Overview Evidence tour Methodology Dead zones Problems

Augmented PN with Time-to-Go Estimation

ADVANTAGES1 · dim 8

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 →

APN with ZEM/t_go^2 command — diverges as t_go->0, capped at t_go_min=0.1s. Adaptive gain N_eff adjusts to estimated maneuver.

Guidance & interception

Problem definition

Zarchan Ch. 8 (augmented PN); Yanushevsky Ch. 4 (optimal guidance)

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 _clamp(x: float, lo: float, hi: float) -> float:
    return max(lo, min(hi, x))

def rhs(t, y):
    rx, ry, rz = y[0], y[1], y[2]
    vx_i, vy_i, vz_i = y[3], y[4], y[5]
    t_go = y[6]
    N_eff = y[7]

    d = np.empty(8)

    R = np.sqrt(rx * rx + ry * ry + rz * rz)
    if R < _RANGE_GUARD:
        d[:] = 0.0
        return d

    vx_rel = vx_i - vtx
    vy_rel = vy_i - vty
    vz_rel = vz_i - vtz

    R_dot = (rx * vx_rel + ry * vy_rel + rz * vz_rel) / R
    V_c = -R_dot

    t_go_safe = max(t_go, t_go_min)
    t_go_sq = t_go_safe * t_go_safe

    zem_x = rx + vx_rel * t_go_safe
    zem_y = ry + vy_rel * t_go_safe
    zem_z = rz + vz_rel * t_go_safe

    a_x = N_eff * zem_x / t_go_sq
    a_y = N_eff * zem_y / t_go_sq
    a_z = N_eff * zem_z / t_go_sq

    a_mag = np.sqrt(a_x * a_x + a_y * a_y + a_z * a_z)
    if a_mag > a_max:
        scale = a_max / a_mag
        a_x *= scale
        a_y *= scale
        a_z *= scale

    wx = np.interp(t, _noise_ts, wind_noise[0])
    wy = np.interp(t, _noise_ts, wind_noise[1])
    wz = np.interp(t, _noise_ts, wind_noise[2])

    d[0] = vx_rel
    d[1] = vy_rel
    d[2] = vz_rel
    d[3] = a_x + wx
    d[4] = a_y + wy
    d[5] = a_z + wz

    d[6] = -V_c / max(R, _RANGE_GUARD)

    zem_mag = np.sqrt(zem_x**2 + zem_y**2 + zem_z**2)
    maneuver_ratio = zem_mag / (a_tgt_est * t_go_sq + 1.0)
    N_target = N_eff_0 + 2.0 * maneuver_ratio
    d[7] = _clamp((N_target - N_eff) / tau_n, -10.0, 10.0)

    return d

Parameters: N_eff_0 = 4
_RANGE_GUARD = 0.1
_noise_ts = [0, 0.01, 0.02, 0.03, 0.04, 0.05, …] [shape=(2201,), min=0, max=22]
a_max = 400
a_tgt_est = 20
t_go_min = 0.1
tau_n = 2
vtx = 200
vty = 30
vtz = -10
wind_noise = [0.0628651105467, -0.0660524316457, 0.320211325222, 0.0524500585765, -0.267834686581, 0.180797527455, …] [shape=(3, 2201), min=-1.94971086503, max=1.62859953736]
Initial condition: y(0) = [5000, 2000, 1000, -250, 0, 0, 20, 4]
Horizon: t ∈ [0, 22]

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: Augmented PN with Time-to-Go Estimation (augmented-pn-with-time-to-go-estimation)

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%	10.0	128,013	853 ms	0.858
2	CVODE Adamsexternal	100%	7.3	31,943	455 ms	0.792
3	SciPy RK23SciPy	100%	7.2	45,560	746 ms	0.791
4	SciPy BDFSciPy	100%	7.0	41,363	1.68 s	0.785
5	FBDFexternal	100%	6.9	51,864	6.59 s	0.782
6	CVODE BDFexternal	100%	6.7	34,627	498 ms	0.779
7	SciPy LSODASciPy	100%	6.6	57,654	634 ms	0.777
8	Vern9external	100%	6.6	132,050	7.45 s	0.776
9	SciPy RadauSciPy	100%	6.4	142,672	4.04 s	0.771
10	Vern7external	100%	6.2	86,692	6.32 s	0.767
11	Tsit5external	100%	6.2	38,466	4.82 s	0.766
12	SciPy DOP853SciPy	100%	6.1	97,142	1.31 s	0.765
13	SciPy RK45SciPy	100%	5.7	25,178	210 ms	0.754
14	TRBDF2external	100%	5.0	17,088	5.80 s	0.739

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_augmented_pn_with_time_to_go_estimation_2026,
  title        = {Resonix Evidence Portal: Augmented PN with Time-to-Go Estimation},
  author       = {{Resonix Labs (Canada) Inc.}},
  year         = {2026},
  howpublished = {\url{https://resonixusa.com/evidence/problems/augmented-pn-with-time-to-go-estimation}},
  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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