Overview Evidence tour Methodology Dead zones Problems

Swarm Track Fusion N=3 dense straight

ADVANTAGES1 · dim 21

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 →

3-target coordinated-turn tracking with proximity-based dynamic coupling. Per-target state [x,y,z,vx,vy,vz,omega] (dim=21). Dense initial spacing (100.0m). Maneuver: straight. 4 noise channels/target.

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Problem definition

Bar-Shalom, Willett & Tian, 'Tracking and Data Fusion', Ch. 6; Blackman & Popoli, 'Design and Analysis of Modern Tracking Systems'

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: float, y: np.ndarray) -> np.ndarray:
    d = np.zeros(dim)

    # ── Per-target coordinated-turn dynamics ─────────────────
    positions = np.empty((N_targets, 3))
    for i in range(N_targets):
        b = i * _STATES_PER_TARGET
        vx, vy, vz = y[b + 3], y[b + 4], y[b + 5]
        omega = y[b + 6]

        d[b + 0] = vx
        d[b + 1] = vy
        d[b + 2] = vz
        d[b + 3] = -omega * vy
        d[b + 4] = omega * vx
        d[b + 5] = 0.0
        d[b + 6] = 0.0

        positions[i, 0] = y[b + 0]
        positions[i, 1] = y[b + 1]
        positions[i, 2] = y[b + 2]

        # Process noise (interpolated)
        ch = 4 * i
        d[b + 3] += np.interp(t, noise_ts, noise_table[ch + 0])
        d[b + 4] += np.interp(t, noise_ts, noise_table[ch + 1])
        d[b + 5] += np.interp(t, noise_ts, noise_table[ch + 2])
        d[b + 6] += sigma_omega * np.interp(t, noise_ts, noise_table[ch + 3])

    # ── Proximity-based dynamic coupling ──────────────────────
    for i in range(N_targets):
        bi = i * _STATES_PER_TARGET
        for j in range(i + 1, N_targets):
            bj = j * _STATES_PER_TARGET
            dx = positions[j, 0] - positions[i, 0]
            dy = positions[j, 1] - positions[i, 1]
            dz = positions[j, 2] - positions[i, 2]
            dist_sq = dx * dx + dy * dy + dz * dz

            if dist_sq < gate_sq:
                # Soft association weight (Gaussian decay within gate)
                w = coupling_strength * np.exp(-0.5 * dist_sq / (gate_sq * 0.25))
                inv_dist = 1.0 / np.sqrt(dist_sq + _EPS)
                ux, uy, uz = dx * inv_dist, dy * inv_dist, dz * inv_dist

                # Symmetric velocity perturbation (proximity-induced track confusion)
                d[bi + 3] += w * ux
                d[bi + 4] += w * uy
                d[bi + 5] += w * uz
                d[bj + 3] -= w * ux
                d[bj + 4] -= w * uy
                d[bj + 5] -= w * uz

                # Cross-coupling bleeds into turn-rate estimates
                bearing_ij = np.arctan2(dy, dx + _EPS)
                d[bi + 6] += 0.1 * w * np.sin(bearing_ij)
                d[bj + 6] -= 0.1 * w * np.sin(bearing_ij)

    return d

Parameters: N_targets = 3
_EPS = 1e-12
_STATES_PER_TARGET = 7
coupling_strength = 0.5
dim = 21
gate_sq = 22500
noise_table = [-4.65006154928, -0.437583327865, -2.49182189451, -1.46453470941, -1.08851796571, -0.632600312738, …] [shape=(12, 601), min=-7.79884346011, max=6.51439814943]
noise_ts = [0, 0.05, 0.1, 0.15, 0.2, 0.25, …] [shape=(601,), min=0, max=30]
sigma_omega = 0.01
Initial condition: y(0) = [50, 0, 102.514604422, -24.1400960653, -3.10899316614, -0.947549941423, …] [shape=(21,), min=-129.903810568, max=102.514604422]
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: extreme

Default noise: medium

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: Swarm Track Fusion N=3 dense straight (swarm-track-fusion-n-3-dense-straight)

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

#	Solver	Survival	SCD	nfev	Wall	Score
1	SolvSRK	100%	9.6	81,626	1.46 s	0.848
2	SciPy LSODASciPy	100%	7.3	40,218	1.18 s	0.794
3	FBDFexternal	100%	6.6	57,595	7.37 s	0.777
4	SciPy RadauSciPy	100%	6.4	97,284	3.62 s	0.772
5	CVODE BDFexternal	100%	6.3	38,175	1.23 s	0.768
6	SciPy RK23SciPy	100%	6.2	35,066	1.19 s	0.765
7	SciPy BDFSciPy	100%	5.7	36,447	2.18 s	0.755
8	CVODE Adamsexternal	100%	5.6	26,175	814 ms	0.752
9	Vern9external	100%	5.4	196,210	13.95 s	0.748
10	Vern7external	100%	5.2	134,172	10.36 s	0.743
11	SciPy DOP853SciPy	100%	5.1	113,162	3.58 s	0.741
12	SciPy RK45SciPy	100%	5.0	51,728	1.68 s	0.739
13	Tsit5external	100%	4.9	80,754	9.55 s	0.736
14	TRBDF2external	100%	3.8	32,271	6.56 s	0.709

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_swarm_track_fusion_n_3_dense_straight_2026,
  title        = {Resonix Evidence Portal: Swarm Track Fusion N=3 dense straight},
  author       = {{Resonix Labs (Canada) Inc.}},
  year         = {2026},
  howpublished = {\url{https://resonixusa.com/evidence/problems/swarm-track-fusion-n-3-dense-straight}},
  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

Problem definition

Versions & freeze

Results matrix

Cite this page

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