EKF Quadrotor Prediction Step (dim=12)
ADVANTAGES1 · dim 12SolvSRK wins. At the comparison noise level, SolvSRK beats the best baseline by at least 10 percentage points of survival, or by at least 0.05 balanced score when survival is tied. Use SolvSRK for this class of problem. All verdicts →
EKF prediction step on 12-state rigid body quadrotor. State = [x, y, z, vx, vy, vz, phi, theta, psi, p, q, r]. Open-loop dynamics at hover thrust with linear drag. Parameters: m=1.5 kg, Ix=Iy=0.029 kg·m², Iz=0.055 kg·m², drag_coeff=0.1. Near-hover initial condition with slight forward velocity and pitch perturbation.
Problem definition
Beard & McLain, 'Small Unmanned Aircraft' (2012) Ch. 3-4; Bar-Shalom et al. (2001) Ch. 5 (EKF prediction)
Canonical RHS excerpt from the registered callable used for this benchmark cell. Expand it to verify the state equations; it is not a standalone runnable fixture.
Show canonical RHS excerpt
def rhs_ekf_drone_predict(t: float, y: np.ndarray) -> np.ndarray:
vx, vy, vz = y[3], y[4], y[5]
phi, theta, psi = y[6], y[7], y[8]
p, q, r = y[9], y[10], y[11]
cp, sp = np.cos(phi), np.sin(phi)
ct, st = np.cos(theta), np.sin(theta)
cy, sy = np.cos(psi), np.sin(psi)
a_thrust = _T_HOVER / _M
fx = a_thrust * (cp * st * cy + sp * sy) - _DRAG * vx
fy = a_thrust * (cp * st * sy - sp * cy) - _DRAG * vy
fz = a_thrust * cp * ct - _G - _DRAG * vz
th_c = np.clip(theta, -_THETA_CLIP, _THETA_CLIP)
tan_th = np.tan(th_c)
ct_c = np.cos(th_c)
sec_th = 1.0 / ct_c if abs(ct_c) > 1e-12 else 1e12 * np.sign(ct_c)
d = np.empty(12)
d[0] = vx
d[1] = vy
d[2] = vz
d[3] = fx
d[4] = fy
d[5] = fz
d[6] = p + q * sp * tan_th + r * cp * tan_th
d[7] = q * cp - r * sp
d[8] = (q * sp + r * cp) * sec_th
d[9] = (_IY - _IZ) / _IX * q * r
d[10] = (_IZ - _IX) / _IY * p * r
d[11] = (_IX - _IY) / _IZ * p * q
return d- Parameters
- _DRAG = 0.1
- _G = 9.81
- _IX = 0.029
- _IY = 0.029
- _IZ = 0.055
- _M = 1.5
- _THETA_CLIP = 1.48
- _T_HOVER = 14.715
- Initial condition
- y(0) = [0, 0, 10, 1, 0, 0, 0, 0.05, 0, 0, 0, 0]
- Horizon
- t ∈ [0, 30]
Canonical RHS excerpt captured from the same registered callable used for the published benchmark. Frozen closure values are summarized below; helper imports and solver settings are intentionally omitted.
Fingerprint
Spread: low
Default noise: medium
Recommendation snapshot
Clean best: Vern9
Noisy best: SolvSRK
Coverage
14 solver arms · clean + 5 noise levels
Ranked on survival, precision, and speed
Versions & freeze
Methodology →- Freeze
- 2026-08-13
- libsolvsrk
- 2.3.0
- SciPy
- 1.14
- SUNDIALS
- CVODE (bundled backend)
20 seeds/cell default · 14 arms · TRL 4–5 · simulation-lab validated · this page: EKF Quadrotor Prediction Step (dim=12) (ekf-quadrotor-prediction-step-dim-12)
Governed SolvTune benchmark freeze; per-arm medians only. RHS definitions and raw trial rows are not published.
Self-reported by Resonix Labs · not independently verified
Results matrix
Pick an objective and a noise level to rank all arms on survival, median SCD, median nfev, and median wall time. Medians across seeds.
Objective
Best overall trade-off of survival, precision, and speed.
Noise level
| # | Solver | Survival | SCD | nfev | Wall | Score |
|---|---|---|---|---|---|---|
| 1 | Vern9external | 100% | 12.8 | 162 | 3.63 s | 0.924 |
| 2 | Vern7external | 100% | 11.4 | 162 | 3.62 s | 0.891 |
| 3 | SolvSRK | 100% | 11.2 | 359 | 23 ms | 0.885 |
| 4 | SciPy RadauSciPy | 100% | 11.1 | 514 | 13 ms | 0.883 |
| 5 | SciPy DOP853SciPy | 100% | 9.9 | 86 | 1 ms | 0.856 |
| 6 | CVODE Adamsexternal | 100% | 9.3 | 76 | 7 ms | 0.841 |
| 7 | Tsit5external | 100% | 9.0 | 138 | 690 ms | 0.834 |
| 8 | SciPy LSODASciPy | 100% | 8.9 | 95 | 1 ms | 0.831 |
| 9 | FBDFexternal | 100% | 8.7 | 193 | 4.71 s | 0.827 |
| 10 | SciPy RK45SciPy | 100% | 8.7 | 158 | 2 ms | 0.825 |
| 11 | SciPy RK23SciPy | 100% | 7.8 | 749 | 10 ms | 0.804 |
| 12 | CVODE BDFexternal | 100% | 7.7 | 125 | 8 ms | 0.803 |
| 13 | SciPy BDFSciPy | 100% | 7.6 | 162 | 7 ms | 0.799 |
| 14 | TRBDF2external | 100% | 5.8 | 743 | 4.70 s | 0.756 |
At Clean, best balanced arm is Vern9 · SolvSRK survival 100%, SCD 11.2.
Values are medians across seeds, measured by Resonix Labs on Resonix hardware and not independently verified; nfev and wall are on reference lab hardware (indicative). Under injected noise only SolvSRK and the SciPy arms are run. How we measure accuracy → · Verification status →
Cite this page
Replace the access date. Pin the freeze ID and library versions when comparing against a later export. Cite it as what it is - a self-reported vendor benchmark, not an independently verified result. The note field says so; please keep it.
@misc{resonix_evidence_ekf_quadrotor_prediction_step_dim_12_2026,
title = {Resonix Evidence Portal: EKF Quadrotor Prediction Step (dim=12)},
author = {{Resonix Labs (Canada) Inc.}},
year = {2026},
howpublished = {\url{https://resonixusa.com/evidence/problems/ekf-quadrotor-prediction-step-dim-12}},
note = {Self-reported vendor benchmark; internally generated by Resonix Labs and not independently verified. Accessed YYYY-MM-DD. Freeze 2026-08-13; libsolvsrk 2.3.0; SciPy 1.14.}
}Related
TRL 4–5 · simulation-lab validated · 398 problems · 14 solver arms · clean + 5 noise levels
Freeze: 2026-08-13 · scipy 1.14 · libsolvsrk 2.3.0 · Methodology
Self-reported by Resonix Labs · not independently verified · Verification status