Pulsed Doppler I/Q — f_d=200Hz, clutter=20dB

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.

Medians below are from a governed Deep FIELD campaign — not ad-hoc tuning runs.

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 = 10
  • 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, 10, 0, 0, 0, 1, 100]
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=20dB (pulsed-doppler-i-q-f-d-200hz-clutter-20db)

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%
7.5107,861649 ms0.797
2SciPy LSODASciPy
100%
4.940,764403 ms0.736
3SciPy RK23SciPy
100%
4.841,102605 ms0.733
4FBDFexternal
100%
4.755,5226.54 s0.731
5SciPy RadauSciPy
100%
4.788,0582.46 s0.730
6Tsit5external
100%
4.558,0265.97 s0.727
7SciPy DOP853SciPy
100%
4.5115,6821.42 s0.727
8Vern9external
100%
4.5171,8267.94 s0.726
9Vern7external
100%
4.4112,7326.94 s0.724
10SciPy RK45SciPy
100%
4.238,588493 ms0.720
11CVODE Adamsexternal
100%
4.222,618299 ms0.720
12CVODE BDFexternal
100%
4.235,720474 ms0.718
13SciPy BDFSciPy
100%
3.942,1581.85 s0.713
14TRBDF2external
100%
0.77,1405.37 s0.634

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_20db_2026,
  title        = {Resonix Evidence Portal: Pulsed Doppler I/Q — f_d=200Hz, clutter=20dB},
  author       = {{Resonix Labs (Canada) Inc.}},
  year         = {2026},
  howpublished = {\url{https://www.resonix.io/evidence/problems/pulsed-doppler-i-q-f-d-200hz-clutter-20db}},
  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 · Deep FIELD · Innovation velocity

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