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Strapdown INS 13-State (dim=13)

ADVANTAGES2 · dim 13

SolvSRK 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 →

13-state strapdown inertial navigation mechanization. States: quaternion (4), NED velocity (3), NED position (3), gyro bias (3). Stiff from Earth-rate Coriolis coupling and fast/slow gyro dynamics. Maneuvering aircraft profile. Envelope ID 132.

Navigation & INS

Problem definition

Savage (2000) Strapdown Analytics; Titterton & Weston (2004) Strapdown Inertial Navigation

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_strapdown_ins(t, y):
    q = y[0:4]
    v = y[4:7]
    p = y[7:10]
    bg = y[10:13]

    qn = np.sqrt(q[0]**2 + q[1]**2 + q[2]**2 + q[3]**2)
    if qn > 0:
        q = q / qn

    q0, q1, q2, q3 = q

    omega_b = np.array([
        0.02 * np.sin(0.5 * t),
        0.01 * np.cos(0.3 * t),
        0.005 * np.sin(0.1 * t),
    ]) - bg

    omega_ie_n = np.array([
        _OMEGA_E * np.cos(_LAT0),
        0.0,
        -_OMEGA_E * np.sin(_LAT0),
    ])

    C_bn = np.array([
        [1 - 2*(q2**2 + q3**2), 2*(q1*q2 - q0*q3),     2*(q1*q3 + q0*q2)],
        [2*(q1*q2 + q0*q3),     1 - 2*(q1**2 + q3**2),  2*(q2*q3 - q0*q1)],
        [2*(q1*q3 - q0*q2),     2*(q2*q3 + q0*q1),      1 - 2*(q1**2 + q2**2)],
    ])

    omega_nb = omega_b - C_bn.T @ omega_ie_n

    dq = 0.5 * np.array([
        -q1*omega_nb[0] - q2*omega_nb[1] - q3*omega_nb[2],
         q0*omega_nb[0] + q2*omega_nb[2] - q3*omega_nb[1],
         q0*omega_nb[1] + q3*omega_nb[0] - q1*omega_nb[2],
         q0*omega_nb[2] + q1*omega_nb[1] - q2*omega_nb[0],
    ])

    f_b = np.array([
        2.0 * np.sin(0.2 * t),
        1.0 * np.cos(0.15 * t),
        -_G + 0.5 * np.sin(0.1 * t),
    ])

    f_n = C_bn @ f_b

    g_n = np.array([0.0, 0.0, _G])
    omega_en_n = np.array([v[1] / _R_EARTH, -v[0] / _R_EARTH, 0.0])

    dv = f_n + g_n - np.cross(2.0 * omega_ie_n + omega_en_n, v)

    dp = np.array([
        v[0],
        v[1],
        v[2],
    ])

    dbg = -bg / _GYRO_BIAS_TAU

    return np.concatenate([dq, dv, dp, dbg])

Parameters: _G = 9.80665
_GYRO_BIAS_TAU = 3600
_LAT0 = 0.785398163397
_OMEGA_E = 7.29212e-05
_R_EARTH = 6.371e+06
Initial condition: y(0) = [1, 0, 0, 0, 50, 0, …] [shape=(13,), min=-1000, max=50]
Horizon: t ∈ [0, 600]

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: extreme

Default noise: high

Recommendation snapshot

Clean best: SciPy Radau

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: Strapdown INS 13-State (dim=13) (strapdown-ins-13-state-dim-13)

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	SciPy RadauSciPy	100%	10.3	25,188	1.62 s	0.864
2	SolvSRK	100%	8.7	4,411	282 ms	0.826
3	SciPy RK45SciPy	100%	8.4	4,706	223 ms	0.820
4	Tsit5external	100%	7.3	4,698	1.40 s	0.792
5	SciPy DOP853SciPy	100%	7.2	3,818	179 ms	0.790
6	CVODE Adamsexternal	100%	7.2	1,740	84 ms	0.789
7	SciPy LSODASciPy	100%	6.6	3,013	133 ms	0.775
8	CVODE BDFexternal	100%	6.5	3,504	162 ms	0.773
9	SciPy RK23SciPy	100%	6.1	24,773	1.25 s	0.764
10	SciPy BDFSciPy	100%	5.5	7,397	611 ms	0.750

At Clean, best balanced arm is SciPy Radau · SolvSRK survival 100%, SCD 8.7.

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_strapdown_ins_13_state_dim_13_2026,
  title        = {Resonix Evidence Portal: Strapdown INS 13-State (dim=13)},
  author       = {{Resonix Labs (Canada) Inc.}},
  year         = {2026},
  howpublished = {\url{https://resonixusa.com/evidence/problems/strapdown-ins-13-state-dim-13}},
  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.}
}

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