Multi-scan Hessian observability gate study (2026-07-15)¶
Decision¶
Reject the normalized-Hessian window as an intervention gate. Keep the code default-off only as a reproducible negative result; do not enable either research profile in a shipped configuration.
This study changes only incremental scan registration while creating a new map. Saved-map loading, localization mode, and relocalization remain excluded.
Candidate¶
The existing persistent weak-direction tracker was extended with a fixed window of per-scan Hessians, each normalized to unit trace in the common world-frame left-perturbation coordinates. Prior blending was allowed only when the tracked axis was weak both instantaneously and in the accumulated window. Synthetic tests cover a stationary weak axis, a slowly rotating weak axis that becomes observable over the window, and exact legacy persistence behavior when the new gate is disabled.
Results¶
| profile | HILTI exp07 APE RMSE (m) | MID-360 delta RMSE (m) | verdict |
|---|---|---|---|
| default-off | 0.318107 | 0.000000 | reference |
| persistent gate | 0.316617 | 0.530182 | prior research candidate |
window ratio 1e-6 |
0.378146 | not run | HILTI regression |
window ratio 1e-5 |
0.359920 | 0.577689 | both gates worse |
At 1e-5, HILTI had 195 intervened scans / 5,270 intervention iterations;
MID-360 had 942 intervened scans / 12,921 iterations. The gate therefore did
not separate the beneficial and harmful cases. The first v1 HILTI artifact
used a stale installed RKO-LIO binary, is bit-identical to the old persistent
candidate, and is explicitly excluded from the table.
Artifacts:
/media/user/aiueo/benchmarks/hilti_exp07_multiscan_observability_20260715_v2/media/user/aiueo/benchmarks/hilti_exp07_multiscan_observability_20260715_v3/media/user/aiueo/benchmarks/mid360_public/multiscan_observability_20260715_v1
What the failed follow-up established¶
A proposed 3x3 translation Schur-complement diagnostic was removed after its origin-invariance test failed. For this point-to-point ICP Jacobian the fixed correspondence translation block is always identity; the corridor ambiguity comes primarily from correspondence changes and local surface geometry, not from a single fixed-correspondence Hessian. The next candidate must therefore use correspondence-level local surface information (for example multi-scan voxel covariance / point-to-plane constraints), rather than another scalar derived from the same 6x6 Hessian.
Local-surface follow-up¶
A cached voxel-covariance prototype then applied anisotropic residual weights
(plane-normal weight 1.0, tangent weight 0.1) using only map points already
stored in the matched voxel. On the allowed exp01 development sequence it did
not improve accuracy:
| exp01 profile | raw APE RMSE (m) | matched GT points | processing RTF |
|---|---|---|---|
| same-build default | 0.066713 | 10/13 | 2.1369 |
| cached local surface | 0.066757 | 11/13 | 1.8759 |
The candidate was removed rather than retained behind a flag: it missed the
3% accuracy gate, remained slower than real time, and its per-voxel cached
statistics would have increased memory even when the feature was disabled.
Artifacts are
/media/user/aiueo/benchmarks/hilti_exp01_local_surface_20260715_default
and
/media/user/aiueo/benchmarks/hilti_exp01_local_surface_20260715_candidate_v1.
Runtime follow-ups¶
Two selective-compute ideas were also rejected. A fixed 10-iteration cap made
exp01 real-time (RTF 0.934) and improved exp04 on seven common checkpoints,
but regressed the exp07 corridor from 0.318107 to 0.419805 m. Extending the
budget after weak-Hessian observations did not restore corridor accuracy:
hold windows of 0, 5, 20, and 50 scans produced exp07 APE 0.399267,
0.389377, 0.342768, and 0.382299 m respectively. A fixed coarse ICP
keypoint multiplier also failed: 2.0x and 2.5x produced 0.351691 and
0.382267 m. Their development configs were removed.
One exact nearest-neighbor optimization was retained. Voxel candidates are now
compared with squared distances and sqrt is evaluated only once for the
winning point. On complete exp01 runs, trajectory APE remained exactly
0.0655590872 m with all 13 checkpoints while processing RTF improved from
3.0761 to 2.0612 (33.0%). The optimized artifact is
/media/user/aiueo/benchmarks/hilti_exp01_squared_nn_20260715_v1.