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EKF Tracker under Spot Jammer with Frequency Hopping

ADVANTAGES2 · dim 12

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 →

EKF tracker against a spot jammer hopping at 100 Hz. Target state (6) + jammer freq/phase/power (3) + SNR on two channels (2) + detection flag (1). Stiffness from 100 Hz hop rate vs ~0.1 Hz target dynamics.

Electronic warfare

Problem definition

Skolnik Ch. 24 (spot jamming); Poisel, 'EW Target Location Methods' (2012) Ch. 7

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 _sigmoid(x: float | np.ndarray) -> float | np.ndarray:
    return 1.0 / (1.0 + np.exp(-np.clip(x, -500.0, 500.0)))

def rhs(t, y):
    d = np.empty(12)

    # target kinematics — straight line
    d[0] = y[3]
    d[1] = y[4]
    d[2] = y[5]
    d[3] = 0.0
    d[4] = 0.0
    d[5] = 0.0

    J_freq = y[6]
    J_phase = y[7]
    J_power = y[8]
    SNR_ch1 = y[9]
    SNR_ch2 = y[10]

    phase_arg = two_pi_fhop * t

    # frequency dynamics — smoothed hopping
    d[6] = -alpha_f * (J_freq - f_center) + delta_f * np.cos(phase_arg)

    # reduced phase accumulation (O(1) scale)
    d[7] = 2.0 * np.pi * (J_freq - f_center) * inv_f_center

    # jammer power with sigmoid switching
    d[8] = -J_power * inv_tau_p + P_jam * _sigmoid(_K_SIG * np.sin(phase_arg))

    # SNR on channel 1 — degrades when jammer overlaps
    overlap_1 = _sigmoid(-_K_SIG * (J_freq - f_ch1))
    J_power_safe = max(J_power, 1e-10)
    d[9] = (SNR_base / max(1.0 + J_power_safe * overlap_1, 1e-10) - SNR_ch1) * inv_tau_snr

    # SNR on channel 2
    overlap_2 = _sigmoid(-_K_SIG * (J_freq - f_ch2))
    d[10] = (SNR_base / max(1.0 + J_power_safe * overlap_2, 1e-10) - SNR_ch2) * inv_tau_snr

    # detection flag tracks whether SNR_ch1 exceeds threshold
    d[11] = (_sigmoid(_K_SIG * (SNR_ch1 - det_thresh)) - y[11]) * inv_tau_det

    return d
Parameters
  • P_jam = 50
  • SNR_base = 30
  • _K_SIG = 50
  • alpha_f = 50
  • delta_f = 1e+06
  • det_thresh = 10
  • f_center = 9.4e+09
  • f_ch1 = 9.4e+09
  • f_ch2 = 9.401e+09
  • inv_f_center = 1.06383e-10
  • inv_tau_det = 100
  • inv_tau_p = 100
  • inv_tau_snr = 200
  • two_pi_fhop = 628.318530718
Initial condition
y(0) = [5000, 2000, 1000, -200, 0, 0, 9.4e+09, 0, 50, 30, 30, 1]
Horizon
t ∈ [0, 30]

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: 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: EKF Tracker under Spot Jammer with Frequency Hopping (ekf-tracker-under-spot-jammer-with-frequency-hopping)

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%
-1,286,87533.10 s0.809
-SciPy BDFSciPy
0%
----
-SciPy RadauSciPy
0%
----
-SciPy RK45SciPy
0%
----
-SciPy LSODASciPy
0%
----
-SciPy DOP853SciPy
0%
----
-SciPy RK23SciPy
0%
----
-CVODE BDFexternal
0%
----
-CVODE Adamsexternal
0%
----
-Tsit5external
0%
----

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 →

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_ekf_tracker_under_spot_jammer_with_frequency_hopping_2026,
  title        = {Resonix Evidence Portal: EKF Tracker under Spot Jammer with Frequency Hopping},
  author       = {{Resonix Labs (Canada) Inc.}},
  year         = {2026},
  howpublished = {\url{https://resonixusa.com/evidence/problems/ekf-tracker-under-spot-jammer-with-frequency-hopping}},
  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