Pulsed Doppler I/Q — f_d=500Hz, clutter=50dB

DISADVANTAGES1 · dim 8

A baseline wins. At the comparison noise level, the best baseline beats SolvSRK by at least 10 percentage points of survival, or by at least 0.05 balanced score when survival is tied. Use the winning baseline named on the problem page — not SolvSRK. 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 = 500
  • 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 = 316.227766017
  • 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, 316.227766017, 0, 0, 0, 1, 100000]
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: medium

Recommendation snapshot

Clean best: SolvSRK

Noisy best: SciPy Radau

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=500Hz, clutter=50dB (pulsed-doppler-i-q-f-d-500hz-clutter-50db)

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%
9.1124,829760 ms0.835
2FBDFexternal
100%
7.283,5987.06 s0.789
3SciPy LSODASciPy
100%
7.049,159500 ms0.787
4SciPy RK23SciPy
100%
6.978,242878 ms0.784
5SciPy BDFSciPy
100%
6.457,3492.51 s0.771
6CVODE Adamsexternal
100%
6.129,166386 ms0.765
7Vern9external
100%
5.9220,3709.19 s0.759
8SciPy RadauSciPy
100%
5.8105,3413.02 s0.757
9CVODE BDFexternal
100%
5.747,596628 ms0.756
10Vern7external
100%
5.5123,9027.36 s0.751
11Tsit5external
100%
5.269,0487.68 s0.742
12SciPy RK45SciPy
100%
4.746,160608 ms0.730
13SciPy DOP853SciPy
100%
4.5136,6341.50 s0.727
14TRBDF2external
100%
2.612,9535.85 s0.680

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_500hz_clutter_50db_2026,
  title        = {Resonix Evidence Portal: Pulsed Doppler I/Q — f_d=500Hz, clutter=50dB},
  author       = {{Resonix Labs (Canada) Inc.}},
  year         = {2026},
  howpublished = {\url{https://resonix.tech/evidence/problems/pulsed-doppler-i-q-f-d-500hz-clutter-50db}},
  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