Proportional navigation (2D)
ADVANTAGES1 · dim 8SolvSRK 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 →
Two-dimensional interceptor engagement using proportional navigation guidance.
Problem definition
Canonical benchmark implementation
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):
x_m, y_m, Vm, th_m = y[0], y[1], y[2], y[3]
x_t, y_t, Vt, th_t = y[4], y[5], y[6], y[7]
dx = x_t - x_m
dy = y_t - y_m
r = np.sqrt(dx * dx + dy * dy) + _EPS_RANGE
lam = np.arctan2(dy, dx)
vx_m = Vm * np.cos(th_m)
vy_m = Vm * np.sin(th_m)
vx_t = Vt * np.cos(th_t)
vy_t = Vt * np.sin(th_t)
# LOS rate: d(lambda)/dt = (dx*(vy_t-vy_m) - dy*(vx_t-vx_m)) / r^2
dlam_dt = (dx * (vy_t - vy_m) - dy * (vx_t - vx_m)) / (r * r)
# closing velocity
V_c = -(dx * (vx_t - vx_m) + dy * (vy_t - vy_m)) / r
a_m = N * V_c * dlam_dt
d = np.empty(8)
d[0] = vx_m
d[1] = vy_m
d[2] = 0.0 # constant speed
d[3] = a_m / max(abs(Vm), 1.0) # heading rate
d[4] = vx_t
d[5] = vy_t
d[6] = 0.0 # constant speed
d[7] = 0.0 # non-maneuvering
return d
def rhs_ig_pn_2d(t, y):
"""Default IG-PN-2D instance (module-level, not parameterized)."""
return _IG_PN_2D_RHS(t, y)- Parameters
- N = 3
- _EPS_RANGE = 1e-06
- Initial condition
- y(0) = [0, 0, 100, 0, 3000, 0, 30, 3.14159265359]
- Horizon
- t ∈ [0, 60]
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: SciPy BDF
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: Proportional navigation (2D) (proportional-navigation-2d)
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 | SciPy BDFSciPy | 100% | 16.4 | 57 | 2 ms | 1.000 |
| 2 | SolvSRK | 100% | 16.4 | 72 | 1 ms | 1.000 |
| 3 | SciPy RadauSciPy | 100% | 15.8 | 80 | 2 ms | 0.996 |
| 4 | TRBDF2external | 100% | 15.8 | 33 | 5.33 s | 0.996 |
| 5 | CVODE BDFexternal | 100% | 15.5 | 22 | 8 ms | 0.989 |
| 6 | CVODE Adamsexternal | 100% | 15.5 | 22 | 7 ms | 0.989 |
| 7 | Tsit5external | 100% | 15.4 | 30 | 750 ms | 0.987 |
| 8 | SciPy RK23SciPy | 100% | 15.4 | 23 | <1 ms | 0.987 |
| 9 | Vern7external | 100% | 15.2 | 72 | 4.04 s | 0.980 |
| 10 | SciPy RK45SciPy | 100% | 14.7 | 38 | <1 ms | 0.969 |
| 11 | SciPy LSODASciPy | 100% | 13.0 | 14 | <1 ms | 0.928 |
| 12 | Vern9external | 100% | 12.6 | 162 | 4.08 s | 0.920 |
| 13 | SciPy DOP853SciPy | 100% | 11.9 | 62 | <1 ms | 0.902 |
| 14 | FBDFexternal | 100% | 7.1 | 502 | 5.29 s | 0.787 |
At Clean, best balanced arm is SciPy BDF · SolvSRK survival 100%, SCD 16.4.
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_proportional_navigation_2d_2026,
title = {Resonix Evidence Portal: Proportional navigation (2D)},
author = {{Resonix Labs (Canada) Inc.}},
year = {2026},
howpublished = {\url{https://resonixusa.com/evidence/problems/proportional-navigation-2d}},
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