fix(tools): correct s6_inspect PSD check and NIS headline

[Ravenwater]

Summary

While running the S6 inspector on real EuRoC to root-cause the VIO pipeline, two of its diagnostics turned out to be measurement artifacts, not filter faults. This corrects both. No SDK/backend change — the filter math was right.

The two artifacts

1. Spurious "non-PSD" on partial-window tracks

psd_after used is_positive_definite (bare Cholesky), which rejects any zero eigenvalue. But the MSCKF covariance is legitimately rank-deficient:

• the newest clone is a stochastic copy of the IMU pose → exact zero-covariance directions, and
• the 4-DoF gauge (yaw + global position) is unobservable.

Those eigenvalues sit at 0 ± machine-eps. Full-window updates nudged them slightly positive (Cholesky passed); partial-window updates left them at ±1e-17 (Cholesky tripped) — producing a deterministic, false "100% non-PSD on partial tracks / 18% overall" signal. Eigendecomposition of a flagged covariance: min eigenvalue −1.1e-17, 6 eigenvalues ≈ 0, all in the gauge / clone-copy directions.

Fix: use is_positive_semidefinite (the invariant the Joseph form actually guarantees). Non-PSD warning drops 18% → 0 on MH_02_easy.

2. NIS headline dominated by the gated outlier tail

The NIS/dof headline averaged over all valid updates including χ²-gated outliers (rejected, never applied), reading ~4.0 and printing "over-confident (R under-modeled)". The updates the filter actually applied are consistent — accepted NIS/dof = 0.28 on MH_02.

Fix: report accepted-only as the honest per-update consistency metric; keep all-valid as a clearly-labelled secondary. (#212 system-level over-confidence is a state-NEES property, measured end-to-end by vio_pipeline, not from these innovation residuals.)

Validation

MH_02_easy, 300 frames, after fix:
  NIS/dof:  accepted 0.284 over 3599 applied updates  → applied updates consistent
            all-valid 4.029 over 3935 (incl. gated outlier tail — not the consistency metric)
  (no non-PSD warning)

Changes

• tools/include/branes/tools/s6_update_inspect.hpp — is_positive_definite → is_positive_semidefinite; field comment corrected.
• tools/src/s6_inspect.cpp — accepted-only NIS accumulator + corrected headline.

Test Results

Target	gcc build	gcc test	clang build	clang test
s6_update_inspect	OK	PASS (38 assertions / 4 cases)	OK	PASS (38 / 4)

Test plan

• Fast CI passes (gcc + clang + MSVC + lint)
• Promote to ready when satisfied

Relates to #371, #380, #212

🤖 Generated with Claude Code

[coderabbitai]

Important

Review skipped

Draft detected.

Please check the settings in the CodeRabbit UI or the .coderabbit.yaml file in this repository. To trigger a single review, invoke the @coderabbitai review command.

⚙️ Run configuration

Configuration used: Path: .coderabbit.yaml

Review profile: ASSERTIVE

Plan: Pro

Run ID: 803482a6-0d5e-4e27-8514-3eaeb959598f

You can disable this status message by setting the reviews.review_status to false in the CodeRabbit configuration file.

Use the checkbox below for a quick retry:

• 🔍 Trigger review

✨ Finishing Touches

🧪 Generate unit tests (beta)

• Create PR with unit tests
• Commit unit tests in branch fix/s6-inspect-psd-and-nis-headline

---

_{Comment @coderabbitai help to get the list of available commands and usage tips.}