Pulsed Doppler I/Q — f_d=200Hz, clutter=30dB

PARITYS1 · dim 8

No clear winner. The survival gap is under 10 percentage points and the balanced-score gap is under 0.05, so neither SolvSRK nor the best baseline clears the win threshold. Either works — choose on cost, licensing, or integration effort. All verdicts →

Wave 1 anti-UAV kill chain. Board approved 2026-05-07.

Radar signal processing

Problem definition

Skolnik (2008), Richards (2010)

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(t, y):
    I_t, Q_t = y[0], y[1]
    I_c, Q_c = y[2], y[3]
    I_n, Q_n = y[4], y[5]
    P_t, P_c = y[6], y[7]

    xi_c_I = np.interp(t, _noise_ts, noise_table[0])
    xi_c_Q = np.interp(t, _noise_ts, noise_table[1])
    xi_n_I = np.interp(t, _noise_ts, noise_table[2])
    xi_n_Q = np.interp(t, _noise_ts, noise_table[3])

    d = np.empty(8)

    # Target echo: damped sinusoid at Doppler frequency
    d[0] = -TWO_PI * f_d * Q_t - (1.0 / tau_t) * I_t
    d[1] = +TWO_PI * f_d * I_t - (1.0 / tau_t) * Q_t

    # Clutter: near-zero Doppler with exponential decorrelation + noise
    d[2] = -TWO_PI * f_c * Q_c - (1.0 / tau_c) * I_c + sigma_c * xi_c_I
    d[3] = +TWO_PI * f_c * I_c - (1.0 / tau_c) * Q_c + sigma_c * xi_c_Q

    # Thermal noise: independent I/Q (BA-RCT-2)
    d[4] = -(1.0 / tau_n) * I_n + sigma_n * xi_n_I
    d[5] = -(1.0 / tau_n) * Q_n + sigma_n * xi_n_Q

    # Power estimates (smoothed envelope)
    d[6] = (1.0 / tau_avg) * (I_t**2 + Q_t**2 - P_t)
    d[7] = (1.0 / tau_avg) * (I_c**2 + Q_c**2 - P_c)

    return d
Parameters
  • TWO_PI = 6.28318530718
  • _noise_ts = [0, 0.0001, 0.0002, 0.0003, 0.0004, 0.0005, …] [shape=(1001,), min=0, max=0.1]
  • f_c = 5
  • f_d = 200
  • noise_table = [0.125730221093, -0.132104863291, 0.640422650443, 0.104900117153, -0.535669373161, 0.361595054909, …] [shape=(4, 1001), min=-3.89942173005, max=3.25719907472]
  • sigma_c = 31.6227766017
  • sigma_n = 1
  • tau_avg = 0.01
  • tau_c = 0.02
  • tau_n = 0.001
  • tau_t = 0.05
Initial condition
y(0) = [1, 0, 31.6227766017, 0, 0, 0, 1, 1000]
Horizon
t ∈ [0, 0.1]

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: low

Recommendation snapshot

Clean best: SolvSRK

Noisy best: SciPy BDF

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: Pulsed Doppler I/Q — f_d=200Hz, clutter=30dB (pulsed-doppler-i-q-f-d-200hz-clutter-30db)

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

#SolverSurvivalSCDnfevWallScore
1SolvSRK
100%
8.1111,648676 ms0.811
2SciPy RadauSciPy
100%
6.296,3622.71 s0.767
3FBDFexternal
100%
6.158,4476.95 s0.764
4SciPy LSODASciPy
100%
5.644,089433 ms0.753
5SciPy RK23SciPy
100%
5.444,099667 ms0.747
6Vern7external
100%
5.3126,9327.34 s0.744
7Tsit5external
100%
5.168,3047.59 s0.741
8Vern9external
100%
4.8195,5548.99 s0.733
9CVODE Adamsexternal
100%
4.824,487330 ms0.732
10CVODE BDFexternal
100%
4.839,345517 ms0.732
11SciPy RK45SciPy
100%
4.645,038586 ms0.729
12SciPy DOP853SciPy
100%
4.6126,3261.55 s0.729
13SciPy BDFSciPy
100%
4.544,4651.88 s0.726
14TRBDF2external
100%
1.48,6065.63 s0.651

At Clean, best balanced arm is SolvSRK.

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 →

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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_pulsed_doppler_i_q_f_d_200hz_clutter_30db_2026,
  title        = {Resonix Evidence Portal: Pulsed Doppler I/Q — f_d=200Hz, clutter=30dB},
  author       = {{Resonix Labs (Canada) Inc.}},
  year         = {2026},
  howpublished = {\url{https://resonix.tech/evidence/problems/pulsed-doppler-i-q-f-d-200hz-clutter-30db}},
  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