground-effect experiment in Section V-E-b reports mean and 2-sigma bounds, demonstrating that such statistics are computable on this platform; their absence in the wind-gust experiment is conspicuous. Please report the number of runs per condition, per-run deviations, mean plus/minus standard deviation (or median and range), and state whether the order of controllers was randomized or the wind conditions were otherwise matched across runs.
  2. [Section V-F-a] The claim that 'both the MPC and PID controllers were tuned to achieve an overdamped position step response with minimum rise time' is too underspecified to establish that the two controllers are at comparable tuning levels, which is important because the headline improvement is relative to a PID baseline. The tuning procedure should be described precisely: what step input was used, what rise time and overshoot were measured, how the gains were chosen, and whether the disturbance-estimator noise variance (identified as a tuning parameter in Section III-A-d) was set identically for all compensated controllers. Without this information, the comparison cannot be independently reproduced or assessed for fairness.
  3. [Section V-F-b and Table I] The metric underlying Table I is not unambiguously defined. The text says the controllers are compared by 'maximum deviations from the position reference,' Figures 12-14 show position error in the Z-X plane, and Table I reports 'Max. horizontal deviation.' Please define the metric precisely, including the coordinate frame, whether the maximum is over the two-dimensional horizontal error or the in-plane error shown in the figures, and whether it is taken over the full maneuver or only over the wind-affected segment. In addition, the wind speed is reported only as a single anemometer measurement in the center of the stream; because the deviation likely depends on the vehicle's distance from the fan and on turbulence, the paper should state the sensor placement relative to the flight path and, ideally, provide a wind profile or repeated wind-speed measurements.
minor comments (5)
  1. [Section I-B] There is a typo in 'whethe the choice of MPC' that should be corrected.
  2. [Section III] The word 'preferrable' should be 'preferable.'
  3. [Section V-B] The word 'repeatibility' should be 'repeatability.'
  4. [Section V-F-b] The statement that without disturbance compensation 'both the PID and the MPC controllers experience an identical deviation' is made without supporting repeated-run data; adding the per-controller traces or statistics would make this claim verifiable.
  5. [Figures 12-14] The figures would be clearer if the wind-affected region and the maximum deviation used in Table I were marked explicitly on the position-error plots.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the paper's central claims are empirical comparisons whose outcomes are not encoded in the models or estimators.

full rationale

This paper is an experimental comparison, not a derivation chain, so there is no equation-level reduction of a predicted quantity to a fitted input. The EKF and UKF disturbance estimators use standard filtering equations, the vehicle dynamics of Section II-A, and the identified thrust/drag maps of Section II-B; their outputs are compared against measured position errors, not reused as inputs to the same comparison. The headline 71-78% wind-gust improvement and the EKF/UKF equivalence are reported from flight tests (Section V-F, Figures 12-14, Table I), not derived from the controller definitions. Self-citations appear: [4] is used to justify the choice of nonlinear MPC and the first-order attitude simplification, [14] for the UKF multiplicative quaternion approach, and [1],[6] for application motivation and robust-control background. These citations support implementation choices and prior art, but the paper's load-bearing claims—MPC with disturbance compensation outperforms PID, and EKF matches UKF at lower cost—are tested experimentally on the same platform and are not forced by those citations. The absence of repeated-run statistics and fully specified tuning is a legitimate statistical-support concern, but it is not circularity: the maximum-deviation measurements are not equivalent by construction to the controller parameters or estimator covariances. Hence no circular step can be exhibited from the paper's own equations or citations.

Assumptions & free parameters 4 free parameters · 7 assumptions · 0 invented entities

The paper introduces no new physical entities. Its assumptions are standard control/estimation modeling choices (random-walk disturbance, constant disturbance over the horizon, first-order attitude dynamics, calibrated thrust map). The free parameters are tuning knobs for filters and MPC, which are not fully disclosed.

free parameters (4)
  • Process noise variance v for disturbance random walk (EKF/UKF)
    Section III-A(d): 'The process noise value v is a tuning parameter that allows to control the convergence speed of the estimate, at the cost of a noisier output signal.' Chosen by hand; directly affects rejection performance.
  • MPC weight matrices Q, R, and terminal cost P_N
    Section IV-D: state/input costs in the optimal control problem (4); tuned manually and not reported numerically.
  • Soft-constraint slack bound e_max = 5 cm
    Section V-F: 'Activating a slack constraint of 5 cm on the cross-error'; this bound partly determines the reported max deviations.
  • Voltage-dependent thrust and drag map coefficients
    Section II-B: quadratic ESC-to-thrust map from [15] extended with linear battery voltage dependency; identified from bench data and used as an input to both estimator and controller.
assumptions (7)
  • standard math Newton-Euler rigid body dynamics and quaternion kinematics
    Used in Section II-A as the basis for filter prediction and the MPC model.
  • standard math Kalman filter and unscented transform equations
    Standard EKF/UKF update equations from [17], [19] used in Section III.
  • domain assumption External disturbance force and torque obey a Gaussian random walk
    Section III-A(d): f_ext,k = f_ext,k-1 + v_f; this model makes the disturbance estimable, and its covariance controls the convergence versus noise trade-off.
  • domain assumption Disturbance force is constant over the 2 s MPC horizon
    Section IV-D(a): 'We assume a constant disturbance force over the MPC prediction horizon.' This is violated by fast gusts and limits rejection, as acknowledged in Section V-F.
  • domain assumption Attitude dynamics can be modeled as a first-order system
    Section IV-D(a): 'As in [4], we identify the attitude dynamics as a first-order system,' decoupling the MPC from the attitude controller.
  • domain assumption All unmodeled dynamics, including aerodynamic drag, are lumped into the disturbance force
    Section IV-D(a): the MPC model includes external disturbance force and lumps all unmodeled dynamics into it.
  • domain assumption The ESC-to-thrust/drag map remains valid during flight
    Section II-B identifies a voltage-dependent quadratic thrust map used by both estimator and controller; if it drifts, the disturbance estimate absorbs the error and the comparison shifts.

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Cite this review

Pith. "Pith review of Disturbance Estimation and Rejection for High-Precision Multirotor Position Control." pith.science (2026). https://pith.science/paper/4OP2QPJP

@misc{pith2026190803166,
  author       = {Pith},
  title        = {Pith review of: Disturbance Estimation and Rejection for High-Precision Multirotor Position Control},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/4OP2QPJP}},
  note         = {Machine review of arXiv:1908.03166}
}
read the original abstract

Many multirotor Unmanned Aerial Systems applications have a critical need for precise position control in environments with strong dynamic external disturbances such as wind gusts or ground and wall effects. Moreover, to maximize flight time, small multirotor platforms have to operate within strict constraints on payload and thus computational performance. In this paper, we present the design and experimental comparison of Model Predictive and PID multirotor position controllers augmented with a disturbance estimator to reject strong wind gusts up to 12 m/s and ground effect. For disturbance estimation, we compare Extended and Unscented Kalman filtering. In extensive in- and outdoor flight tests, we evaluate the suitability of the developed control and estimation algorithms to run on a computationally constrained platform. This allows to draw a conclusion on whether potential performance improvements justify the increased computational complexity of MPC for multirotor position control and UKF for disturbance estimation.

Figures

Figures reproduced from arXiv: 1908.03166 by the authors.

Figure 1
Figure 1. Example of the effect of a strong wind gust on a quadrotor. [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Quadrotor free-body diagram and coordinate systems. [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 4
Figure 4. Recursive filtering architecture for disturbance estimation. [PITH_FULL_IMAGE:figures/full_fig_p003_4.png] view at source ↗
Figures from the paper (7 more)
Figure 5
Figure 5. Figure 5: Guidance and control system architecture. Shaded modules are [PITH_FULL_IMAGE:figures/full_fig_p004_5.png]
Figure 7
Figure 7. Figure 7: EKF/UKF comparison of the estimated disturbance force in z￾axis and estimated roll torque distur￾bance [PITH_FULL_IMAGE:figures/full_fig_p005_7.png]
Figure 8
Figure 8. Figure 8: Step response of the EKF force and torque disturbance estimator [PITH_FULL_IMAGE:figures/full_fig_p005_8.png]
Figure 10
Figure 10. Figure 10: Ground effect experiment setup. Reference flight path in green. [PITH_FULL_IMAGE:figures/full_fig_p006_10.png]
Figure 11
Figure 11. Figure 11: Top: Mean and 2σ bounds of the estimated force disturbance along the z-axis during repeated flights over a table surface (see [PITH_FULL_IMAGE:figures/full_fig_p006_11.png]
Figure 13
Figure 13. Figure 13: 10 m/s wind gust experiment. Left: Disturbance force estimate in Z-X plane during runs with disturbance rejection. Right: Comparison of position error in Z-X plane during landing through strong wind gust for PID and MPC controllers, with and without disturbance reject…
Figure 14
Figure 14. Figure 14: 12 m/s wind gust experiment. Left: Disturbance force estimate in Z-X plane during runs with disturbance rejection. Right: Comparison of position error in Z-X plane during landing through strong wind gust for PID and MPC controllers, with and without disturbance reject…

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Reviewed August 14, 2026 · model on record in the stance chip above.