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 = 100
- 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, 100, 0, 0, 0, 1, 10000]
- 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.
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_40db_2026,
title = {Resonix Evidence Portal: Pulsed Doppler I/Q — f_d=200Hz, clutter=40dB},
author = {{Resonix Labs (Canada) Inc.}},
year = {2026},
howpublished = {\url{https://resonix.tech/evidence/problems/pulsed-doppler-i-q-f-d-200hz-clutter-40db}},
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