docs/research/sota-2026-05-22/R6_2_4-3d-chest-multistatic.md
Status: prediction validation + counter-finding on ceiling mounts · 2026-05-22
R6.2.2.1 (3D N-anchor on body-footprint zones) showed N=5 gives only 49% coverage in 3D vs 97% in 2D. It predicted: switching to chest-centric zones (R6.2.3) should recover 80%+ at N=5 in 3D. This tick tests that prediction.
| N anchors | Coverage | Marginal | Heights (L / M / H) |
|---|---|---|---|
| 2 | 11.3% | +11.3 pp | 1 / 1 / 0 |
| 3 | 60.3% | +49.0 pp | 1 / 2 / 0 |
| 4 | 76.1% | +15.8 pp | 2 / 2 / 0 |
| 5 | 76.8% | +0.6 pp | 3 / 2 / 0 |
| 6 | 81.6% | +4.8 pp | 4 / 2 / 0 |
R6.2.2.1's prediction of 80%+ at N=5 was off by 3.2 pp. N=5 hits 76.8%; N=6 hits 81.6% — the 80%+ knee shifts one anchor higher than predicted.
| Configuration | N=5 coverage |
|---|---|
| R6.2.2 (2D body) | 96.8% |
| R6.2.3 (2D chest) | 82.4% |
| R6.2.2.1 (3D body) | 49.4% |
| R6.2.4 (3D chest) | 76.8% |
3D chest-centric recovers 27 pp over 3D body-centric — most of the 47 pp gap that R6.2.2.1 surfaced. The architectural fix mostly works.
R6.2.1 recommended "one ceiling anchor + low + mid" as the winning 3D strategy. R6.2.4 finds something different: at no N does greedy select a ceiling (z=2.4 m) anchor for chest-centric zones. The heights are 100% low (0.8 m) + mid (1.5 m).
Why: chest zones live at z=0.3-1.5 m. Ceiling anchors (z=2.4 m) put their Fresnel ellipsoid envelopes at z≈2.4 m — well above the chest targets. The targets are at heights matching the chosen anchor mid-points, not between anchor extremes.
Sharpened recommendation: anchor heights should match the target-zone heights.
| Target | Best anchor heights |
|---|---|
| Bed-only (z=0.3-0.6) | Low (0.5-0.8 m) on opposite sides of bed |
| Chair / sitting (z=0.5-1.0) | Low + mid |
| Standing chest (z=1.2-1.5) | Mid (1.2-1.5 m) |
| Full body (z=0.3-1.7) | Mixed low / mid / high (per R6.2.1) |
| Mixed chest (z=0.3-1.5) | Low + mid only — NO ceiling |
R6.2.1's "include ceiling" recommendation was correct for full-body coverage, not for chest-centric coverage. The two regimes diverge.
The +0.6 pp marginal at N=4→5 is suspicious — likely a greedy local-optimum artefact. N=6 jumps +4.8 pp, suggesting the global optimum has a slightly different 5-anchor configuration than greedy found. With more restarts (8-16) the N=5 number might recover to ~80%.
This is honest scope on the greedy algorithm: it's an approximation, and the N=5 result is probably 2-4 pp shy of the true global optimum. Not a research finding worth fixing in this tick; documented for future productisation.
Replacing the simple "5 anchors hits the knee" rec from R6.2.2 with the dimension- and zone-aware version:
| Configuration | Recommended N | Realistic coverage |
|---|---|---|
| 2D body-centric | 5 | 97% (R6.2.2) |
| 2D chest-centric | 5 | 82% (R6.2.3) |
| 3D body-centric | 7-8 | 65%+ (R6.2.2.1) |
| 3D chest-centric | 6 | 82% (R6.2.4) |
For vital-signs cogs in real 3D deployments: N=6 + chest-centric zones + low/mid anchor heights. This is the strongest single recommendation the R6 family produces.
It's the fourth tick in the R6 family + the second self-corrective tick in the loop. R6.2.2.1 made an explicit prediction; R6.2.4 verifies + corrects it. This is the right structure for research progress:
Each tick has a clear hypothesis and a clear empirical result that either confirms or revises the previous.
After R6, R6.1, R6.2, R6.2.1, R6.2.2, R6.2.2.1, R6.2.3, R6.2.4 — the R6 family has covered: forward model (R6), multi-scatterer (R6.1), 2D placement (R6.2), 3D placement (R6.2.1), N-anchor (R6.2.2), 3D N-anchor (R6.2.2.1), chest-centric (R6.2.3), 3D chest N-anchor (R6.2.4). The family is substantively complete for placement-strategy purposes.
Remaining R6 follow-ups (pose-trajectory-aware, multi-subject union) need empirical AETHER + R3 data — out of scope for synthetic-data ticks.