R12 — Physics-Anchored Background Subtraction (PABS) implementation: NEGATIVE → POSITIVE

Status: working implementation, ~100× lift over R12 naive SVD baseline · 2026-05-22

What changed

R12 (tick 5 of this loop) was a NEGATIVE result: naive SVD-spectrum-cosine-distance failed because the eigenshift signal was 0.69× the natural drift floor (signal-to-drift < 1 = undetectable). R12 explicitly identified the revision path: PABS over a Fresnel-grounded basis.

R6.1 (tick 18) shipped the multi-scatterer Fresnel forward operator. That made PABS implementable as a concrete experiment:

PABS = ||y_observed − y_predicted||² / ||y_observed||²

where y_predicted is computed from R6.1's multi-scatterer model using a "what the scene should look like" prior (subject at known position + wall reflectors at known positions).

This tick implements PABS and benchmarks it against R12's naive SVD baseline on the same scenarios.

Method

5 m link at 2.4 GHz; the "expected" scene is:

• 1 subject at (2.5, 2.75) — 25 cm off the LOS line (R6.1 said on-LOS is degenerate)
• 4 wall reflectors at the room corners with descending reflectivity

The forward operator computes y_predicted for this expected scene. Six observed scenarios are then tested:

Results

The headline contrast:

PABS detects an unexpected human at 1,161× the natural drift floor. R12's naive SVD detected the same at 11×.

That's a ~100× lift, achieved purely by using physics-grounded prediction instead of statistical eigenshift. The original R12 NEGATIVE finding (signal-to-drift 0.69× = undetectable) is now a positive 1,161× = trivially detectable.

Why PABS works where SVD didn't

• SVD on |y| treats CSI as a generic 1-D vector and looks for statistical deviation from a learned baseline. It can't tell the difference between "wall drift" and "extra person" because both look like generic spectrum shifts.
• PABS compares against a forward-modelled "what should be there" prediction. New scatterers produce residuals in the precise per-subcarrier signature the forward model predicts is missing. Natural drift produces residuals in diffuse, low-amplitude patterns. The geometry separates them — and the separation is what gives the 100× ratio.

The subject-moved-10cm scenario

Scenario F deserves a note. The subject moved only 10 cm from expected → PABS = 21,966× drift. That's not a bug; it's exactly correct behaviour:

• The forward model predicted "subject at (2.5, 2.75)"
• The observation has "subject at (2.5, 2.85)"
• The residual is the per-subcarrier signature of a scatterer moved by 10 cm — which is large

For a real "structure detection" pipeline, PABS must be coupled with a pose tracker that updates the expected scene model in real-time. The actual structure-detection signal is PABS-after-pose-update — i.e. residual that remains AFTER accounting for the subject's tracked position. New furniture / intruders cause residuals the pose tracker can't explain; subject motion does not.

The repo already ships pose tracking (pose_tracker.rs, ADR-079, ADR-101); the missing piece is the closed-loop coupling between pose updates and the PABS forward model. ~50-100 lines of Rust glue.

R12 NEGATIVE → POSITIVE: what changed

Two negative results in this loop (R12 + R13). R12 has now been revisited and turned positive — the kind of follow-up that makes a research loop's NEGATIVE entries productive rather than dead. R13 cannot be similarly revisited (its 5 dB shortfall is a hard physics floor, not a missing model).

Composes with prior threads

• R5 (saliency) — PABS's residual could itself be saliency-decomposed to localise where the structural change is (which body part / which voxel). Not implemented; natural next step.
• R6 — single-scatterer Fresnel; provides the building block.
• R6.1 — multi-scatterer forward operator; the thing that unblocked this tick.
• R6.2 / R6.2.2 — placement that maximises Fresnel coverage maximises PABS sensitivity (residuals in covered zones are reliably detected).
• R7 (mincut adversarial) — PABS residual against per-link forward models gives R7's multi-link consistency check a precise definition: residual norm should be small across all links simultaneously; spike on a single link = either local structure OR compromised link, R7 mincut disambiguates.
• R10 (foliage / wildlife) — PABS-vs-forest-canopy works as long as the forest's static scatterers can be modelled or learned as a per-installation baseline.
• R11 (maritime) — PABS in cabins detects "container tampered" by residual against the sealed-cabin scene model.
• R12 NEGATIVE — now POSITIVE.
• R14 / ADR-105 / ADR-106 — PABS is a per-cog primitive that the federation protocol can ship; same privacy framework applies.

Honest scope

• PABS needs a pose-aware forward model in real-time to avoid false alarms from subject motion (Scenario F). Without the closed-loop pose-PABS coupling, every subject move triggers a structural alarm.
• The natural drift floor is geometry-specific. The 5% wall reflectivity drift assumption is generic; specific installations may have higher (10-15%) drift floors from humidity / temperature cycles.
• No multipath modelled here either. Wall reflectors are static point scatterers; the model doesn't include floor / ceiling reflections.
• No labelled real-world test. The benchmark is on synthetic data. Real-world PABS on actual CSI captures is the next step.
• Population-prior body assumption. PABS uses a generic body model; per-subject body modelling would tighten the residual further (R3 + R15 give the embedding handle).
• Single time-frame. A real PABS pipeline should integrate over a temporal window for noise rejection; the current results are single-frame.

What this DOES enable

1. R12 NEGATIVE → POSITIVE. The dead thread now has a working implementation with a 100× lift.
2. Concrete next-step for the multistatic ADR-029 implementation: PABS over per-link forward models is the structural-detection primitive.
3. A worked-out example of how negative-result + new-tool unblocking can convert dead research into shippable functionality.

What this DOES NOT enable

• Production-ready structure detection (needs pose-PABS closed loop + temporal averaging + real-world calibration).
• Localisation of the structural change (residual norm gives detection; residual direction would give localisation — natural next step).
• Cross-room structure transfer (each installation has its own forward model; cross-installation transfer goes through ADR-105 / ADR-106).

Next ticks (R12 PABS follow-ups)

• R12.1 — Pose-PABS closed loop. Couple pose_tracker.rs updates to the expected scene model. ~50-100 LOC Rust glue.
• R12.2 — Localised residual decomposition. Project residual onto a per-voxel basis to identify where the structural change is.
• R12.3 — Real-world validation. Run PABS on actual CSI captures from the bench ESP32; measure real-world drift floor and real intruder detection.
• ADR amendment: ADR-029 (multistatic sensing) should reference PABS as the structure-detection primitive.

Connection back

• R12 NEGATIVE → POSITIVE (this tick).
• R6.1 → enabled this implementation.
• R7 → gets a precise per-link consistency definition.
• R11 → enables maritime container-tamper / hatch-seal applications.
• R14 → security feature (intruder detection) becomes a V0 vertical: "alert me if someone unexpected enters". The privacy framework allows this without storing biometrics (just the existence of a residual, not who).